John Nash: game theory

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pages: 998 words: 211,235

A Beautiful Mind by Sylvia Nasar


Al Roth, Albert Einstein, Andrew Wiles, Brownian motion, cognitive dissonance, Columbine, experimental economics, fear of failure, Gunnar Myrdal, Henri Poincaré, invisible hand, Isaac Newton, John Conway, John Nash: game theory, John von Neumann, Kenneth Arrow, Kenneth Rogoff, linear programming, lone genius, market design, medical residency, Nash equilibrium, Norbert Wiener, Paul Erdős, Paul Samuelson, prisoner's dilemma, RAND corporation, Ronald Coase, second-price auction, Silicon Valley, Simon Singh, spectrum auction, The Wealth of Nations by Adam Smith, Thorstein Veblen, upwardly mobile, zero-sum game

A decline in measured intelligence within a short time of the onset of schizophrenia has been documented in a series of studies. Jed Wyatt, personal communication, 6.97. 4. Letter from John Nash to Donald Spencer, undated, spring 1961. 5. Interviews with Armand Borel, 3.1.96, and Atle Selberg, 1.23.96. 6. Letter from Atle Selberg to John Nash, 9.25.61; letter from Robert Oppenheimer to John Nash, 10.3.61. 7. John Nash, membership application, 7.17.61, Institute for Advanced Study Archive. 8. Letter from J. Nash to D. Spencer. 9. Shlomo Sternberg, interview, 3.5.96. Also postcards from John Nash to Virginia Nash, 8.1.61 and 8.3.61. 10. Alicia Nash, interview, 8.15.96. 11. Interviews with John Danskin, 10.19.95, and Odette Larde, 12.7.95. 12. O. Larde, interview. 13. “Recent Advances in Game Theory,” Princeton, October 4–6, 1961. 14. Reinhard Selten, professor of economics, University of Bonn, interview, 6.27.95. 15.

Leonard, “From Parlor Games to Social Science: Von Neumann, Morgenstern and the Creation of Game Theory, 1928–1944,” Journal of Economic Literature (1995). 16. See, for example, Harold Kuhn, ed., Classics in Game Theory (Princeton: Princeton University Press, 1997); John Eatwell, Murray Milgate, and Peter Newman, The New Palgrave: Game Theory (New York: Norton, 1987); Avinash K. Dixit and Bam J. Nalebuff, Thinking Strategically (New York: Norton, 1991). 17. Robert J. Leonard, “Reading Cournot, Reading Nash: The Creation and Stabilization of the Nash Equilibrium,” The Economic Journal (May 1994), pp. 492–511; Martin Shubik, “Antoine Augustin Cournot,” in Eatwell, Milgate, and Newman, op. cit., pp. 117–28. 18. Joseph Baratta, historian, interview, 6.12.97. 19. John Nash, “Non-Cooperative Games,” Ph.D. thesis, Princeton University Press (May 1950).

Nash was in Seattle in February of 1967, apparently for a month. Letter from John Nash to Virginia Nash, 2.67. 16. Klee, interview. 17. This scene is reconstructed on the basis of recollections from Martha Nash Legg, interview, 9.2.95. 18. Postcard from John Nash to Virginia and John Nash, Sr., 7.12.56. 19. Jerome Neuwirth, interview, 5.21.97. 20. Jacob Bricker, interview, 5.22.97. 29: Death and Marriage 1. Postcard from John Nash to Virginia and John Nash, Sr., 8.11.56. 2. Ibid., 9.18.56. 3. Elizabeth Hardwick, “Boston: A Lost Ideal,” Harper’s, December 1959, quoted in Paul Mariani, Lost Puritan: A Life of Robert Lowell (New York: Norton, 1994), p. 271. 4. Postcards from John Nash to Virginia and John Nash, Sr., 8.53, 9.53, 12.2.53, 1.2.55. 5. Martha Nash Legg, interview, 3.29.96. 6.

pages: 360 words: 85,321

The Perfect Bet: How Science and Math Are Taking the Luck Out of Gambling by Adam Kucharski

Ada Lovelace, Albert Einstein, Antoine Gombaud: Chevalier de Méré, beat the dealer, Benoit Mandelbrot, butterfly effect, call centre, Chance favours the prepared mind, Claude Shannon: information theory, collateralized debt obligation, correlation does not imply causation, diversification, Edward Lorenz: Chaos theory, Edward Thorp, Everything should be made as simple as possible, Flash crash, Gerolamo Cardano, Henri Poincaré, Hibernia Atlantic: Project Express, if you build it, they will come, invention of the telegraph, Isaac Newton, John Nash: game theory, John von Neumann, locking in a profit, Louis Pasteur, Nash equilibrium, Norbert Wiener, p-value, performance metric, Pierre-Simon Laplace, probability theory / Blaise Pascal / Pierre de Fermat, quantitative trading / quantitative finance, random walk, Richard Feynman, Richard Feynman, Ronald Reagan, Rubik’s Cube, statistical model, The Design of Experiments, Watson beat the top human players on Jeopardy!, zero-sum game

As Ferguson discovered when he applied game theory to poker, sometimes an idea that seems unremarkable to scientists can prove extremely powerful when used in a different context. While the fiery debate between von Neumann and Fréchet sparked and crackled, John Nash was busy finishing his doctorate at Princeton. By establishing the Nash equilibrium, he had managed to extend von Neumann’s work, making it applicable to a wider number of situations. Whereas von Neumann had looked at zero-sum games with two players, Nash showed that optimal strategies exist even if there are multiple players and uneven payoffs. But knowing perfect strategies always exist is just the start for poker players. The next problem is working out how to find them. MOST PEOPLE WHO HAVE a go at creating poker bots don’t rummage through game theory to find optimal strategies.

In Marihuana: A Signal of Misunderstanding (report of the National Commission on Marihuana and Drug Abuse, 1972). 136Far from hurting tobacco companies’ profits: McAdams, David. Game-Changer: Game Theory and the Art of Transforming Strategic Situations (New York: W. W. Norton, 2014), 61. 137Yet tobacco revenues held steady: Hamilton, James. “The Demand for Cigarettes: Advertising, the Health Scare, and the Cigarette Advertising Ban.” Review of Economics and Statistics 54, no. 4 (1972). 137“Mr. Nash is nineteen years old”: The letter was posted online by Princeton University after John Nash’s death in 2015. It went viral. 138Despite his prodigious academic record: Halmos, Paul. “The Legend of John von Neumann.” American Mathematical Monthly 8 (1973): 382–394. 138“Real life consists of bluffing”: Harford, Tim. “A Beautiful Theory.” Forbes, December 14, 2006.

Journal of Theoretical and Applied Physics, 1913. 158“Checkers is solved”: Schaeffer, Jonathan, Neil Burch, Yngvi Björnsson, Akihiro Kishimoto, Martin Müller, Robert Lake, Paul Lu, and Steve Sutphen. “Checkers Is Solved.” Science 317, no. 5844 (2007): 1518–1522. doi:10.1126/science.1144079. 158John Nash showed in 1949: Demaine, Erik D., and Robert A. Hearn. “Playing Games with Algorithms: Algorithmic Combinatorial Game Theory.” Mathematical Foundations of Computer Science (2001): 18–32. 159Twenty-six moves later: Schaeffer, Jonathan, and Robert Lake. “Solving the Game of Checkers.” Games of No Chance 29 (1996): 119–133. 160“might have died in 1990”: Schaeffer et al., “Chinook.” 160Doyne Farmer has started to question: Galla, Tobias, and J.

pages: 422 words: 131,666

Life Inc.: How the World Became a Corporation and How to Take It Back by Douglas Rushkoff


affirmative action, Amazon Mechanical Turk, banks create money, big-box store, Bretton Woods, car-free, colonial exploitation, Community Supported Agriculture, complexity theory, computer age, corporate governance, credit crunch, currency manipulation / currency intervention, David Ricardo: comparative advantage, death of newspapers, don't be evil, Donald Trump, double entry bookkeeping, easy for humans, difficult for computers, financial innovation, Firefox, full employment, global village, Google Earth, greed is good, Howard Rheingold, income per capita, invention of the printing press, invisible hand, Jane Jacobs, John Nash: game theory, joint-stock company, Kevin Kelly, laissez-faire capitalism, loss aversion, market bubble, market design, Marshall McLuhan, Milgram experiment, moral hazard, mutually assured destruction, Naomi Klein, negative equity, new economy, New Urbanism, Norbert Wiener, peak oil, peer-to-peer, place-making, placebo effect, Ponzi scheme, price mechanism, price stability, principal–agent problem, private military company, profit maximization, profit motive, race to the bottom, RAND corporation, rent-seeking, RFID, road to serfdom, Ronald Reagan, short selling, Silicon Valley, Simon Kuznets, social software, Steve Jobs, Telecommunications Act of 1996, telemarketer, The Wealth of Nations by Adam Smith, Thomas L Friedman, too big to fail, trade route, trickle-down economics, union organizing, urban decay, urban planning, urban renewal, Vannevar Bush, Victor Gruen, white flight, working poor, Works Progress Administration, Y2K, young professional, zero-sum game

In every single experiment, however, instead of making choices in the self-interested way that Rand expected, the secretaries chose to cooperate. This didn’t deter John Nash, the Rand mathematician portrayed by Russell Crowe in the movie A Beautiful Mind, from continuing to develop game scenarios for the government based on presumptions of fear and self-interest. An undiagnosed paranoid schizophrenic, Nash blamed the failed experiments on the secretaries themselves. They were unfit subjects, incapable of following the simple “ground rules” that they should strategize selfishly. Nash remained committed to the rather paranoid view that human beings are suspicious creatures, constantly making strategic assessments about one another and calculating how to gain a competitive advantage in any situation. Game theory worked quite well in poker, anyway, from which it originated. And what better model existed for the high-stakes nuclear standoff between the United States and the U.S.S.R.?

Freakonomics, the runaway best seller and its follow-up New York Times Magazine column, applied this model of “rational utility-maximization” to human behaviors ranging from drug dealing to cheating among sumo wrestlers. Economics explained everything with real numbers, and the findings were bankable. Even better, the intellectual class had a new way of justifying its belief that people really do act the way they’re supposed to in one of John Nash’s game scenarios. Ironically, while the intelligentsia were using social evolution to confirm laissez-faire capitalism to one another, the politicians promoting these policies to the masses were making the same sale through creationism. Right-wing conservatives turned to fundamentalist Christians to promote the free-market ethos, in return promising lip service to hot-button Christian issues such as abortion and gay marriage.

The principles of the intentionally corporatized marketplace are not embedded in the human genome, nor is self-interested behavior an innate human instinct. If anything, it’s the other way around: a landscape defined by the competitive market will promote self-interested behavior. It’s the surest path to a corporatist society. Maybe that was the objective all along. Central Currency The economy in which we all participate is no more natural than the game scenarios John Nash set up to test the Rand Corporation’s secretaries. It is a model for human interaction, based on a set of false assumptions about human behavior. Even if we buy the proposition that people act as self-interestedly as they possibly can, we must accept the reality that people’s actual choices don’t correspond with their own financial well-being. They do not act in their own best financial interests.

Gaming the Vote: Why Elections Aren't Fair (And What We Can Do About It) by William Poundstone

affirmative action, Albert Einstein, Debian, desegregation, Donald Trump,, Everything should be made as simple as possible, global village, guest worker program, hiring and firing, illegal immigration, invisible hand, jimmy wales, John Nash: game theory, John von Neumann, Kenneth Arrow, manufacturing employment, Nash equilibrium, Paul Samuelson, Pierre-Simon Laplace, prisoner's dilemma, Ralph Nader, RAND corporation, Ronald Reagan, Silicon Valley, slashdot, the map is not the territory, Thomas Bayes, transcontinental railway, Unsafe at Any Speed, Y2K

'The idea was that because of the new nature of warfare, particularly the bomb, all the old views were wrong ... It was an invitation to take a very wild point of view." RAND took pride in hiring a diverse group of specialists and encouraging everyone to talk to one another. Over the years, RAND's scholars and consultants have ranged from John Nash to Condoleezza Rice. In its first decade, however, the guiding spirit of the place was unquestionably John von Neumann. "Everyone sat up in great awe" when von Neumann spoke, Arrow said. Politically, von Neumann was conservative and a hawk. He believed that game theory provided useful models for nuclear deterrence and arms races. RAND's people pondered questions such as would the Soviet Union launch a first strike against the United States if it meant losing twenty million people in the counterattack? Would building a hydrogen bomb enhance or diminish U.S. security?

Bad Santa 201 Donald Saari • Kris Kringle • the nobody problem • rigged elections • Peter Fishburn· Samuel Merrill III • Jill Van Newenhizen • indeterminacy· rebuttals and counter-rebuttals • Unsophisticated Voter System· unmitigated evil • symmetry • polyhedra • behavioral assumptions I find to be >'ery dangerous • Mr. Mediocre· Thomas Edison· electrocuted dogs· "'President Perot" • Alexander Tabarrok • '"Buddy" Roemer· how to buy kitchen cabinets· "'wherever you go, there you are"· polls· chameleon on a mirror· bandwagon effect· Jesse Ventura· Roger B. Myerson· John Nash· self-interest· bullet voting· Terry Sanford· air bags· Burr's dilemma , Contents 13. Last Man Standing 219 Orange County· John Wayne· American machismo· the Condorcet winner· Linux • Markus Schulze· CSSD • Wikipedia • trolls· Queen Elizabeth· Kim Jongil • sarcasm· simplicity· Ka-Ping Yee· Microsoft Windows· manipulative behavior • how ro prevent carjacking· Mathematics Awareness Week • lain Mclean· permanent pointlessness 231 14.

One of those present, Roger B. Myerson, saw a clever way of treating the problem. Myerson and Weber ended up collaborating on a 1993 article, "A Theory of Voting Equilibria." In Weber's words, 'This is the paper that, I believe, makes the strongest theoretical case for approval voting." The publication invokes another idea with roots in the cold war, the "Nash equilibrium." As a RAND consultant, mathematician John Nash (of A Beautiful Mind fame) proposed a particular kind of solution to the "games" of nuclear deterrence or voting or anything else, A Nash equilibrium is an outcome where everyone is satisfied with his or her decision, given what everyone else did. No one has any regrets about doing what he did. In the case of voting, this means that all the voters are happy with the way they voted (though not necessarily happy with the election's outcome).

pages: 88 words: 25,047

The Mathematics of Love: Patterns, Proofs, and the Search for the Ultimate Equation by Hannah Fry

Brownian motion, John Nash: game theory, linear programming, Nash equilibrium, Pareto efficiency, recommendation engine, Skype, statistical model

Say you’re at a party with a group of single friends, all trying to decide how best to boost your chances of meeting someone. Should you sit back and wait for them to come to you, or walk right up to the prettiest partygoer, risking a humiliating rejection? And who should you approach to give you the best chance of success? If we all go for the blonde Anybody who has seen the 2001 film A Beautiful Mind might think that maths already has the answer. The film follows the life of mathematics superstar John Nash and includes some dramatized explanations of his major mathematical breakthroughs. In one famous scene, Nash and his three charming gentlemen friends spot a group of five women in a bar: four brunettes and one particularly beautiful blonde. All of the men are immediately drawn to the blonde. But, rather than all rushing to shower her with attention, Nash argues for a different tactic. Strategically, he suggests they would all do better by ignoring the blonde and aiming for her four brunette friends instead: If we all go for the blonde, we block each other and not a single one of us is going to get her.

This is the motivation of international bestsellers like The Game and The Rules of the Game, which have paved the way for men and women to treat each other as conquests. And both are based on a single idea: how to exploit stereotypes to try and maximize your own reward. As we’ve already seen, the mathematics of game theory can be used to beat other suitors. And if you’re looking to turn the dating game into a dating war, it is also ideally placed to provide the best strategy in a romantic contest between two opponents. A warning: game theory encourages you to exploit the weaknesses of your opponents. When applied to dating, this view comes with a slightly cynical picture of the world. As a result, the first half of this chapter will show you some of the best tenets of game theory, not the best tenets of human morality. And because they rely on exploiting the supposed differences between men and women, they don’t really work for any non-traditional or non-heterosexual couples.

The result is the eligible bachelor paradox, and it comes with a clear, if slightly harsh, take-home message: no matter how hot you are, if your goal is partnership, don’t get complacent. But before we consign ourselves to dying alone and rush out to buy a houseful of cats, it’s worth pausing and looking at these examples objectively. As neat an application of game theory as they are mathematically, they have one flawed assumption at their core: that men are trying to trick women into having sex with them and women are desperate for commitment. In reality, don’t both sexes want both? Crazily enough, I suspect there may even be some women who want sex and some men who want commitment. And thus this particular game-theory house of cards comes tumbling down. Thankfully, there are ways to use game theory that don’t require men and women to conform to stereotypes, and in particular, a formulation that can apply to many of the most common dating conundrums for every type of relationship.

pages: 523 words: 143,139

Algorithms to Live By: The Computer Science of Human Decisions by Brian Christian, Tom Griffiths


4chan, Ada Lovelace, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, algorithmic trading, anthropic principle, asset allocation, autonomous vehicles, Bayesian statistics, Berlin Wall, Bill Duvall, bitcoin, Community Supported Agriculture, complexity theory, constrained optimization, cosmological principle, cryptocurrency, Danny Hillis, David Heinemeier Hansson, delayed gratification, dematerialisation, diversification, Donald Knuth, double helix, Elon Musk, fault tolerance, Fellow of the Royal Society, Firefox, first-price auction, Flash crash, Frederick Winslow Taylor, George Akerlof, global supply chain, Google Chrome, Henri Poincaré, information retrieval, Internet Archive, Jeff Bezos, John Nash: game theory, John von Neumann, knapsack problem, Lao Tzu, Leonard Kleinrock, linear programming, martingale, Nash equilibrium, natural language processing, NP-complete, P = NP, packet switching, Pierre-Simon Laplace, prediction markets, race to the bottom, RAND corporation, RFC: Request For Comment, Robert X Cringely, sealed-bid auction, second-price auction, self-driving car, Silicon Valley, Skype, sorting algorithm, spectrum auction, Steve Jobs, stochastic process, Thomas Bayes, Thomas Malthus, traveling salesman, Turing machine, urban planning, Vickrey auction, Vilfredo Pareto, Walter Mischel, Y Combinator, zero-sum game

What makes this equilibrium stable is that, once both players adopt this 1⁄3 - 1⁄3 - 1⁄3 strategy, there is nothing better for either to do than stick with it. (If we tried playing, say, more rock, our opponent would quickly notice and start playing more paper, which would make us play more scissors, and so forth until we both settled into the 1⁄3 - 1⁄3 - 1⁄3 equilibrium again.) In one of the seminal results in game theory, the mathematician John Nash proved in 1951 that every two-player game has at least one equilibrium. This major discovery would earn Nash the Nobel Prize in Economics in 1994 (and lead to the book and film A Beautiful Mind, about Nash’s life). Such an equilibrium is now often spoken of as the “Nash equilibrium”—the “Nash” that Dan Smith always tries to keep track of. On the face of it, the fact that a Nash equilibrium always exists in two-player games would seem to bring us some relief from the hall-of-mirrors recursions that characterize poker and many other familiar contests.

As we’ve seen, it’s not enough for a problem to have a solution if that problem is intractable. In a game-theory context, knowing that an equilibrium exists doesn’t actually tell us what it is—or how to get there. As UC Berkeley computer scientist Christos Papadimitriou writes, game theory “predicts the agents’ equilibrium behavior typically with no regard to the ways in which such a state will be reached—a consideration that would be a computer scientist’s foremost concern.” Stanford’s Tim Roughgarden echoes the sentiment of being unsatisfied with Nash’s proof that equilibria always exist. “Okay,” he says, “but we’re computer scientists, right? Give us something we can use. Don’t just tell me that it’s there; tell me how to find it.” And so, the original field of game theory begat algorithmic game theory—that is, the study of theoretically ideal strategies for games became the study of how machines (and people) come up with strategies for games.

On the contrary, it represents a situation in which the dice are as loaded against the emergence of cooperation as they could possibly be.”* Well, if the rules of the game force a bad strategy, maybe we shouldn’t try to change strategies. Maybe we should try to change the game. This brings us to a branch of game theory known as “mechanism design.” While game theory asks what behavior will emerge given a set of rules, mechanism design (sometimes called “reverse game theory”) works in the other direction, asking: what rules will give us the behavior we want to see? And if game theory’s revelations—like the fact that an equilibrium strategy might be rational for each player yet bad for everyone—have proven counterintuitive, the revelations of mechanism design are even more so. Let’s return you and your bank-robbing co-conspirator to the jail cell for another go at the prisoner’s dilemma, with one crucial addition: the Godfather.

pages: 503 words: 131,064

Liars and Outliers: How Security Holds Society Together by Bruce Schneier


airport security, barriers to entry, Berlin Wall, Bernie Madoff, Bernie Sanders, Brian Krebs, Broken windows theory, carried interest, Cass Sunstein, Chelsea Manning, commoditize, corporate governance, crack epidemic, credit crunch, crowdsourcing, cuban missile crisis, Daniel Kahneman / Amos Tversky, David Graeber, desegregation, don't be evil, Double Irish / Dutch Sandwich, Douglas Hofstadter, experimental economics, Fall of the Berlin Wall, financial deregulation, George Akerlof, hydraulic fracturing, impulse control, income inequality, invention of agriculture, invention of gunpowder, iterative process, Jean Tirole, John Nash: game theory, joint-stock company, Julian Assange, mass incarceration, meta analysis, meta-analysis, microcredit, moral hazard, mutually assured destruction, Nate Silver, Network effects, Nick Leeson, offshore financial centre, patent troll, phenotype, pre–internet, principal–agent problem, prisoner's dilemma, profit maximization, profit motive, race to the bottom, Ralph Waldo Emerson, RAND corporation, rent-seeking, RFID, Richard Thaler, risk tolerance, Ronald Coase, security theater, shareholder value, slashdot, statistical model, Steven Pinker, Stuxnet, technological singularity, The Market for Lemons, The Nature of the Firm, The Spirit Level, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, theory of mind, too big to fail, traffic fines, transaction costs, ultimatum game, UNCLOS, union organizing, Vernor Vinge, WikiLeaks, World Values Survey, Y2K, zero-sum game

Many researchers Sylvia Nasar (2001), A Beautiful Mind: The Life of Mathematical Genius and Nobel Laureate John Nash, Simon & Schuster. John Nash (2008), “The Agencies Method for Modeling Coalitions & Cooperations in Games,” International Game Theory Review, 10:539–64. Robert Axelrod and William D. Hamilton (1981), “The Evolution of Cooperation,” Science, 211:1390–6. Robert Axelrod (1984), The Evolution of Cooperation, Basic Books. open grazing pasture Garrett Hardin (1968), “The Tragedy of the Commons,” Science, 162:1243–8. Chapter 6 predictably irrational Dan Ariely (2008), Predictably Irrational: The Hidden Forces That Shape our Decisions, Harper Perennial. Cuban Missile Crisis Steven J. Brams (24 Jan 2001), “Game Theory and the Cuban Missile Crisis,” Plus Magazine. worst in people Morton Deutsch and Robert M.

How else can you explain that so many of our Facebook pages include people we would never have even considered talking to in high school, and yet we help water their imaginary plants? Chapter 5 (1) The Prisoner's Dilemma was originally framed in the 1950s by Merrill Flood and Melvin Dresher at the RAND Corporation, and was named several years later by Albert Tucker.Many researchers have informed and analyzed this game, most famously John Nash and then Robert Axelrod, who used it to help explain the evolution of cooperation. (2) I should probably explain about Alice and Bob. Cryptographers—and I started as a cryptographer—name the two actors in any security discussion Alice and Bob. To us, anyone we don't know is either Alice or Bob. If you meet me, don't be surprised if I call you Alice or Bob. (3) As stylized as the story is, this sort of thing is not uncommon.

Spammers do better if they don't clog e-mail to the point where no one uses it anymore, and rogue banks are more profitable if they don't crash the entire economy. All parasites do better if they don't destroy whatever system they've latched themselves onto. Parasites thrive only if they don't thrive too well. There's a clever model from game theory that illustrates this: the Hawk-Dove game. It was invented by geneticists John Maynard Smith and George R. Price in 1971 to explain conflicts between animals of the same species. Like most game theory models, it's pretty simplistic. But what it illuminates about the real world is profound. The game works like this. Assume a population of individuals with differing survival strategies. Some cooperate and some defect. In the language of the game, the defectors are hawks. They're aggressive; they attack other individuals, and fight back if attacked.

pages: 389 words: 98,487

The Undercover Economist: Exposing Why the Rich Are Rich, the Poor Are Poor, and Why You Can Never Buy a Decent Used Car by Tim Harford


Albert Einstein, barriers to entry, Berlin Wall, collective bargaining, congestion charging, Corn Laws, David Ricardo: comparative advantage, decarbonisation, Deng Xiaoping, Fall of the Berlin Wall, George Akerlof, information asymmetry, invention of movable type, John Nash: game theory, John von Neumann, Kenneth Arrow, market design, Martin Wolf, moral hazard, new economy, Pearl River Delta, price discrimination, Productivity paradox, race to the bottom, random walk, rent-seeking, Robert Gordon, Robert Shiller, Robert Shiller, Ronald Reagan, sealed-bid auction, second-price auction, second-price sealed-bid, Shenzhen was a fishing village, special economic zone, spectrum auction, The Market for Lemons, Thomas Malthus, trade liberalization, Vickrey auction

(You also receive a bad payoff if we have a head-on collision, but in game theory I don’t usually care about your payoff for its own sake. I care about your payoffs only because they help me predict your behavior.) Games are often described in just that way, using little stories or anecdotes, but these stories conceal the fact that for a game theorist, games are mathematical objects. The great game theorists are brilliant mathematicians, such as Von Neumann himself, or Nobel Prize winner John Nash, the subject of A Beautiful Mind. As in the case of all game theory, Nash’s revolutionary new way to predict a game’s outcome was an inspired application of well-understood mathematics. Von Neumann was fascinated by poker, and as he turned his mind to the game he developed mathematical tools that are not only handy for economists but for people trying to understand everything from dating to evolutionary biology or the cold war.

Losses due to internet music piracy from “Rock profits and boogie woogie blues,” May 2, 2004, BBC Online News, 3622285.stm. Data from Robert Shiller are available at his home page, http:// Chapter 7 See Prisoner’s Dilemma by William Poundstone (New York: Doubleday, 1992) to find out more about Von Neumann and the use of game theory in the cold war. For an analysis of poker models by Emile Borel, Von Neumann, John Nash, and Lloyd Shapley, see chapter 12 of Ken Binmore’s textbook Fun and Games (Lexington: D. C. Heath, 1992). This is the same Ken Binmore who later went on to lead the auction design team for the UK 3G auction. The United States spectrum auctions are expertly discussed in John McMillan’s “Selling Spectrum Rights,” Journal of Economic Perspectives 8, no. 3 (Summer 1994): 145–62; also McAfee and McMillan’s “Analysing the Airwaves Auction,” Journal of Economic Perspectives 10, no. 1 (Winter 1996): 159–75.

One of the most difficult challenges of all is rooted in the very origins of game theory: it was developed by men of nearly superhuman intellect like Nash and Von Neumann. That is both its great strength and its great weakness, because for game theory to be successful, it has to provide insight into what mere mortals do. Game theory expresses the way people would act as the solution to a mathematical equation. It presumes hyperrational players who are able instantly to solve very tough problems, and this description starts to look unrealistic if game theory is to be a practical tool for explaining how real people actually behave. Nash and Von Neumann really could solve such problems instantly. The rest of us cannot. For instance, game theory tells us that chess is not worth playing because in theory its outcome is predetermined: one player can force a result.

pages: 137 words: 36,231

Information: A Very Short Introduction by Luciano Floridi


agricultural Revolution, Albert Einstein, bioinformatics, carbon footprint, Claude Shannon: information theory, conceptual framework, double helix, Douglas Engelbart, Douglas Engelbart, George Akerlof, Gordon Gekko, industrial robot, information asymmetry, intangible asset, Internet of things, invention of writing, John Nash: game theory, John von Neumann, moral hazard, Nash equilibrium, Norbert Wiener, Pareto efficiency, phenotype, Pierre-Simon Laplace, prisoner's dilemma, RAND corporation, RFID, Thomas Bayes, Turing machine, Vilfredo Pareto

Unlike the other three outcomes, the case in which both prisoners defect can also be described as a Nash equilibrium: it is the only outcome in which each player is doing the best he can, given the available information about the other player's actions. Nash equilibria are crucial features in game theory, as they represent situations in which no player's position can be improved by selecting any other available strategy while all the other players are also playing their best option and not changing their strategies. They are named after John Nash (born 1928), who, in 1994, shared the Nobel Prize in Economics with Reinhard Selten (born 1930) and John Harsanyi (1920-2000) for their foundational work on game theory. Complete information makes simultaneous games interesting. Without such a condition, the players would be unable to predict the effects of their actions on the other players' behaviour.

Indeed, information-theoretical approaches to economic topics have become so popular and pervasive that one may be forgiven for mistaking economics for a branch of information science. In the rest of this chapter, we will look at some essential ways in which economic information is used. For the sake of simplicity, and following current trends, the presentation will be framed in game-theoretic terms. But instead of presenting a standard analysis of types of games first, we will focus on the concepts of information and then see how they are used. Complete information Game theory is the formal study of strategic situations and interactions (games) among agents (players, not necessarily human), who are fully rational (they always maximize their payoffs, without any concern for the other players), aware of each other, and aware that their decisions are mutually dependent and affect the resulting payoffs. Generally speaking, a game is described by four elements: (a) its players, how many and who they are; (b) each player's strategies, what they may rationally decide to do given the known circumstances (a strategy is a complete plan of action specifying a feasible action for every move the player might have to make); (c) the resulting payoffs from each outcome, what they will gain by their moves; and (d) the sequence (timing or order) of the actual moves or states, if the game is sequential (see below), basically in what position the player is at a certain stage of the game.

Generally speaking, a game is described by four elements: (a) its players, how many and who they are; (b) each player's strategies, what they may rationally decide to do given the known circumstances (a strategy is a complete plan of action specifying a feasible action for every move the player might have to make); (c) the resulting payoffs from each outcome, what they will gain by their moves; and (d) the sequence (timing or order) of the actual moves or states, if the game is sequential (see below), basically in what position the player is at a certain stage of the game. One of game theory's main goals is to identify the sort of stable situations (equilibria) in which the game players have adopted strategies that they are unlikely to change, even if, from a sort of God's eye perspective, they may not be rationally optimal. There are many kinds of game and hence forms of equilibrium. One way of classifying them is by checking how much game-relevant information the players enjoy, that is, who has what kind of access to (a)-(d).

pages: 338 words: 106,936

The Physics of Wall Street: A Brief History of Predicting the Unpredictable by James Owen Weatherall


Albert Einstein, algorithmic trading, Antoine Gombaud: Chevalier de Méré, Asian financial crisis, bank run, beat the dealer, Benoit Mandelbrot, Black Swan, Black-Scholes formula, Bonfire of the Vanities, Bretton Woods, Brownian motion, butterfly effect, capital asset pricing model, Carmen Reinhart, Claude Shannon: information theory, collateralized debt obligation, collective bargaining, dark matter, Edward Lorenz: Chaos theory, Edward Thorp, Emanuel Derman, Eugene Fama: efficient market hypothesis, financial innovation, fixed income, George Akerlof, Gerolamo Cardano, Henri Poincaré, invisible hand, Isaac Newton, iterative process, John Nash: game theory, Kenneth Rogoff, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, martingale, Myron Scholes, new economy, Paul Lévy, Paul Samuelson, prediction markets, probability theory / Blaise Pascal / Pierre de Fermat, quantitative trading / quantitative finance, random walk, Renaissance Technologies, risk-adjusted returns, Robert Gordon, Robert Shiller, Robert Shiller, Ronald Coase, Sharpe ratio, short selling, Silicon Valley, South Sea Bubble, statistical arbitrage, statistical model, stochastic process, The Chicago School, The Myth of the Rational Market, tulip mania, V2 rocket, Vilfredo Pareto, volatility smile

He made a list of the courses he would need to take, most of which were in a then-burgeoning field known as functional analysis, and discovered that if he took them all, he’d have enough for a PhD in mathematics, while his work on physics would have just begun. And so he switched to math. All the while, his ideas about the physics of roulette spun around in his mind. He was sure that with the right resources — a professional roulette wheel and some computer know-how — he could strike it rich. Soon after finishing his PhD, Thorp was awarded the prestigious C.L.E. Moore instructorship in mathematics at MIT — a position held a decade earlier by John Nash, the pioneering mathematician profiled by Sylvia Nasar in her book A Beautiful Mind. Thorp and his wife, Vivian, left Southern California and moved to Cambridge, Massachusetts. They spent only two years on the East Coast before moving back west, to New Mexico. But it was enough to set their lives on a different track: it was at MIT that Thorp met Claude Shannon. Shannon may be the only person in the twentieth century who can claim to have founded an entirely new science.

In The Cambridge History of Science, 275–305. New York: Cambridge University Press. Morley, Henry. 1854. The Life of Girolamo Cardano, of Milan, Physician. London: Chapman and Hall. Moynihan, Daniel P. 1996. Miles to Go: A Personal History of Social Policy. Cambridge, MA: Harvard University Press. Nasar, Sylvia. 1998. A Beautiful Mind: The Life of Mathematical Genius and Nobel Laureate John Nash. New York: Touchstone. Ndiaye, Pap A. 2007. Nylon and Bombs. Baltimore, MD: Johns Hopkins University Press. Niederhoffer, Victor. 1998. The Education of a Speculator. Hoboken, NJ: John Wiley and Sons. Niederhoffer, Victor, and M.F.M. Osborne. 1966. “Market Making and Reversals on the Stock Exchange.” Journal of the American Statistical Association 61 (316): 897–916. Nocera, Joe. 2007.

Card counting is a process by which you gain information about the deck of cards — you learn how the composition of the deck has changed with each hand. This is just what you need to calculate your advantage, as Kelly proposed. Information flows and your money grows. As Thorp and Kimmel made their preparations for Reno, Shannon and Thorp were collaborating on Thorp’s roulette plan. When he heard Thorp’s ideas, Shannon was mesmerized, in large part because Thorp’s roulette idea combined game theory with Shannon’s real passion: machines. At the heart of the idea was a wearable computer that would perform the necessary calculations for the player. They began testing ideas for how the actual gambling would work, assuming they could make sufficient progress on the prediction algorithm. They agreed that it would take more than one person for it to go smoothly, because one person couldn’t focus sufficiently on the wheel to input the necessary data and still be prepared to bet before the ball slowed down and the croupier (roulette’s equivalent of a dealer) announced that betting was closed.

pages: 463 words: 118,936

Darwin Among the Machines by George Dyson


Ada Lovelace, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, anti-communist, British Empire, carbon-based life, cellular automata, Claude Shannon: information theory, combinatorial explosion, computer age, Danny Hillis, Donald Davies, fault tolerance, Fellow of the Royal Society, finite state, IFF: identification friend or foe, invention of the telescope, invisible hand, Isaac Newton, Jacquard loom, Jacquard loom, James Watt: steam engine, John Nash: game theory, John von Neumann, Menlo Park, Nash equilibrium, Norbert Wiener, On the Economy of Machinery and Manufactures, packet switching, pattern recognition, phenotype, RAND corporation, Richard Feynman, Richard Feynman, spectrum auction, strong AI, the scientific method, The Wealth of Nations by Adam Smith, Turing machine, Von Neumann architecture, zero-sum game

A substantial section of the 625-page book is devoted to showing how seemingly intractable situations can be rendered solvable through the assumption of coalitions among the players, and how non-zero-sum games can be reduced to zero-sum games by including a fictitious, impartial player (sometimes called Nature) in the game. Game theory was applied to fields ranging from nuclear deterrence to evolutionary biology. “The initial reaction of the economists to this work was one of great reserve, but the military scientists were quick to sense its possibilities in their field,” wrote J. D. Williams in The Compleat Strategyst, a RAND Corporation best-seller that made game theory accessible through examples drawn from everyday life.6 The economists gradually followed. When John Nash was awarded a Nobel Prize for the Nash equilibrium in 1994, he became the seventh Nobel laureate in economics whose work was influenced directly by von Neumann’s ideas. Nash and von Neumann had collaborated at RAND.

., New York: John Wiley, 1947), 2 (page citation is to the 2d edition). 3.Loren Eiseley, Darwin’s Century (New York: Doubleday, 1958), 39. 4.André-Marie Ampère, Considérations sur la théorie mathématique du jeu (Lyons, France: Frères Perisse, 1802), 3. (Author’s translation.) 5.Jacob Marschak, “Neumann’s and Morgenstern’s New Approach to Static Economics,” Journal of Political Economy 54, no. 2 (April 1946): 114. 6.J. D. Williams, The Compleat Strategyst (Santa Monica, Calif.: RAND Corporation, 1954), 216. 7.John Nash, Parallel Control, RAND Corporation Research Memorandum RM-1361, 27 August 1954, 14. 8.John von Neumann, “A Model of General Economic Equilibrium,” Review of Economic Studies 13 (1945): 1. 9.John von Neumann, The Computer and the Brain (New Haven, Conn.: Yale University Press, 1958), 79–82. 10.John von Neumann, 1948, “General and Logical Theory of Automata,” in Lloyd A. Jeffress, ed., Cerebral Mechanisms in Behavior: The Hixon Symposium (New York: Hafner, 1951), 24. 11.Stan Ulam, quoted by Gian-Carlo Rota, “The Barrier of Meaning,” Letters in Mathematical Physics 10 (1985): 99. 12.von Neumann, “Automata,” 24. 13.Stan Ulam, quoted by Rota, “The Barrier of Meaning,” 98. 14.D.

Von Neumann played an enthusiastic role in the development of thermonuclear weapons, ballistic missiles, the application of game theory to nuclear deterrence, and other known and unknown black arts. He was one of the few Manhattan Project scientists who was not sequestered at Los Alamos, appearing periodically, like a comet, in the course of his transcontinental rounds. Advocating a hard line against the Soviet Union and publicly favoring a preventive nuclear attack, his views on nuclear war were encapsulated in his 1950 motto “Not whether but when.” Nonetheless, he helped construct a policy of peace through the power of assured destruction that has avoided nuclear war for fifty years. Von Neumann’s statements must be viewed not only in historical perspective, but also in the context of his pioneering work in game theory, which demonstrated the possibility of stabilizing a dangerously unstable situation by a convincing bluff—if and only if there appears to be the determination to back it up.

pages: 545 words: 137,789

How Markets Fail: The Logic of Economic Calamities by John Cassidy


Albert Einstein, Andrei Shleifer, anti-communist, asset allocation, asset-backed security, availability heuristic, bank run, banking crisis, Benoit Mandelbrot, Berlin Wall, Bernie Madoff, Black-Scholes formula, Bretton Woods, British Empire, capital asset pricing model, centralized clearinghouse, collateralized debt obligation, Columbine, conceptual framework, Corn Laws, corporate raider, correlation coefficient, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, crony capitalism, Daniel Kahneman / Amos Tversky, debt deflation, diversification, Elliott wave, Eugene Fama: efficient market hypothesis, financial deregulation, financial innovation, Financial Instability Hypothesis, financial intermediation, full employment, George Akerlof, global supply chain, Gunnar Myrdal, Haight Ashbury, hiring and firing, Hyman Minsky, income per capita, incomplete markets, index fund, information asymmetry, Intergovernmental Panel on Climate Change (IPCC), invisible hand, John Nash: game theory, John von Neumann, Joseph Schumpeter, Kenneth Arrow, laissez-faire capitalism, Landlord’s Game, liquidity trap, London Interbank Offered Rate, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, margin call, market bubble, market clearing, mental accounting, Mikhail Gorbachev, money market fund, Mont Pelerin Society, moral hazard, mortgage debt, Myron Scholes, Naomi Klein, negative equity, Network effects, Nick Leeson, Northern Rock, paradox of thrift, Pareto efficiency, Paul Samuelson, Ponzi scheme, price discrimination, price stability, principal–agent problem, profit maximization, quantitative trading / quantitative finance, race to the bottom, Ralph Nader, RAND corporation, random walk, Renaissance Technologies, rent control, Richard Thaler, risk tolerance, risk-adjusted returns, road to serfdom, Robert Shiller, Robert Shiller, Ronald Coase, Ronald Reagan, shareholder value, short selling, Silicon Valley, South Sea Bubble, sovereign wealth fund, statistical model, technology bubble, The Chicago School, The Great Moderation, The Market for Lemons, The Wealth of Nations by Adam Smith, too big to fail, transaction costs, unorthodox policies, value at risk, Vanguard fund, Vilfredo Pareto, wealth creators, zero-sum game

The article was long and involved. Unlike Wald’s work from 1934, it didn’t use any simplifying assumptions about the factors that influence demand, and unlike von Neumann’s 1937 paper, it treated both consumers and firms extensively. Mathematically sophisticated, it eschewed calculus, which was rapidly becoming old hat, and instead made extensive use of convex sets, game theory, and fixed-point theorems—borrowing an application of the last from John Nash, the Princeton mathematician and game theorist. The Arrow-Debreu paper was nobody’s idea of bedtime reading, but when their colleagues had made their way through it, they were agreed: Walras’s problem had finally been solved, and the case for competitive markets had been placed on a sound analytical foundation, or so it seemed. More than half a century later, the argument is still resting on the same support.

In games of that nature, the players compete against one another, and one player’s winnings are another player’s losses. But many types of economic activity, such as international trade and investing in the stock market, involve the possibility of cooperation and mutual gains: they are positive-sum games. During the late 1940s, some progress was made in tackling this broader category of problems when John Nash, a Princeton mathematician, introduced a general method for solving non-zero-sum games, but much remained unclear. Merrill Flood and Melvin Dresher were two mathematicians working at the RAND Corporation, which the Pentagon had founded in the aftermath of World War II to engage in scientific research “for the public welfare and security of the United States of America.” Much of the work undertaken at RAND had military implications, but it was also an important center of operations research and other applications of mathematics.

THE PRISONER’S DILEMMA AND RATIONAL IRRATIONALITY 143 Flood’s babysitting experiment: See William Poundstone, The Prisoner’s Dilemma: John Von Neumann, Game Theory, and the Puzzle of the Bomb (New York: Doubleday, 1992), 103. 143 Non-cooperative pair experiment: Ibid., 106–107. 145 “Both Flood and Dresher . . .”: Ibid., 122. 147 90 percent of the players choose: Ken Binmore, Game Theory: A Very Short Introduction (New York: Oxford University Press, 2007), 21. 149 “Adding together the component . . .”: Garrett Hardin, “The Tragedy of the Commons,” Science 162 (1968): 1244. 150 “Game theorists get . . .”: Binmore, Game Theory, 67. 12. HIDDEN INFORMATION AND THE MARKET FOR LEMONS 151 “I belonged to . . .”: From George Akerlof’s Nobel autobiography, available at 152 “a major reason as to why . . .”: George Akerlof, “Writing ‘The Market for Lemons’: A Personal and Interpretive Essay,” available at 153 “[M]ost cars traded . . .”: George Akerlof, “The Market for ‘Lemons’: Quality Uncertainty and the Market Mechanism,” Quarterly Journal of Economics 84 (1970): 489. 154 “was potentially an issue . . .”: Akerlof, “Writing ‘The Market for Lemons.’ ” 155 “marginally attached”: Bureau of Labor Statistics, Issues in Labor Statistics, Summary 90–04 (April 2009): 1. 156 “it is quite possible . . .”: Akerlof, “The Market for ‘Lemons,’ ” 494. 157 2006 health care spending: “National Health Spending in 2006: A Year of Change for Prescription Drugs,” Health Affairs 27, no. 1 (2008): 14. 158 “The most obvious . . .”: Kenneth J.

pages: 251 words: 44,888

The Words You Should Know to Sound Smart: 1200 Essential Words Every Sophisticated Person Should Be Able to Use by Bobbi Bly


Albert Einstein, Alistair Cooke, Anton Chekhov, British Empire, Columbine, Donald Trump, George Santayana, haute couture, Honoré de Balzac, John Nash: game theory, Network effects, placebo effect, Ralph Waldo Emerson, school vouchers, Stephen Hawking, Steve Jobs

frisson (FREE-son), noun A sudden strong feeling of excitement, conflict, or danger. “Pregnant women! They had that weird FRISSON, an aura of magic that combined awkwardly with an earthy sense of duty.” – Ruth Morgan, American novelist fruition (froo-ISH-un), noun The completion of a task; the achievement of a goal as the result of significant and persistent effort. John Nash, a mathematician whose life was featured in “A Beautiful Mind,” received the Nobel Prize for the FRUITION of his work in game theory decades after he completed it. fulsome (FULL-sum), adjective Describes words or actions that praise or flatter someone to an excessive degree. Katie’s introduction of the keynote speaker was so FULSOME that he led his speech with a few self-effacing remarks. fungible (FUHN-jih-bull), adjective Freely exchangeable for another of like nature; interchangeable.

pages: 252 words: 73,131

The Inner Lives of Markets: How People Shape Them—And They Shape Us by Tim Sullivan


Airbnb, airport security, Al Roth, Alvin Roth, Andrei Shleifer, attribution theory, autonomous vehicles, barriers to entry, Brownian motion, centralized clearinghouse, Chuck Templeton: OpenTable, clean water, conceptual framework, constrained optimization, continuous double auction, creative destruction, deferred acceptance, Donald Trump, Edward Glaeser, experimental subject, first-price auction, framing effect, frictionless, fundamental attribution error, George Akerlof, Goldman Sachs: Vampire Squid, Gunnar Myrdal, helicopter parent, information asymmetry, Internet of things, invisible hand, Isaac Newton, iterative process, Jean Tirole, Jeff Bezos, Johann Wolfgang von Goethe, John Nash: game theory, John von Neumann, Joseph Schumpeter, Kenneth Arrow, late fees, linear programming, Lyft, market clearing, market design, market friction, medical residency, multi-sided market, mutually assured destruction, Nash equilibrium, Occupy movement, Pareto efficiency, Paul Samuelson, Peter Thiel,, pez dispenser, pre–internet, price mechanism, price stability, prisoner's dilemma, profit motive, proxy bid, RAND corporation, ride hailing / ride sharing, Robert Shiller, Robert Shiller, Ronald Coase, school choice, school vouchers, sealed-bid auction, second-price auction, second-price sealed-bid, sharing economy, Silicon Valley, spectrum auction, Steve Jobs, Tacoma Narrows Bridge, technoutopianism, telemarketer, The Market for Lemons, The Wisdom of Crowds, Thomas Malthus, Thorstein Veblen, trade route, transaction costs, two-sided market, uranium enrichment, Vickrey auction, Vilfredo Pareto, winner-take-all economy

When Arrow spoke with one of his mentors at Columbia, the great statistician Abraham Wald, about this question of proving the existence of equilibrium, he was told “it is a very difficult issue”—as in, “too difficult for the likes of you.” That challenge helped spur Arrow, who went ahead and proved it anyway. The year 1951 had seen a major technical advance that made proof of existence far easier than Wald might have realized. John Nash, the game theorist made famous by the book and movie A Beautiful Mind, had borrowed the fixed-point theorem of Japanese mathematician Shizuo Kakutani to prove the existence of Nash equilibrium in game theory. In Arrow’s retelling, at that point it was obvious how to go about proving the existence of competitive equilibrium, and it was a race among himself, French economist Debreu, and several others to see who could do it first and do it best. As Arrow recalls, he summarized his first attempt at proving the existence theorem in a working paper just before heading to Europe to give some lectures.

The foundation’s founding motto was “Science is Measurement.”11 The second, the RAND Corporation, first established as a joint project by the Douglas Aircraft Company and the US Department of War in 1945, used game theory to analyze the United States’s geopolitical position relative to the Soviet Union. Game theory—a mathematical approach to analyzing strategic choices—emerged from the work of Princeton mathematician John von Neumann in the 1930s, who collaborated with his economist colleague Oskar Morgenstern to write Theory of Games and Economic Behavior (published in 1944), which launched the field. Their book provided an analytical framework for figuring out, say, what Pepsi should do if Coke lowers its prices. That depends on how Pepsi’s CEO thinks Coke will respond, which in turn depends on what Coke’s CEO expects that Pepsi’s response to their price reduction will be. And so on. Game theory was a way of cutting through the infinite regression of “what he thinks I think he thinks . . .”

Game theory was a way of cutting through the infinite regression of “what he thinks I think he thinks . . .” Although technical, some of von Neumann and Morgenstern’s ideas eventually filtered into the mainstream, and so resonated with the public imagination that the two researchers found themselves on the front page of the New York Times in 1946 under the headline, “Mathematical Theory of Poker Is Applied to Business Problems.”12 Game theory, though, was about much more than just business. Most famously, perhaps, RAND economists and mathematicians developed the doctrine of nuclear deterrence by mutually assured destruction (MAD) under the guidance of then defense secretary Robert McNamara (himself an economist by training). Von Neumann and Morgenstern’s Theory of Games and Economic Behavior is, in concentrated form, the story of how the new mathematical science of economics could operate and change the way the world works in arenas small (poker) and earth shattering (thermonuclear war).

pages: 295 words: 66,824

A Mathematician Plays the Stock Market by John Allen Paulos


Benoit Mandelbrot, Black-Scholes formula, Brownian motion, business climate, butterfly effect, capital asset pricing model, correlation coefficient, correlation does not imply causation, Daniel Kahneman / Amos Tversky, diversified portfolio, Donald Trump, double entry bookkeeping, Elliott wave, endowment effect, Erdős number, Eugene Fama: efficient market hypothesis, four colour theorem, George Gilder, global village, greed is good, index fund, intangible asset, invisible hand, Isaac Newton, John Nash: game theory, Long Term Capital Management, loss aversion, Louis Bachelier, mandelbrot fractal, margin call, mental accounting, Myron Scholes, Nash equilibrium, Network effects, passive investing, Paul Erdős, Paul Samuelson, Ponzi scheme, price anchoring, Ralph Nelson Elliott, random walk, Richard Thaler, Robert Shiller, Robert Shiller, short selling, six sigma, Stephen Hawking, survivorship bias, transaction costs, ultimatum game, Vanguard fund, Yogi Berra

Imagine the Andersen accountants muttering anxiously that there weren’t enough leading “1s” on the documents they were feeding into the shredders. A 1-derful fantasy! The Numbers Man—A Screen Treatment An astonishing amount of attention has been paid recently to fictional and narrative treatments of mathematical topics. The movies Good Will Hunting, Pi, and The Croupier come to mind; so do plays such as Copenhagen, Arcadia, and The Proof, the two biographies of Paul Erdos, A Beautiful Mind, the biography of John Nash (with its accompanying Academy Award-winning movie), TV specials on Fermat’s Last Theorem, and other mathematical topics, as well as countless books on popular mathematics and mathematicians. The plays and movies, in particular, prompted me to expand the idea in the stock-newsletter scam discussed above (I changed the focus, however, from stocks to sports) into a sort of abbreviated screen treatment that highlights the relevant mathematics a bit more than has been the case in the productions just cited.

It requires faster machines, better data, improved models, and the smarter use of mathematical tools, from conventional statistics to neural nets (computerized learning networks, the connections between the various nodes of which are strengthened or weakened over a period of training). If this is possible for anyone or any group to achieve, it’s not likely to remain so for long. Game Theory and Supernatural Investor/Psychologists But what if, contrary to fact, there were an entity possessing sufficient complexity and speed that it was able with reasonably high probability to predict the market and the behavior of individuals within it? The mere existence of such an entity leads to Newcombe’s paradox, a puzzle that calls into question basic principles of game theory. My particular variation of Newcombe’s paradox involves the World Class Options Market Maker (WCOMM), which (who?) claims to have the power to predict with some accuracy which of two alternatives a person will choose.

Chapter 8 - Connectedness and Chaotic Price Movements Insider Trading and Subterranean Information Processing Trading Strategies, Whim, and Ant Behavior Chaos and Unpredictability Extreme Price Movements, Power Laws, and the Web Economic Disparities and Media Disproportions Chapter 9 - From Paradox to Complexity The Paradoxical Efficient Market Hypothesis The Prisoner’s Dilemma and the Market Pushing the Complexity Horizon Game Theory and Supernatural Investor/Psychologists Absurd Emails and the WorldCom Denouement Bibliography Index Copyright Page Also by John Allen Paulos Mathematics and Humor (1980) I Think Therefore I Laugh (1985) Innumeracy: Mathematical Illiteracy and its Consequences (1988) Beyond Numeracy: Ruminations of a Numbers Man (1991) A Mathematician Reads the Newspaper (1995) Once Upon a Number: The Hidden Mathematical Logic of Stories (1998) To my father, who never played the market and knew little about probability, yet understood one of the prime lessons of both.

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The Simpsons and Their Mathematical Secrets by Simon Singh


Albert Einstein, Andrew Wiles, Benoit Mandelbrot, cognitive dissonance, Donald Knuth, Erdős number, Georg Cantor, Grace Hopper, Isaac Newton, John Nash: game theory, mandelbrot fractal, Menlo Park, Norbert Wiener, Norman Mailer, P = NP, Paul Erdős, probability theory / Blaise Pascal / Pierre de Fermat, Richard Feynman, Richard Feynman, Rubik’s Cube, Schrödinger's Cat, Simon Singh, Stephen Hawking, Wolfskehl Prize, women in the workforce

Although we have not yet discussed the Erdős-Bacon numbers for the rest of the writing team behind The Simpsons, I can confirm that none of them can beat Westbrook’s score. In other words, out of the entire gang of Tinseltown nerds, Westbrook is overall the tinseliest and the nerdiest.8 I first became aware of Erdős-Bacon numbers thanks to Dave Bayer, a mathematician at Colombia University. He was a consultant on the film A Beautiful Mind, based on Sylvia Nasar’s acclaimed biography of the mathematician John Nash, who had won the Nobel Prize in Economic Sciences in 1994. Bayer’s responsibilities included checking the equations that appeared on screen and acting as Russell Crowe’s hand double in the blackboard scenes. Bayer was also given a minor role toward the end of the film, when the Princeton mathematics professors offer their pens to Nash to acknowledge his great discoveries. Bayer proudly explained: “In my scene, known as the Pen Ceremony, I say, ‘A privilege, professor.’

Joel Sokol at the Georgia Institute of Technology gives a lecture titled “Making Decisions Against an Opponent: An Application of Mathematical Optimization,” which includes slides describing games of rock-paper-scissors played by characters in The Simpsons. The lecture focuses on game theory, an area of mathematics concerned with modeling how participants behave in situations of conflict and cooperation. Game theory can offer insights into everything from dominoes to warfare, from animal altruism to trade union negotiations. Similarly, Dirk Mateer, an economist at Pennsylvania State University with a strong interest in mathematics, also makes use of The Simpsons and scenes involving rock-paper-scissors when he teaches game theory to his students. Rock-paper-scissors (RPS) seems like a trivial game, so you might be surprised that it is of any mathematical interest. However, in the hands of a game theorist, RPS becomes a complex battle between two competitors trying to outwit each other.

However, all these philosophers, psychologists, theologians, and politicians have missed the primary subtext of the world’s favorite TV series. The truth is that many of the writers of The Simpsons are deeply in love with numbers, and their ultimate desire is to drip-feed morsels of mathematics into the subconscious minds of viewers. In other words, for more than two decades we have been tricked into watching an animated introduction to everything from calculus to geometry, from π to game theory, and from infinitesimals to infinity. “Homer3,” the third segment in the three-part episode “Treehouse of Horror VI” (1995) demonstrates the level of mathematics that appears in The Simpsons. In one sequence alone, there is a tribute to history’s most elegant equation, a joke that only works if you know about Fermat’s last theorem, and a reference to a $1 million mathematics problem. All of this is embedded within a narrative that explores the complexities of higher-dimensional geometry.

pages: 323 words: 95,939

Present Shock: When Everything Happens Now by Douglas Rushkoff


algorithmic trading, Andrew Keen, bank run, Benoit Mandelbrot, big-box store, Black Swan, British Empire, Buckminster Fuller, cashless society, citizen journalism, clockwork universe, cognitive dissonance, Credit Default Swap, crowdsourcing, Danny Hillis, disintermediation, Donald Trump, double helix, East Village, Elliott wave, European colonialism, Extropian, facts on the ground, Flash crash, game design, global supply chain, global village, Howard Rheingold, hypertext link, Inbox Zero, invention of agriculture, invention of hypertext, invisible hand, iterative process, John Nash: game theory, Kevin Kelly, laissez-faire capitalism, Law of Accelerating Returns, loss aversion, mandelbrot fractal, Marshall McLuhan, Merlin Mann, Milgram experiment, mutually assured destruction, negative equity, Network effects, New Urbanism, Nicholas Carr, Norbert Wiener, Occupy movement, passive investing, pattern recognition, peak oil, price mechanism, prisoner's dilemma, Ralph Nelson Elliott, RAND corporation, Ray Kurzweil, recommendation engine, selective serotonin reuptake inhibitor (SSRI), Silicon Valley, Skype, social graph, South Sea Bubble, Steve Jobs, Steve Wozniak, Steven Pinker, Stewart Brand, supply-chain management, the medium is the message, The Wisdom of Crowds, theory of mind, Turing test, upwardly mobile, Whole Earth Catalog, WikiLeaks, Y2K, zero-sum game

Even if there were millions of possible actors, actions, and connections, there were only two real superpowers—the Soviet Union and the United States. Military leaders figured that game theory, based on the mathematics of poker, should be able to model this activity and give us simple enough rules for engagement. And so the RAND Corporation was hired to conduct experiments (like the Prisoner’s Dilemma, which we looked at earlier), determine probable outcomes, and then program computers to respond appropriately in any number of individual circumstances. Led by the as yet undiagnosed paranoid schizophrenic John Nash (the mathematician portrayed in the movie A Beautiful Mind), they adopted a principle called MAD, or mutually assured destruction, which held that if the use of any nuclear device could effectively guarantee the complete and utter annihilation of both sides in the conflict, then neither side would opt to use them.

While this didn’t stop the superpowers from fighting smaller proxy wars around the world, it did serve as a deterrent to direct conflict. Encouraged by this success, Nash applied his game theory to all forms of human interaction. He won a Nobel Prize for showing that a system driven by suspicion and self-interest could reach a state of equilibrium in which everyone’s needs were met. “It is understood not to be a cooperative ideal,” he later admitted, but—at least at the time—neither he nor RAND thought human beings to be cooperative creatures. In fact, if the people in Nash’s equations attempted to cooperate, the results became much more dangerous, messy, and unpredictable. Altruism was simply too blurry. Good planning required predictable behaviors, and the assumption of short-term self-interest certainly makes things easy to see coming. A few decades of game theory and analysis since then have revealed the obvious flaws in Nash’s and RAND’s thinking.

A few decades of game theory and analysis since then have revealed the obvious flaws in Nash’s and RAND’s thinking. As Hungarian mathematician and logician László Méro explains it in his rethink of game theory, Moral Calculations,9 the competitive assumptions in game theory have not been proved by consistent results in real-world examples. In study after study, people, animals, and even bacteria are just as likely to cooperate as they are to compete. The reason real human behavior differs from that of the theoretically self-interested prisoners is that the latter are prisoners to begin with. An incarcerated person is the most literal example of one living within a closed environment. These are individuals without access to information and incapable of exercising basic freedoms. All feedback and iteration are removed, other than that between the prisoner and his keepers.

pages: 394 words: 108,215

What the Dormouse Said: How the Sixties Counterculture Shaped the Personal Computer Industry by John Markoff


Any sufficiently advanced technology is indistinguishable from magic, Apple II, back-to-the-land, beat the dealer, Bill Duvall, Bill Gates: Altair 8800, Buckminster Fuller, California gold rush, card file, computer age, computer vision, conceptual framework, cuban missile crisis, Donald Knuth, Douglas Engelbart, Douglas Engelbart, Dynabook, Edward Thorp, El Camino Real, Electric Kool-Aid Acid Test, general-purpose programming language, Golden Gate Park, Hacker Ethic, hypertext link, informal economy, information retrieval, invention of the printing press, Jeff Rulifson, John Markoff, John Nash: game theory, John von Neumann, Kevin Kelly, knowledge worker, Mahatma Gandhi, Menlo Park, Mother of all demos, Norbert Wiener, packet switching, Paul Terrell, popular electronics, QWERTY keyboard, RAND corporation, RFC: Request For Comment, Richard Stallman, Robert X Cringely, Sand Hill Road, Silicon Valley, Silicon Valley startup, South of Market, San Francisco, speech recognition, Steve Crocker, Steve Jobs, Steve Wozniak, Steven Levy, Stewart Brand, Ted Nelson, Thorstein Veblen, Turing test, union organizing, Vannevar Bush, Whole Earth Catalog, William Shockley: the traitorous eight

He watched the Moscow show trials of the early fifties, hoping that the abuses of the Soviets would moderate. In the end, because he had left home, he was able to quit the party without being embarrassed or embarrassing his family. At Princeton, McCarthy was a contemporary of John Nash, who later won a Nobel Prize in economics for his work in game theory, and whose life was chronicled by Sylvia Nasar in A Beautiful Mind. As graduate students, McCarthy, Nash, and several of the other students enjoyed constantly scheming and playing practical jokes on one another, justifying their antics in terms of their game-theory explorations. McCarthy arrived at Stanford for the second time (he had taught math there briefly in the early fifties) as a thirty-five-year-old former wunderkind who had invented the term “artificial intelligence.” While teaching math at Dartmouth during the summer of 1956, he had been the principal organizer of the first conference on modeling intelligence in computers and coined the term as part of the conference proposal.

pages: 302 words: 83,116

SuperFreakonomics by Steven D. Levitt, Stephen J. Dubner


agricultural Revolution, airport security, Andrei Shleifer, Atul Gawande, barriers to entry, Bernie Madoff, call centre, clean water, cognitive bias, collateralized debt obligation, creative destruction, credit crunch, Daniel Kahneman / Amos Tversky, deliberate practice, Did the Death of Australian Inheritance Taxes Affect Deaths, disintermediation, endowment effect, experimental economics, food miles, indoor plumbing, Intergovernmental Panel on Climate Change (IPCC), John Nash: game theory, Joseph Schumpeter, Joshua Gans and Andrew Leigh, loss aversion, Louis Pasteur, market design, microcredit, Milgram experiment, oil shale / tar sands, patent troll, presumed consent, price discrimination, principal–agent problem, profit motive, randomized controlled trial, Richard Feynman, Richard Feynman, Richard Thaler, selection bias, South China Sea, Stephen Hawking, The Wealth of Nations by Adam Smith, too big to fail, trickle-down economics, ultimatum game, urban planning, William Langewiesche, women in the workforce, young professional

Most of the problems they traditionally worry about—the effect of tax increases, for instance, or the causes of inflation—are difficult to capture there. But if the lab could unravel the scientific mysteries of the universe, surely it could help figure out something as benign as altruism. These new experiments typically took the form of a game, run by college professors and played by their students. This path had been paved by the beautiful mind of John Nash and other economists who, in the 1950s, experimented broadly with the Prisoner’s Dilemma, a game-theory problem that came to be seen as a classic test of strategic cooperation. (It was invented to glean insights about the nuclear standoff between the United States and the Soviet Union.) By the early 1980s, the Prisoner’s Dilemma had inspired a lab game called Ultimatum, which works as follows. Two players, who remain anonymous to each other, have a onetime chance to split a sum of money.

List, “What Do Laboratory Experiments Measuring Social Preferences Tell Us About the Real World,” Journal of Economic Perspectives 21, no. 2 (2007). See also: Daniel Kahneman, Jack L. Knetsch, and Richard Thaler, “Fairness as a Constraint on Profit Seeking: Entitlements in the Market,” American Economic Review 76, no. 4 (September 1986); Robert Forsythe, Joel L. Horowitz, N. E. Savin, and Martin Sef-ton, “Fairness in Simple Bargaining Experiments,” Games and Economic Behavior 6, no. 3 (May 1994); Colin F. Camerer, Behavioral Game Theory (Princeton University Press, 2003); and John A. List, “Dictator Game Giving Is an Experimental Artifact,” working paper, 2005. ORGAN TRANSPLANTS: The first successful long-term kidney transplant was performed at the Peter Bent Brigham Hospital in Boston by Joseph Murray in December 1954, as related in Nicholas Tilney, Transplant: From Myth to Reality (Yale University Press, 2003). / 111 “Donorcyclists”: see Stacy Dickert-Conlin, Todd Elder, and Brian Moore, “Donorcycles: Do Motorcycle Helmet Laws Reduce Organ Donations?”

pages: 304 words: 88,773

The Ghost Map: A Street, an Epidemic and the Hidden Power of Urban Networks. by Steven Johnson


call centre, clean water, correlation does not imply causation, creative destruction, Dean Kamen, digital map, double helix, edge city, germ theory of disease, Google Earth, Jane Jacobs, John Nash: game theory, John Snow's cholera map, lone genius, Louis Pasteur, mass immigration, megacity, mutually assured destruction, New Urbanism, nuclear winter, pattern recognition, peak oil, side project, Steven Pinker, Stewart Brand, The Death and Life of Great American Cities, the scientific method, trade route, unbiased observer, working poor

But somehow the nonstop traffic and bustle of Regent Street is almost imperceptible from the smaller lanes and alleys of western Soho, largely because there are very few conduits that open directly onto Regent Street. Walking around the neighborhood, it feels almost as if a barricade has been erected, keeping you from reaching the prominent avenue that you know is only a few feet away. And indeed, the street layout was explicitly designed to serve as a barricade. When John Nash designed Regent Street to connect Marylebone Park with the Prince Regent’s new home at Carlton House, he planned the thoroughfare as a kind of cordon sanitaire separating the well-to-do of Mayfair from the growing working-class community of Soho. Nash’s explicit intention was to create “a complete separation between the streets occupied by the Nobility and Gentry, and the narrower Streets and meaner houses occupied by mechanics and the trading part of the community.… My purpose was that the new street should cross the eastern entrance to all the streets occupied by the higher classes and to leave out to the east all the bad streets.”

On a planet of more than 6 billion people, there have to be thousands and thousands of lost souls ready and willing to detonate one of those weapons in a crowded urban center. How long before those two sets intersect? That driver with the rigged SUV isn’t going to be deterred by the conventional logic of détente-era nuclear politics. Mutually assured destruction isn’t much of a deterrent to him. Mutually assured destruction, in fact, sounds like a pretty good outcome. Game theory has always had trouble accounting for players with no rational self-interest, and the theories of nuclear deterrence are no exception. And once the bomb goes off, there’s no second line of defense—no vaccines or quarantines to block off the worst-case scenario. There will be maps, but they’ll be maps of incineration and fallout and mass graves. They won’t help us understand the threat the way Snow’s map helped us understand cholera.

pages: 415 words: 125,089

Against the Gods: The Remarkable Story of Risk by Peter L. Bernstein


Albert Einstein, Alvin Roth, Andrew Wiles, Antoine Gombaud: Chevalier de Méré, Bayesian statistics, Big bang: deregulation of the City of London, Bretton Woods, buttonwood tree, capital asset pricing model, cognitive dissonance, computerized trading, Daniel Kahneman / Amos Tversky, diversified portfolio, double entry bookkeeping, Edmond Halley, Edward Lloyd's coffeehouse, endowment effect, experimental economics, fear of failure, Fellow of the Royal Society, Fermat's Last Theorem, financial deregulation, financial innovation, full employment, index fund, invention of movable type, Isaac Newton, John Nash: game theory, John von Neumann, Kenneth Arrow, linear programming, loss aversion, Louis Bachelier, mental accounting, moral hazard, Myron Scholes, Nash equilibrium, Paul Samuelson, Philip Mirowski, probability theory / Blaise Pascal / Pierre de Fermat, random walk, Richard Thaler, Robert Shiller, Robert Shiller, spectrum auction, statistical model, The Bell Curve by Richard Herrnstein and Charles Murray, The Wealth of Nations by Adam Smith, Thomas Bayes, trade route, transaction costs, tulip mania, Vanguard fund, zero-sum game

The opposite view would prevail among the politicians. Looking downward vertically, we find that both the choices rank higher than 4: the politicians would rather do nothing or run a deficit than follow a policy that cost them their jobs if their constituents lose their jobs as a result. This outcome is known as a Nash Equilibrium, named after John Nash, another Princetonian and one of the 1994 winners of the Nobel Prize for his contributions to game theory.18 Under the Nash Equilibrium the outcome, though stable, is less than optimal. Both sides would obviously prefer almost anything to this one. Yet they cannot reach a better bargain unless they drop their adversarial positions and work together on a common policy that would give each a supportive, or at least a neutral, role that would keep them from getting into each other's way.

The theory focuses on decision-making, but bears little resemblance to the many other theories that originated in games of chance. Despite its nineteenth-century forebears, game theory represents a dramatic break from earlier efforts to incorporate mathematical inevitability into decision-making. In the utility theories of both Daniel Bernoulli and Jevons, the individual makes choices in isolation, unaware of what others might be doing. In game theory, however, two or more people try to maximize their utility simultaneously, each aware of what the others are about. Game theory brings a new meaning to uncertainty. Earlier theories accepted uncertainty as a fact of life and did little to identify its source. Game theory says that the true source of uncertainty lies in the intentions of others. From the perspective of game theory, almost every decision we make is the result of a series of negotiations in which we try to reduce uncertainty by trading off what other people want in return for what we want ourselves.

."*' Another contemporary recalls that the Princeton economics department `just hated Oskar."9 Morgenstern himself complained about the lack of attention his beloved masterpiece received from others. After visiting Harvard in 1945 he noted "none of them" had any interest in game theory.10 He reported in 1947 that a fellow economist named Ropke said that game theory "was Viennese coffeehouse gossip."t When he visited a group of distinguished economists in Rotterdam in 1950, he discovered that they "wanted to know nothing about [game theory] because it disturbs them." Although an enthusiast for the uses of mathematics in economic analysis-he despised Keynes's nonrigorous treatment of expectations and described The General Theory as "simply horrible"-Morgenstern complained constantly about his problems with the advanced material into which von Neumann had lured him.11 Throughout their collaboration Morgenstern held von Neumann in awe.

Culture and Prosperity: The Truth About Markets - Why Some Nations Are Rich but Most Remain Poor by John Kay


Albert Einstein, Asian financial crisis, Barry Marshall: ulcers, Berlin Wall, Big bang: deregulation of the City of London, California gold rush, complexity theory, computer age, constrained optimization, corporate governance, corporate social responsibility, correlation does not imply causation, Daniel Kahneman / Amos Tversky, David Ricardo: comparative advantage, Donald Trump, double entry bookkeeping, double helix, Edward Lloyd's coffeehouse, equity premium, Ernest Rutherford, European colonialism, experimental economics, Exxon Valdez, failed state, financial innovation, Francis Fukuyama: the end of history, George Akerlof, George Gilder, greed is good, Gunnar Myrdal, haute couture, illegal immigration, income inequality, industrial cluster, information asymmetry, intangible asset, invention of the telephone, invention of the wheel, invisible hand, John Meriwether, John Nash: game theory, John von Neumann, Kenneth Arrow, Kevin Kelly, knowledge economy, labour market flexibility, late capitalism, light touch regulation, Long Term Capital Management, loss aversion, Mahatma Gandhi, market bubble, market clearing, market fundamentalism, means of production, Menlo Park, Mikhail Gorbachev, money: store of value / unit of account / medium of exchange, moral hazard, Myron Scholes, Naomi Klein, Nash equilibrium, new economy, oil shale / tar sands, oil shock, Pareto efficiency, Paul Samuelson,, popular electronics, price discrimination, price mechanism, prisoner's dilemma, profit maximization, purchasing power parity, QWERTY keyboard, Ralph Nader, RAND corporation, random walk, rent-seeking, Right to Buy, risk tolerance, road to serfdom, Ronald Coase, Ronald Reagan, second-price auction, shareholder value, Silicon Valley, Simon Kuznets, South Sea Bubble, Steve Jobs, telemarketer, The Chicago School, The Death and Life of Great American Cities, The Market for Lemons, The Nature of the Firm, the new new thing, The Predators' Ball, The Wealth of Nations by Adam Smith, Thorstein Veblen, total factor productivity, transaction costs, tulip mania, urban decay, Vilfredo Pareto, Washington Consensus, women in the workforce, yield curve, yield management

Von Neumann, born in Hungary, was one of the geniuses of his age. 19 At eighteen he was studying for three different degrees in different subjects at different universities in different countries. After making fundamental contributions to mathematics and quantum physics, he turned his attention briefly to economics, which he found "a million miles away from an advanced science." 20 Von Neumann became head of the U.S. Atomic Energy Commission-and the inspiration for Dr. Strangelove-before dying at the age of fifty-three. John Nash was author of the principal solution concept in game theory-the Nash equilibrium-but his productive career was ended by schizophrenia. His health partially restored, he was awarded the Nobel Prize in 1994. 21 Nash was played by Russell Crowe in an Oscar-winning film of his life, A Beautiful Mind. Institutional (or transactions cost) economics regards as its founder Ronald Coase,n a British economist who spent most of his career at the University of Chicago.

If Part III of the book was mostly concerned with these anonymous interactions, Part IV describes how the working of markets differs when these interactions are not anonymous. Game theory established mathematical Culture and Prosperity {205} tools for discussing strategic interrelationships in small groups and is essential for this analysis. 18 Game theory has a popular appeal that fixed-point theorems will never achieve. This is partly the product of larger-than-life examples. The Prisoner's Dilemma, the most preposterous but the best known of all contributions to game theory, will appear in chapter 21. Game theory's characters are also larger-than-life. Von Neumann, born in Hungary, was one of the geniuses of his age. 19 At eighteen he was studying for three different degrees in different subjects at different universities in different countries.

The Arrow-Debreu results are the culmination of a long tradition in economics that emphasizes supply and demand, perfectly competitive markets, and the search for market equilibrium, conducted by independent, self-regarding agents. Economic research since Arrow and Debreu has drawn game theory, transactions costs, and most recently behavioral economics into the mainstream of economic theory. In the Arrow-Debreu framework, interactions are anonymous and every market has many buyers and sellers. In game theory, the players are few and not anonymous. In the Arrow-Debreu framework, institutions do not exist or are dealt with in a reductionist way. Institutional, or transactions costs, economics recognizes that economic lives are lived in and through economic institutions. Behavioral economics contemplates alternative assumptions about motives and the nature of economic behavior. I will introduce game theory and institutional economics in the present chapter and take up behavioral economics in the chapter that follows.

pages: 500 words: 145,005

Misbehaving: The Making of Behavioral Economics by Richard H. Thaler


3Com Palm IPO, Albert Einstein, Alvin Roth, Amazon Mechanical Turk, Andrei Shleifer, Apple's 1984 Super Bowl advert, Atul Gawande, Berlin Wall, Bernie Madoff, Black-Scholes formula, capital asset pricing model, Cass Sunstein, Checklist Manifesto, choice architecture, clean water, cognitive dissonance, conceptual framework, constrained optimization, Daniel Kahneman / Amos Tversky, delayed gratification, diversification, diversified portfolio, Edward Glaeser, endowment effect, equity premium, Eugene Fama: efficient market hypothesis, experimental economics, Fall of the Berlin Wall, George Akerlof, hindsight bias, Home mortgage interest deduction, impulse control, index fund, information asymmetry, invisible hand, Jean Tirole, John Nash: game theory, John von Neumann, Kenneth Arrow, late fees, law of one price, libertarian paternalism, Long Term Capital Management, loss aversion, market clearing, Mason jar, mental accounting, meta analysis, meta-analysis, money market fund, More Guns, Less Crime, mortgage debt, Myron Scholes, Nash equilibrium, Nate Silver, New Journalism, nudge unit, Paul Samuelson, payday loans, Ponzi scheme, presumed consent, pre–internet, principal–agent problem, prisoner's dilemma, profit maximization, random walk, randomized controlled trial, Richard Thaler, Robert Shiller, Robert Shiller, Ronald Coase, Silicon Valley, South Sea Bubble, statistical model, Steve Jobs, technology bubble, The Chicago School, The Myth of the Rational Market, The Signal and the Noise by Nate Silver, The Wealth of Nations by Adam Smith, Thomas Kuhn: the structure of scientific revolutions, transaction costs, ultimatum game, Vilfredo Pareto, Walter Mischel, zero-sum game

Here is another question for you: What is the Nash equilibrium for this scenario? Named for John Nash, the subject of the popular book (and biopic) A Beautiful Mind, the Nash equilibrium in this game is a number that if everyone guessed it, no one would want to change their guess. And the only Nash equilibrium in this game is zero. To see why, suppose everyone guessed 3. Then the average guess would be 3 and you would want to guess two-thirds of that, or 2. But if everyone guessed 2 you would want to guess 1.33, and so forth. If and only if all participants guessed zero would no one want to change his or her guess. Perhaps you have now formulated the question that might have been worth asking before submitting your guess: who are the other players, and how much math and game theory do they know? If you are playing at your local bar, especially late in the evening, other people are probably not thinking too deeply, so you might make a guess around 33.

Another was Robert Shiller, who appeared above and plays a starring role in the next section, and the third was Colin Camerer. I first met Colin when he was on the academic job market. At that point he had picked up an MBA and was nearly done with a PhD from the University of Chicago, and he had not yet turned twenty-one. Colin has made many important contributions to behavioral economics. Two stand out. First, he more or less invented the field of behavioral game theory, the study of how people actually play games, as opposed to standard game theory, which studies how Econs would play games if they knew that everyone else playing was also an Econ. More recently, he has been at the forefront of neuro-economics, which uses techniques such as brain imaging to learn more about how people make decisions. Colin has many talents. While still a teenager in grad school, he formed a record company and signed the famously satirical punk band called the Dead Milkmen.

S467. 168 “I tend to view”: Shiller (1986), p. S501. Chapter 18: Anomalies 169 The Structure of Scientific Revolutions: Kuhn (1962). 174 the first two columns: Thaler (1987a, 1987b). 174 A burst of papers: Rozeff and Kinney (1976). 174 Another anomaly came from bettors at the racetrack: Thaler (1992). Chapter 19: Forming a Team 176 game theory in the 1940s: The catalyst was arguably von Neumann and Morgenstern (1947), the first edition of which was published in 1944. 176 the field of behavioral game theory: Camerer (2003). 180 Stanley Schachter: Schachter et al. (1985a, 1985b), Hood et al. (1985). 180 generating new psychology of our own: An exception is the research associated with Sendhil Mullainathan and Eldar Shafir’s (2013) book Scarcity, one of those rare collaborations between an economist and a psychologist. 182 paper by Fehr that captured our attention: Fehr, Kirchsteiger, and Riedl (1993). 182 employment contracts could be viewed partially as a gift exchange: Akerlof (1982). 182 Rabin’s model: Rabin (1993). 20: Narrow Framing on the Upper East Side 186 bold forecasts and timid choices: Kahneman and Lovallo (1993). 186 described . . . in Thinking, Fast and Slow: Kahneman (2011), ch. 22. 189 benefits are demonstrably large: Mullainathan (2013), Baicker, Mullainathan, and Schwartzstein (2013). 191 equity premium puzzle: Mehra and Prescott (1985). 192 six years to get the paper published: Rajnish Mehra told me this. 192 none of the explanations had proven to be completely satisfactory: Mehra (2007). 194 words with one syllable: Samuelson (1979), p. 306. 194 “Risk and Uncertainty: A Fallacy of Large Numbers”: Samuelson (1963). 195 “myopic loss aversion”: Benartzi and Thaler (1995). 195 The only way you can ever take 100 attractive bets: Barberis, Huang and Santos (2001) formalize this intuition in a dynamic model. 195 experiment using recently hired non-faculty employees: Benartzi and Thaler (1999). 197 Quarterly Journal of Economics dedicated to Amos’s memory: Thaler et al. (1997). 198 A paper by . . .

pages: 461 words: 128,421

The Myth of the Rational Market: A History of Risk, Reward, and Delusion on Wall Street by Justin Fox


activist fund / activist shareholder / activist investor, Albert Einstein, Andrei Shleifer, asset allocation, asset-backed security, bank run, beat the dealer, Benoit Mandelbrot, Black-Scholes formula, Bretton Woods, Brownian motion, capital asset pricing model, card file, Cass Sunstein, collateralized debt obligation, complexity theory, corporate governance, corporate raider, Credit Default Swap, credit default swaps / collateralized debt obligations, Daniel Kahneman / Amos Tversky, David Ricardo: comparative advantage, discovery of the americas, diversification, diversified portfolio, Edward Glaeser, Edward Thorp, endowment effect, Eugene Fama: efficient market hypothesis, experimental economics, financial innovation, Financial Instability Hypothesis, fixed income, floating exchange rates, George Akerlof, Henri Poincaré, Hyman Minsky, implied volatility, impulse control, index arbitrage, index card, index fund, information asymmetry, invisible hand, Isaac Newton, John Meriwether, John Nash: game theory, John von Neumann, joint-stock company, Joseph Schumpeter, Kenneth Arrow, libertarian paternalism, linear programming, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, market bubble, market design, Myron Scholes, New Journalism, Nikolai Kondratiev, Paul Lévy, Paul Samuelson, pension reform, performance metric, Ponzi scheme, prediction markets, pushing on a string, quantitative trading / quantitative finance, Ralph Nader, RAND corporation, random walk, Richard Thaler, risk/return, road to serfdom, Robert Bork, Robert Shiller, Robert Shiller, rolodex, Ronald Reagan, shareholder value, Sharpe ratio, short selling, side project, Silicon Valley, South Sea Bubble, statistical model, The Chicago School, The Myth of the Rational Market, The Predators' Ball, the scientific method, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, Thomas Kuhn: the structure of scientific revolutions, Thomas L Friedman, Thorstein Veblen, Tobin tax, transaction costs, tulip mania, value at risk, Vanguard fund, Vilfredo Pareto, volatility smile, Yogi Berra

Barber, “Irving Fisher (1867–1947): Career Highlights and Formative Influences,” in Hans-E. Loef and Hans G. Monissen, The Economics of Irving Fisher: Reviewing the Scientific Work of a Great Economist (Cheltenham, UK, Northampton, Mass.: Edward Elgar, 1999), 6. 5. E. Roy Weintraub, “On the Existence of Competitive Equilibrium: 1930–1954,” Journal of Economic Literature (March 1983): 13. 6. It was left to others, such as John Nash of A Beautiful Mind fame, to develop a multiplayer theory of games better suited to modeling economic interactions. 7. John von Neumann and Oskar Morgenstern, Theory of Games and Economic Behavior, 65th Anniversary Edition (Princeton: Princeton University Press, 2004), 177–78. 8. Daniel Bernoulli, “Exposition of a New Theory on the Measurement of Risk,” Econometrica (Jan. 1954): 23–36. 9. The story is Herbert Simon’s: In the early 1950s, when I was on a faculty recruiting trip from Pittsburgh, I had dinner with Marschak one evening in the Quadrangle Club at the University of Chicago.

The result was the 641-page Theory of Games and Economic Behavior, coauthored by von Neumann and Morgenstern and published in 1944. As far as pure game theory went, the book added little to what von Neumann had written in 1928,6 although it gave form and heft to von Neumann’s big idea. It also solved the quandary faced by poor Sherlock Holmes and Dr. Moriarty. According to von Neumann’s calculations, Holmes should choose randomly with a 60 percent probability of getting off at the intermediate station, while Moriarty should pick with a 60 percent probability of proceeding straight to Dover.7 Got that? For economists, the part of the book that made the biggest immediate impression was not game theory itself but the chapter outlining how one should weigh potential outcomes before deciding on a move. The gist of it: When outcomes are uncertain, think probabilistically.

After a brief and spectacularly eventful career as a teenaged social-democratic politician during the years immediately following the Russian Revolution, Marschak fled to Germany, where he studied economics and met von Neumann. At Cowles, he gathered around him a spectacular assemblage of future Nobel winners (“I pick people with good eyes,” he explained9) who together explored the cutting edge of mathematical economics. Von Neumann and Morgenstern’s book was on that cutting edge, and Marschak brought von Neumann to Chicago for a two-day seminar on game theory in 1945. Soon afterward, he wrote an article translating von Neumann and Morgenstern’s concept of expected utility into language that would be understood by his fellow economists. “To be an ‘economic man,’” Marschak summed up, “implies being a ‘statistical man.’”10 IF EVER THERE WAS A statistical man, it was Harry Markowitz. A grocer’s son from northwest Chicago, he sped through a special two-year undergraduate program at the University of Chicago and was pursuing a Ph.D. as a “student member” of the Cowles Commission.

pages: 561 words: 120,899

The Theory That Would Not Die: How Bayes' Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant From Two Centuries of Controversy by Sharon Bertsch McGrayne


Bayesian statistics, bioinformatics, British Empire, Claude Shannon: information theory, Daniel Kahneman / Amos Tversky, double helix, Edmond Halley, Fellow of the Royal Society, full text search, Henri Poincaré, Isaac Newton, John Markoff, John Nash: game theory, John von Neumann, linear programming, meta analysis, meta-analysis, Nate Silver, p-value, Pierre-Simon Laplace, placebo effect, prediction markets, RAND corporation, recommendation engine, Renaissance Technologies, Richard Feynman, Richard Feynman, Richard Feynman: Challenger O-ring, Ronald Reagan, speech recognition, statistical model, stochastic process, Thomas Bayes, Thomas Kuhn: the structure of scientific revolutions, traveling salesman, Turing machine, Turing test, uranium enrichment, Yom Kippur War

In economics and finance Bayes appears at multiple levels, ranging from theoretical mathematics and philosophy to nitty-gritty money making. The method figured prominently in three Nobel Prizes awarded for theoretical economics, in 1990, 1994, and 2004. The first Nobel involved the Italian Bayesian de Finetti, who anticipated the Nobel Prize–winning work of Harry Markowitz by more than a decade. Mathematical game theorists John C. Harsanyi and John Nash (the latter the subject of a book and movie, A Beautiful Mind) shared a Bayesian Nobel in 1994. Harsanyi often used Bayes to study competitive situations where people have incomplete or uncertain information about each other or about the rules. Harsanyi also showed that Nash’s equilibrium for games with incomplete or imperfect information was a form of Bayes’ rule. In 2002 Bayes won perhaps not an entire Nobel Prize but certainly part of one.

., 81, 82 Food and Drug Administration, 228–29 forensic science, 235–36 Fox, Robert, 35 Franco, Francisco, 190, 194 French Revolution, 29, 35–36 frequentism: Bayes’ rule accepted in, 233–34 Bayes’ rule compared empirically, 157–58, 159–61 business and, 141, 142 change points and, 216–17 computation and, 214, 225 Cornfield and, 116–17 decision theory and, 236 dimensionality and, 214 expert opinion and, 179 The Federalist papers and, 157–58, 159–61 genetic science and, 47–48 hypotheses and, 116–17, 142, 217, 234 image analysis and, 219 insurance and, 92, 94 likelihood principle and, 132, 233 Lindley’s Paradox and, 132–33 military and, 241 movies and, 178 nuclear weapons and, 123 philosophy and, 253–54 practical applications and, generally, 209 priors and, 104, 177 probability and, 36, 50, 55–57, 99, 130, 142, 145–46, 156, 170 social science and, 217 statistics and, 47–48, 87–88, 98–99, 104–5, 142, 214, 234, 253 Stein’s Paradox and, 131–32 subjectivity and, 104, 129 Tukey and, 169–70 uncertainty and, 55–57, 142 unified approach and, 170 Friedman, Milton, 102, 159, 235 Fuchs, Klaus, 85 gambling: astronomy and, 36 Bayes’ rule and, 11 beliefs and, 51–52 game theory, 236 at Harvard Business School, 148 Laplace and, 19, 20, 21, 32 probability and, 6, 9, 51–52 statistics and, 106–7 subjectivity and, 185 game theory, 236. See also gambling Gastwirth, Joseph L., 227 Gates, Bill, 242 Gauss, C. F., 102 Gelfand, Alan E., 220–22, 224–25 Geman, Donald, 218–19, 221 Geman, Stuart, 218–19, 221, 251 gender, x, 24–27 generating functions, 25 genetic science, xi, 45–48, 225, 235–36, 238–40 Gerrodette, Timothy, 230 Gibbs, Josiah Willard, 219 Gibbs sampling, 218–19, 221, 225–26 Gilbert, Edgar N., 169 Gillispie, Charles Coulston, 35 Gini, Corrado, 52 Gleason, Andrew, 83 God: Bayes’ rule and, ix, 10, 11, 253–54 cause-and-effect and, 5–6 evil and, 4 existence of, 177, 235 happiness and, 4 natural law and, 6, 30 probability and, 19–20.

The philosophical rationale for using Bayesian methods had been largely settled. It was becoming the only mathematics of uncertainty with an explicit, powerful, and secure foundation in logic. How to apply it, though, remained a controversial question. Lindley’s enormous influence as a teacher and organizer bore fruit in the generation to come, while Savage’s book spread Bayesian methods to the military and to business, history, game theory, psychology, and beyond. Although Savage wrote about rabbit ears and neon light in beer, he personally encouraged researchers who would apply Bayes’ rule to life-and-death problems. 8. jerome cornfield, lung cancer, and heart attacks Bayes came to medical research through the efforts of a single scientist, Jerome Cornfield, whose only degree was a B.A. in history and who relied on the rule to identify the causes of lung cancer and heart attacks.

pages: 374 words: 114,600

The Quants by Scott Patterson


Albert Einstein, asset allocation, automated trading system, beat the dealer, Benoit Mandelbrot, Bernie Madoff, Bernie Sanders, Black Swan, Black-Scholes formula, Bonfire of the Vanities, Brownian motion, buttonwood tree, buy low sell high, capital asset pricing model, centralized clearinghouse, Claude Shannon: information theory, cloud computing, collapse of Lehman Brothers, collateralized debt obligation, commoditize, computerized trading, Credit Default Swap, credit default swaps / collateralized debt obligations, diversification, Donald Trump, Doomsday Clock, Edward Thorp, Emanuel Derman, Eugene Fama: efficient market hypothesis, fixed income, Gordon Gekko, greed is good, Haight Ashbury, I will remember that I didn’t make the world, and it doesn’t satisfy my equations, index fund, invention of the telegraph, invisible hand, Isaac Newton, job automation, John Meriwether, John Nash: game theory, law of one price, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, margin call, merger arbitrage, money market fund, Myron Scholes, NetJets, new economy, offshore financial centre, old-boy network, Paul Lévy, Paul Samuelson, Ponzi scheme, quantitative hedge fund, quantitative trading / quantitative finance, race to the bottom, random walk, Renaissance Technologies, risk-adjusted returns, Rod Stewart played at Stephen Schwarzman birthday party, Ronald Reagan, Sergey Aleynikov, short selling, South Sea Bubble, speech recognition, statistical arbitrage, The Chicago School, The Great Moderation, The Predators' Ball, too big to fail, transaction costs, value at risk, volatility smile, yield curve, éminence grise

He contacted Baldwin and requested the data behind the strategy. It arrived in the spring of 1959, just before Thorp moved from UCLA to the Massachusetts Institute of Technology. At MIT, Thorp found a hotbed of intellectual creativity that was quietly revolutionizing modern society. The job he stepped into, the coveted position of C. L. E. Moore Instructor, had previously been held by John Nash, the math prodigy who eventually won the Nobel Prize in economics in 1994 for his work on game theory, a mathematical approach to how people compete and cooperate. (Nash later became known as the subject of A Beautiful Mind, the book and movie about the competing forces of his genius and mental illness.) That first summer in Cambridge, Thorp crunched the numbers on blackjack, slowly evolving what would become a historic breakthrough in the game.

In the mid-1980s, Simons and Ax spun a fund out of Monemetrics called Axcom Ltd. In 1985, Ax moved the operation to Huntington Beach, California. Axcom was to act as the trading advisor for the fund, which was nominally run as an investing firm owned by a company Simons had founded in July 1982 called Renaissance Technologies. Soon Simons’s growing crew of quants added another math wizard, Elwyn Berlekamp, a game theory expert at Berkeley. Like Ed Thorp, Berlekamp had worked with Claude Shannon and John Kelly at MIT. He’d briefly met Simons during a stint at IDA in the 1960s. The fund put up solid returns for several years, even managing to trade through Black Monday with relatively little damage. In 1988, Ax and Simons renamed the fund Medallion in honor of a math award they’d both won. Almost as soon as they’d renamed the fund, things started going south for Medallion.

The fund had a rough start, but it eventually started hitting on all cylinders. In 1997, it was absorbed into the Medallion mother ship and called the Factor Nova Funds, adding stat arb firepower to an already state-of-the-art investment machine. It was the first step in making Medallion a genuine multistrategy fund. By then, Berlekamp was gone. He’d left Renaissance at the end of 1990 to pursue academic interests at Berkeley, where he went on to crack game theory puzzlers such as mathematical chess. But the Medallion legend continued to grow. To be sure, the fund has had a few hiccups over the years. In March 2000, when the dot-com bubble began to implode, reversing trends in technology stocks that had been in place for several years, Medallion lost $250 million in three days, nearly wiping out its year-to-date profit. But the fund quickly bounced back and put up another year of stellar returns.

pages: 412 words: 115,266

The Moral Landscape: How Science Can Determine Human Values by Sam Harris


Albert Einstein, banking crisis, Bayesian statistics, cognitive bias, end world poverty, endowment effect, energy security, experimental subject, framing effect, hindsight bias, impulse control, John Nash: game theory, loss aversion, meta analysis, meta-analysis, out of africa, pattern recognition, placebo effect, Ponzi scheme, Richard Feynman, Richard Feynman, risk tolerance, stem cell, Stephen Hawking, Steven Pinker, the scientific method, theory of mind, ultimatum game, World Values Survey

.), but because of their neurological and social deficits, they are doing a very bad job of it. We can say that a psychopath like Ted Bundy takes satisfaction in the wrong things, because living a life purposed toward raping and killing women does not allow for deeper and more generalizable forms of human flourishing. Compare Bundy’s deficits to those of a delusional physicist who finds meaningful patterns and mathematical significance in the wrong places. The mathematician John Nash, while suffering the symptoms of his schizophrenia, seems a good example: his “Eureka!” detectors were poorly calibrated; he saw meaningful patterns where his peers would not—and these patterns were a very poor guide to the proper goals of science (i.e., understanding the physical world). Is there any doubt that Ted Bundy’s “Yes! I love this!” detectors were poorly coupled to the possibilities of finding deep fulfillment in this life, or that his obsession with raping and killing young women was a poor guide to the proper goals of morality (i.e., living a fulfilling life with others)?

For the purposes of this discussion, however, it seems sufficient to point out that we are beginning to understand the kinds of brain pathologies that lead to the most extreme forms of human evil. And just as some people have obvious moral deficits, others must possess moral talent, moral expertise, and even moral genius. As with any human ability, these gradations must be expressed at the level of the brain. Game theory suggests that evolution probably selected for two stable orientations toward human cooperation: tit for tat (often called “strong reciprocity”) and permanent defection.91 Tit for tat is generally what we see throughout society: you show me some kindness, and I am eager to return the favor; you do something rude or injurious, and the temptation to respond in kind becomes difficult to resist. But consider how permanent defection would appear at the level of human relationships: the defector would probably engage in continuous cheating and manipulation, sham moralistic aggression (to provoke guilt and altruism in others), and strategic mimicry of positive social emotions like sympathy (as well as of negative emotions like guilt).

But consider how permanent defection would appear at the level of human relationships: the defector would probably engage in continuous cheating and manipulation, sham moralistic aggression (to provoke guilt and altruism in others), and strategic mimicry of positive social emotions like sympathy (as well as of negative emotions like guilt). This begins to sound like garden-variety psychopathy. The existence of psychopaths, while otherwise quite mysterious, would seem to be predicted by game theory. And yet, the psychopath who lives his entire life in a tiny village must be at a terrible disadvantage. The stability of permanent defection as a strategy would require that a defector be able to find people to fleece who are not yet aware of his terrible reputation. Needless to say, the growth of cities has made this way of life far more practicable than it has ever been. Evil When confronted with psychopathy at its most extreme, it is very difficult not to think in terms of good and evil.

pages: 467 words: 154,960

Trend Following: How Great Traders Make Millions in Up or Down Markets by Michael W. Covel


Albert Einstein, asset allocation, Atul Gawande, backtesting, beat the dealer, Bernie Madoff, Black Swan, buy low sell high, capital asset pricing model, Clayton Christensen, commodity trading advisor, computerized trading, correlation coefficient, Daniel Kahneman / Amos Tversky, delayed gratification, deliberate practice, diversification, diversified portfolio, Edward Thorp, Elliott wave, Emanuel Derman, Eugene Fama: efficient market hypothesis, Everything should be made as simple as possible, fiat currency, fixed income, game design, hindsight bias, housing crisis, index fund, Isaac Newton, John Meriwether, John Nash: game theory, linear programming, Long Term Capital Management, mandelbrot fractal, margin call, market bubble, market fundamentalism, market microstructure, mental accounting, money market fund, Myron Scholes, Nash equilibrium, new economy, Nick Leeson, Ponzi scheme, prediction markets, random walk, Renaissance Technologies, Richard Feynman, Richard Feynman, risk tolerance, risk-adjusted returns, risk/return, Robert Shiller, Robert Shiller, shareholder value, Sharpe ratio, short selling, South Sea Bubble, Stephen Hawking, survivorship bias, systematic trading, the scientific method, Thomas L Friedman, too big to fail, transaction costs, upwardly mobile, value at risk, Vanguard fund, volatility arbitrage, William of Occam, zero-sum game

Now, suppose the payoff was changed to 3/2, a gain of $1.50 in addition to a $1 bet—the expectation would change to: (.5) (1.5) + (.5) (–1) = +.25 Playing this game 100 times would give us a positive expectation of .25.8 This is the kind of edge cultivated and honed daily by trend followers. You might ask, “If everyone knows about expectation, how can I ever find my edge?” Think about it this way. Consider a scene from the movie A Beautiful Mind, the biography of mathematician John Nash. Nash and some of his mathematician buddies are in a bar when a sexy blonde and four brunettes walk in. After they admire the new arrivals, Nash and his friends decide to compete for the blonde. However, Nash has reservations, correctly observing that, if everyone goes for the same woman, they will just end up blocking each other out. Worse, they will offend the rest of the women. The Volatility, risk, and profit are closely related.

Traders pay close attention to volatility because price changes affect their profits and losses. Periods of high volatility are highly risky to traders. Such periods, however, can also present them with opportunities for great profits.9 252 Trend Following (Updated Edition): Learn to Make Millions in Up or Down Markets only way for everyone to succeed is to ignore the blonde and hit on the brunettes. The scene dramatizes the Nash Equilibrium, his most important contribution to game theory. Nash proved that in any competitive situation—war, chess, even picking up a date at a bar—if the participants are rational and they know that their opponents are rational, there is only one optimal strategy. That theory won Nash a Nobel Prize in economics and transformed the way we think about competition in both games and the real world.10 Building off Nash’s general thoughts, Ed Seykota lays out a basic risk definition from a trading perspective: “Risk is the possibility of loss.”

, 273-274 fashion metaphor, 50 fat tails, 228 Faulkner, Charles, 3, 15, 21, 28, 33, 66, 193-194, 197-198, 201-203, 206-208, 214, 223, 253, 282, 299-302 Fawcett, George, 273 Federal Reserve announcements, reaction to, 56-57 Feinstein, Diane, 146 Feynman, Richard, 16 “fight-or-flight” mode, 197 First Gulf War, 176-178 five-year notes trading, 130 Florida Marlins, 187 Forrester, Jay, 62-63 Fouts, Roger, 209 Franiak, Frank J., 167 Freud, Sigmund, 206, 221 Friedman, Thomas, 28, 143, 256, 267 FTSE chart (2002), trend-followers and, 141 fundamental analysis, 7-9, 177, 212 Futures and Options Expo, 72 futures exchanges, 3 Futures Magazine, xvi Galilei, Galileo, 68 Galton, Francis, 32 game theory, 251 game, trading as, 277-278 Garcia, Jerry, 243 Gardner, David, 9 Gardner, Tom, 9 Gartman, Dennis, 116 “The Gartman Letter,” 116 Gawande, Atul, 209 generalists, trend followers as, 28 German Bund chart (1998), trend-followers and, 159 Gigerenzer, Gerd, 211, 213-214, 216, 224 Gladwell, Malcolm, 158, 169 Glassman, James, 231-232, 235 gold trading, 129 Goldman Sachs, 153 Goleman, Daniel, 196, 200-201 Good to Great (Collins), xviii, 33 Goodman, Marc, 105 Gould, Stephen Jay, 189 government, market system and, 4 Graham Capital Management, 21, 147 greed and behavioral finance, 196 Greenberg, Alan “Ace”, 205 Griffin, Ken, 111 Griffith, Bill, 18 Gulf War (first), 176-178 Gunther, Max, 283 Hamer, Jim, 66 Harding, David, xv, xx, 29-32, 105, 109, 124, 182, 199, 215, 230, 281, 289, 295 Harris, Larry, 114-115, 278 Harrison, Alfred, 235 “Has Trend Following Changed?”

pages: 462 words: 150,129

The Rational Optimist: How Prosperity Evolves by Matt Ridley


23andMe, agricultural Revolution, air freight, back-to-the-land, banking crisis, barriers to entry, Bernie Madoff, British Empire, call centre, carbon footprint, Cesare Marchetti: Marchetti’s constant, charter city, clean water, cloud computing, cognitive dissonance, collateralized debt obligation, colonial exploitation, colonial rule, Corn Laws, creative destruction, credit crunch, David Ricardo: comparative advantage, decarbonisation, dematerialisation, demographic dividend, demographic transition, double entry bookkeeping, Edward Glaeser,, everywhere but in the productivity statistics, falling living standards, feminist movement, financial innovation, Flynn Effect, food miles, Gordon Gekko, greed is good, Hans Rosling, happiness index / gross national happiness, haute cuisine, Hernando de Soto, income inequality, income per capita, Indoor air pollution, informal economy, Intergovernmental Panel on Climate Change (IPCC), invention of agriculture, invisible hand, James Hargreaves, James Watt: steam engine, Jane Jacobs, John Nash: game theory, joint-stock limited liability company, Joseph Schumpeter, Kevin Kelly, knowledge worker, Kula ring, Mark Zuckerberg, meta analysis, meta-analysis, mutually assured destruction, Naomi Klein, Northern Rock, nuclear winter, oil shale / tar sands, out of africa, packet switching, patent troll, Pax Mongolica, Peter Thiel, phenotype, Plutocrats, plutocrats, Ponzi scheme, Productivity paradox, profit motive, purchasing power parity, race to the bottom, Ray Kurzweil, rent-seeking, rising living standards, Silicon Valley, spice trade, spinning jenny, stem cell, Steve Jobs, Steven Pinker, Stewart Brand, supervolcano, technological singularity, The Wealth of Nations by Adam Smith, Thorstein Veblen, trade route, transaction costs, ultimatum game, upwardly mobile, urban sprawl, Vernor Vinge, Vilfredo Pareto, wage slave, working poor, working-age population, Y2K, Yogi Berra, zero-sum game

The Ascent of Money. Allen Lane. p. 85 Homicide rate graph. Spierenburg, P. 2008. A History of Murder. Polity Press. See also Eisner, M. 2001. Modernization, Self-Control and Lethal Violence. The Long-term Dynamics of European Homicide Rates in Theoretical Perspective The British Journal of Criminology 41:618-638. p. 85 ‘Greenstreet whispers to Bogart’. Siegfried, T. 2006. A Beautiful Math: John Nash, Game Theory and the Modern Quest for a Code of Nature. Joseph Henry Press. p. 86 ‘As the economist Herb Gintis puts it’. p. 86 ‘people in fifteen mostly small-scale tribal societies were enticed to play the Ultimatum Game’. Henrich, J. et al. 2005. ‘Economic man’ in crosscultural perspective: Behavioral experiments in 15 small-scale societies. Behavioral and Brain Sciences 28:795–815.

pages: 402 words: 110,972

Nerds on Wall Street: Math, Machines and Wired Markets by David J. Leinweber


AI winter, algorithmic trading, asset allocation, banking crisis, barriers to entry, Big bang: deregulation of the City of London, butterfly effect, buttonwood tree, buy low sell high, capital asset pricing model, citizen journalism, collateralized debt obligation, corporate governance, Craig Reynolds: boids flock, creative destruction, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, Danny Hillis, demand response, disintermediation, distributed generation, diversification, diversified portfolio, Emanuel Derman,, experimental economics, financial innovation, fixed income, Gordon Gekko, implied volatility, index arbitrage, index fund, information retrieval, intangible asset, Internet Archive, John Nash: game theory, Kenneth Arrow, Khan Academy, load shedding, Long Term Capital Management, Machine translation of "The spirit is willing, but the flesh is weak." to Russian and back, market fragmentation, market microstructure, Mars Rover, Metcalfe’s law, moral hazard, mutually assured destruction, Myron Scholes, natural language processing, negative equity, Network effects, optical character recognition, paper trading, passive investing, pez dispenser, phenotype, prediction markets, quantitative hedge fund, quantitative trading / quantitative finance, QWERTY keyboard, RAND corporation, random walk, Ray Kurzweil, Renaissance Technologies, Richard Stallman, risk tolerance, risk-adjusted returns, risk/return, Robert Metcalfe, Ronald Reagan, Rubik’s Cube, semantic web, Sharpe ratio, short selling, Silicon Valley, Small Order Execution System, smart grid, smart meter, social web, South Sea Bubble, statistical arbitrage, statistical model, Steve Jobs, Steven Levy, Tacoma Narrows Bridge, the scientific method, The Wisdom of Crowds, time value of money, too big to fail, transaction costs, Turing machine, Upton Sinclair, value at risk, Vernor Vinge, yield curve, Yogi Berra, your tax dollars at work

It depends how fast your information decays, and how willing you are to gamble that it will be known before you finish trading. Source: Robert Almgren and Neil Chriss, “Optimal Execution of Portfolio Transactions,” Journal of Risk 3, no. 2 (Winter 2000/2001). 10 Share Holdings 8 C B 6 4 A 2 0 0 1 2 3 Time Periods 77 4 5 Mathematical models of markets can become very elaborate. Game theoretic approaches to other market participants, human and machine, in the spirit of the Beautiful Mind ideas of John Nash, bring another level of insight. Known Unknowns and Unknown Unknowns Almgren and Chriss close with an important point about the limitations of all model-driven strategies. As part of the Algos 201 track, here is what they say about connecting algorithms to real-world events: Finally, we note that any optimal execution strategy is vulnerable to unanticipated events. If such an event occurs during the course of trading and causes a material shift in the parameters of the price dynamics, then indeed a shift in the optimal trading strategy must also occur.

I was blissfully unaware that I was passing through the same hallways used by some of the seminal thinkers of modern finance and economics: William Sharpe, Harry Markowitz, Kenneth Arrow, and George Dantzig. Markowitz and Sharpe, in particular, pioneered the ideas of balancing risk and reward in a systematic way, which when applied to finance, eventually led to their sharing the Nobel Prize in 1990. To digress just a bit, RAND’s interest in systematically approaching risk and reward, optimization, decision under uncertainty, and game theory was not initially conceived in the context of finance. RAND was motivated by the challenges of World War II and the Cold War.Think of the types of problems faced by the Army Air Corps, predecessor of the modern U.S. Air Force, in World War I. Military aviation involved flying small planes to take a look at the situation on the ground, occasionally encountering someone doing the same thing for the other side.

One Bullet Away: The Making of a Marine Officer by Fick, Nathaniel C.(October 3, 2005) Hardcover by Nathaniel C. Fick


clean water, defense in depth, double helix, friendly fire, John Nash: game theory, Khyber Pass, Silicon Valley

A portion of this book’s proceeds will be donated to veterans’ organizations, including the Marine Corps Scholarship Foundation, dedicated to funding higher education for the children of Marines killed in action. I thank my parents, Niel and Jane, and my sisters, Maureen and Stephanie, for their boundless love and support. In worrying, mailing cookies, and listening, they also served. My fellow platoon commanders were, and are, comrades in the truest sense. Thank you to Patrick English, Vijay George, Ed Hinman, Ty Moore, Walt Messick, Brendan Sullivan, John Nash, and Jim Beal. My former commanding officer Rich Whitmer taught me more than he will ever acknowledge. Thank you, Oden Six. To Keith Marine, I can only say “Dang.” I am forever grateful to Mike Wynn, Brad Colbert, Shawn Patrick, Rudy Reyes, Steve Lovell, Tony Espera, Tim Bryan, Mike Stinetorf, Hector Leon, Gabe Garza, Evan Stafford, Anthony “Manimal” Jacks, Walt Hasser, Nathan Christopher, James Chaffin, Harold Trombley, Teren “T” Holsey, John Christeson, Michael Brunmeier, Jason Lilley, Josh Person, Leandro “Shady” Baptista, Eric Kocher, Dan Redman, and A.

We used METT-T to estimate a tactical situation in order to complete the plan: mission, enemy, terrain, troops and fire support available, time. Most of all, we began to issue orders. Not yelled commands in mid-assault, but multipage written orders built around the five-paragraph format called SMEAC: situation, mission, execution, administration and logistics, command and signal. We wrote dozens of them. Instruction at TBS goes far beyond rote memorization, growing into some amalgamation of chess, history, boxing, and game theory. We studied the fog and friction of war, how the simplest things become difficult. During our written test on the subject, the instructors cranked Metallica at full volume, hurled tennis balls at our heads, and sprayed our faces with water pistols. The lesson was focus: ignore the distractions and do your job. We learned about warfare’s dynamism. We wouldn’t be fighting wax men in castles. In our instructors’ words, “The enemy has a vote, too.”

pages: 505 words: 142,118

A Man for All Markets by Edward O. Thorp


3Com Palm IPO, Albert Einstein, asset allocation, beat the dealer, Bernie Madoff, Black Swan, Black-Scholes formula, Brownian motion, buy low sell high, carried interest, Chuck Templeton: OpenTable, Claude Shannon: information theory, cognitive dissonance, collateralized debt obligation, compound rate of return, Credit Default Swap, credit default swaps / collateralized debt obligations, diversification, Edward Thorp, Erdős number, Eugene Fama: efficient market hypothesis, financial innovation, George Santayana, German hyperinflation, Henri Poincaré, high net worth, High speed trading, index arbitrage, index fund, interest rate swap, invisible hand, Jarndyce and Jarndyce, Jeff Bezos, John Meriwether, John Nash: game theory, Kenneth Arrow, Livingstone, I presume, Long Term Capital Management, Louis Bachelier, margin call, Mason jar, merger arbitrage, Murray Gell-Mann, Myron Scholes, NetJets, Norbert Wiener, passive investing, Paul Erdős, Paul Samuelson, Pluto: dwarf planet, Ponzi scheme, price anchoring, publish or perish, quantitative trading / quantitative finance, race to the bottom, random walk, Renaissance Technologies, RFID, Richard Feynman, Richard Feynman, risk-adjusted returns, Robert Shiller, Robert Shiller, rolodex, Sharpe ratio, short selling, Silicon Valley, statistical arbitrage, stem cell, survivorship bias, The Myth of the Rational Market, The Predators' Ball, the rule of 72, The Wisdom of Crowds, too big to fail, Upton Sinclair, value at risk, Vanguard fund, Vilfredo Pareto, Works Progress Administration

MIT had become one of the world’s great mathematics centers, following its transformation by projects for the government during World War II from a technical school to a scientific powerhouse. Simply walking down the hall, I would chat with people like the prodigy Professor Norbert Wiener (cybernetics) and the future Abel Prize winner Isadore Singer. The C. L. E. Moore Instructorship program, of which I was part, had brought in new PhDs like John Nash, who later won the Nobel for economics, and future Fields Medal winner Paul Cohen. Though there’s no Nobel Prize for mathematics, the Fields and the Abel prizes have that status. Cohen had left a few days before I arrived; his name was just being scraped off his door. I finally decided not to stay on. From a career standpoint, I thought I had the talent to keep up with the big boys but I felt I needed more mathematical background.

Kassouf) helped start the derivatives revolution that transformed world securities markets. Based on his work, he launched the first market-neutral hedge fund in 1969. Dr. Thorp, with Claude Shannon, also invented the first wearable computer in 1961 to win at roulette. He has also written Elementary Probability (1966), The Mathematics of Gambling (1984), and numerous mathematical papers on probability, game theory, and functional analysis. He completed undergraduate and graduate work at UCLA, receiving the BA and MA in physics, and the PhD in mathematics in 1958. He has taught at UCLA, MIT, and New Mexico State University, and was Professor of Mathematics and Finance at the University of California, Irvine. What’s next on your reading list? Discover your next great read!

pages: 829 words: 186,976

The Signal and the Noise: Why So Many Predictions Fail-But Some Don't by Nate Silver


airport security, availability heuristic, Bayesian statistics, Benoit Mandelbrot, Berlin Wall, Bernie Madoff, big-box store, Black Swan, Broken windows theory, Carmen Reinhart, Claude Shannon: information theory, Climategate, Climatic Research Unit, cognitive dissonance, collapse of Lehman Brothers, collateralized debt obligation, complexity theory, computer age, correlation does not imply causation, Credit Default Swap, credit default swaps / collateralized debt obligations, cuban missile crisis, Daniel Kahneman / Amos Tversky, diversification, Donald Trump, Edmond Halley, Edward Lorenz: Chaos theory,, equity premium, Eugene Fama: efficient market hypothesis, everywhere but in the productivity statistics, fear of failure, Fellow of the Royal Society, Freestyle chess, fudge factor, George Akerlof, haute cuisine, Henri Poincaré, high batting average, housing crisis, income per capita, index fund, Intergovernmental Panel on Climate Change (IPCC), Internet Archive, invention of the printing press, invisible hand, Isaac Newton, James Watt: steam engine, John Nash: game theory, John von Neumann, Kenneth Rogoff, knowledge economy, locking in a profit, Loma Prieta earthquake, market bubble, Mikhail Gorbachev, Moneyball by Michael Lewis explains big data, Monroe Doctrine, mortgage debt, Nate Silver, negative equity, new economy, Norbert Wiener, PageRank, pattern recognition,, Pierre-Simon Laplace, prediction markets, Productivity paradox, random walk, Richard Thaler, Robert Shiller, Robert Shiller, Rodney Brooks, Ronald Reagan, Saturday Night Live, savings glut, security theater, short selling, Skype, statistical model, Steven Pinker, The Great Moderation, The Market for Lemons, the scientific method, The Signal and the Noise by Nate Silver, The Wisdom of Crowds, Thomas Bayes, Thomas Kuhn: the structure of scientific revolutions, too big to fail, transaction costs, transfer pricing, University of East Anglia, Watson beat the top human players on Jeopardy!, wikimedia commons

We may focus on those signals which advance our preferred theory about the world, or might imply a more optimistic outcome. Or we may simply focus on the ones that fit with bureaucratic protocol, like the doctrine that sabotage rather than an air attack was the more likely threat to Pearl Harbor. The Unfamiliar and the Improbable Rumsfeld’s favorite part of Wohlstetter’s book is the foreword, composed by the Nobel Prize–winning economist Thomas Schelling, who was instrumental in translating John Nash’s early work on game theory into national-security contexts. Schelling writes of our propensity to mistake the unfamiliar for the improbable: There is a tendency in our planning to confuse the unfamiliar with the improbable. The contingency we have not considered seriously looks strange; what looks strange is thought improbable; what is improbable need not be considered seriously. Because of the United States’ isolation from the European and Asian continents and the relatively good relations we have maintained with the rest of the Americas since the promulgation of the Monroe Doctrine, we have infrequently been the subject of foreign attack.

At the same time, the system was designed to be slightly biased toward complicated positions, which played more to its strengths. “Positions that are good for computers are complex positions with lots of pieces on the board so there’s lots of legal moves available,” Campbell told me. “We want the positions where tactics are more important than strategy. So you can do some minor things to encourage that.” In this sense, Deep Blue was more “human” than any chess computer before or since. Although game theory does not come into play in chess to the same degree it does in games of incomplete information like poker, the opening sequences are one potential exception. Making a slightly inferior move to throw your opponent off-balance can undermine months of his preparation time—or months of yours if he knows the right response to it. But most computers try to play “perfect” chess rather than varying their game to match up well against their opponent.

Eventually, some of my opponents caught on to my more aggressive style, but this wasn’t all bad. It meant that they were more likely to call down when I did have a “predictable” hand like a pair of kings, making these hands more profitable for me. In fact, bluffing and aggressive play is not just a luxury in poker but a necessity—otherwise your play is just too predictable. Poker games have become extremely aggressive since I stopped playing regularly five years ago, and game theory13 as well as computer simulations14 strongly suggest this is the optimal approach. Blitzing your opponent with a deluge of possibilities is the best way to complicate his probability calculations. Sometimes you may also be able to identify situations where your opponents’ intuitive estimates of the probabilities are too crude. Whenever a poker player thinks that his opponent might never play a certain hand in a certain way—never bluff in a certain situation, for instance—that’s when you have the opportunity to exploit him by confusing his sense of the improbable and the impossible.