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Game theory

Game theory is the study of mathematical models of strategic interactions.[1] It has applications in many fields of social science, used extensively in economics as well as in logic, systems science and computer science.[2] Initially game theory addressed two-person zero-sum games, in which a participant's gains or losses are exactly balanced by the losses and gains of the other participant. In the 1950’s it was extended to the study of non zero-sum games and was eventually game applied to a wide range of behavioral relations, and is now an umbrella term for the science of rational decision making in humans, animals, as well as computers.

This article is about the mathematical study of strategic behavior. For the mathematical study of sequential games, see Combinatorial game theory. For the study of playing games for entertainment, see Game studies. For the YouTube series, see MatPat. For other uses, see Game theory (disambiguation).

Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum game and its proof by John von Neumann. Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics. His paper was followed by Theory of Games and Economic Behavior (1944), co-written with Oskar Morgenstern, which considered cooperative games of several players.[3] The second edition provided an axiomatic theory of expected utility, which allowed mathematical statisticians and economists to treat decision-making under uncertainty.[4]


Game theory was developed extensively in the 1950s, and was explicitly applied to evolution in the 1970s, although similar developments go back at least as far as the 1930s. Game theory has been widely recognized as an important tool in many fields. John Maynard Smith was awarded the Crafoord Prize for his application of evolutionary game theory in 1999, and fifteen game theorists have won the Nobel Prize in economics as of 2020, including most recently Paul Milgrom and Robert B. Wilson.

application of game theory to procurement activity has increased – at the time it was at 19% across all survey respondents

65% of participants predict that use of game theory applications will grow

70% of respondents say that they have "only a basic or a below basic understanding" of game theory

20% of participants had undertaken in game theory

on-the-job training

50% of respondents said that new or improved software solutions were desirable

90% of respondents said that they do not have the software they need for their work.

[111]

Based on by Sylvia Nasar,[157] the life story of game theorist and mathematician John Nash was turned into the 2001 biopic A Beautiful Mind, starring Russell Crowe as Nash.[158]

the 1998 book

The 1959 novel Starship Troopers by Robert A. Heinlein mentioned "games theory" and "theory of games".[159] In the 1997 film of the same name, the character Carl Jenkins referred to his military intelligence assignment as being assigned to "games and theory".

military science fiction

The 1964 film satirizes game theoretic ideas about deterrence theory. For example, nuclear deterrence depends on the threat to retaliate catastrophically if a nuclear attack is detected. A game theorist might argue that such threats can fail to be credible, in the sense that they can lead to subgame imperfect equilibria. The movie takes this idea one step further, with the Soviet Union irrevocably committing to a catastrophic nuclear response without making the threat public.[160]

Dr. Strangelove

The 1980s band Game Theory was founded by singer/songwriter Scott Miller, who described the band's name as alluding to "the study of calculating the most appropriate action given an adversary ... to give yourself the minimum amount of failure".[161]

power pop

, a 2005 Japanese manga and 2007 television series, presents the main characters in each episode with a game or problem that is typically drawn from game theory, as demonstrated by the strategies applied by the characters.[162]

Liar Game

The 1974 novel by Len Deighton explores elements of game theory in regard to cold war army exercises.

Spy Story

The 2008 novel by Liu Cixin explores the relationship between extraterrestrial life, humanity, and game theory.

The Dark Forest

Joker, the prime antagonist in the 2008 film presents game theory concepts—notably the prisoner's dilemma in a scene where he asks passengers in two different ferries to bomb the other one to save their own.

The Dark Knight

In the 2018 film , the female lead Rachel Chu is a professor of economics and game theory at New York University. At the beginning of the film she is seen in her NYU classroom playing a game of poker with her teaching assistant and wins the game by bluffing;[163] then in the climax of the film, she plays a game of mahjong with her boyfriend's disapproving mother Eleanor, losing the game to Eleanor on purpose but winning her approval as a result.[164]

Crazy Rich Asians

In the 2017 film , Brad, an inexperienced poker player, makes an irrational betting decision without realising and causes his opponent Harlan to deviate from his Nash Equilibrium strategy, resulting in a significant loss when Harlan loses the hand.[165]

Molly's Game

 – Practical application of moral considerations

Applied ethics

 – Type of resource allocation game

Bandwidth-sharing game

 – Game theory paradox

Chainstore paradox

 – Intentionality that occurs when two or more individuals undertake a task together

Collective intentionality

 – term in game theory

Core (game theory)

 – List of definitions of terms and concepts used in game theory

Glossary of game theory

 – negotiations between members of a household to reach decisions

Intra-household bargaining

 – an endgame situation where a player who is unable to win has the capacity to determine which player among others will win

Kingmaker scenario

 – Application of economic theory to analysis of legal systems

Law and economics

 – Doctrine of military strategy

Mutual assured destruction

 – Overview of and topical guide to artificial intelligence

Outline of artificial intelligence

 – Paradox in game theory

Parrondo's paradox

 – Risk management strategy

Precautionary principle

Quantum refereed game

 – Identification, evaluation and control of risks

Risk management

Self-confirming equilibrium

 – Self-interests causing depletion of a shared resource

Tragedy of the commons

 – non-zero-sum game thought experiment

Traveler's dilemma

 – Argument in economic theory

Wilson doctrine (economics)

Compositional game theory

Lists

(1987), "game theory", The New Palgrave: A Dictionary of Economics, vol. 2, pp. 460–82.

Aumann, Robert J

(2003), "Introduction", Behavioral Game Theory: Experiments in Strategic Interaction, Russell Sage Foundation, pp. 1–25, ISBN 978-0-691-09039-9, archived from the original on 14 May 2011, retrieved 9 February 2011, Description.

Camerer, Colin

Dutta, Prajit K. (1999), Strategies and games: theory and practice, , ISBN 978-0-262-04169-0. Suitable for undergraduate and business students.

MIT Press

Fernandez, L F.; Bierman, H S. (1998), Game theory with economic applications, , ISBN 978-0-201-84758-1. Suitable for upper-level undergraduates.

Addison-Wesley

Fisher, Sir Ronald Aylmer (1930). . Clarendon Press.

The Genetical Theory of Natural Selection

Gaffal, Margit; Padilla Gálvez, Jesús (2014). Dynamics of Rational Negotiation: Game Theory, Language Games and Forms of Life. Springer.

ISBN

Gintis, Herbert (2000), Game theory evolving: a problem-centered introduction to modeling strategic behavior, Princeton University Press,  978-0-691-00943-8

ISBN

Green, Jerry R.; ; Whinston, Michael D. (1995), Microeconomic theory, Oxford University Press, ISBN 978-0-19-507340-9. Presents game theory in formal way suitable for graduate level.

Mas-Colell, Andreu

Joseph E. Harrington (2008) Games, strategies, and decision making, Worth,  0-7167-6630-2. Textbook suitable for undergraduates in applied fields; numerous examples, fewer formalisms in concept presentation.

ISBN

Howard, Nigel (1971), Paradoxes of Rationality: Games, Metagames, and Political Behavior, Cambridge, : The MIT Press, ISBN 978-0-262-58237-7

MA

(1999), Differential Games: A Mathematical Theory With Applications to Warfare and Pursuit, Control and Optimization, New York: Dover Publications, ISBN 978-0-486-40682-4

Isaacs, Rufus

Kavka, Gregory S. (1986). . Princeton University Press. ISBN 978-0-691-02765-4.

Hobbesian Moral and Political Theory

Maschler, Michael; Solan, Eilon; Zamir, Shmuel (2013), Game Theory, Cambridge University Press,  978-1-108-49345-1. Undergraduate textbook.

ISBN

Miller, James H. (2003), Game theory at work: how to use game theory to outthink and outmaneuver your competition, New York: , ISBN 978-0-07-140020-6. Suitable for a general audience.

McGraw-Hill

Osborne, Martin J. (2004), An introduction to game theory, Oxford University Press,  978-0-19-512895-6. Undergraduate textbook.

ISBN

Poundstone, William (1993). (1st Anchor Books ed.). New York: Anchor. ISBN 0-385-41580-X.

Prisoner's Dilemma

Osborne, Martin J.; (1994), A course in game theory, MIT Press, ISBN 978-0-262-65040-3. A modern introduction at the graduate level.

Rubinstein, Ariel

Shoham, Yoav; Leyton-Brown, Kevin (2009), , New York: Cambridge University Press, ISBN 978-0-521-89943-7, retrieved 8 March 2016

Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations

Watson, Joel (2013), , New York: W.W. Norton and Co., ISBN 978-0-393-91838-0. A leading textbook at the advanced undergraduate level.

Strategy: An Introduction to Game Theory (3rd edition)

McCain, Roger A. (2010), (Revised ed.), World Scientific, ISBN 978-981-4289-65-8

Roger McCain's Game Theory: A Nontechnical Introduction to the Analysis of Strategy

Webb, James N. (2007), Game theory: decisions, interaction and evolution, Undergraduate mathematics, Springer,  978-1-84628-423-6 Consistent treatment of game types usually claimed by different applied fields, e.g. Markov decision processes.

ISBN

James Miller (2015): .

Introductory Game Theory Videos

, Encyclopedia of Mathematics, EMS Press, 2001 [1994]

"Games, theory of"

Paul Walker: .

History of Game Theory Page

David Levine:

Game Theory. Papers, Lecture Notes and much more stuff.

Alvin Roth:. Archived from the original on 15 August 2000. Retrieved 13 September 2003. — Comprehensive list of links to game theory information on the Web

"Game Theory and Experimental Economics page"

Adam Kalai: — Lecture notes on Game Theory and Computer Science

Game Theory and Computer Science

Mike Shor: — Lecture notes, interactive illustrations and other information.

GameTheory.net

Jim Ratliff's (lecture notes).

Graduate Course in Game Theory

Don Ross: in the Stanford Encyclopedia of Philosophy.

Review Of Game Theory

Bruno Verbeek and Christopher Morris:

Game Theory and Ethics

Elmer G. Wiens: — Introduction, worked examples, play online two-person zero-sum games.

Game Theory

Marek M. Kaminski: Archived 20 October 2006 at the Wayback Machine — Syllabuses and lecture notes for game theory and political science.

Game Theory and Politics

Websites on game theory and social interactions

Kesten Green's at the Wayback Machine (archived 11 April 2011) — See Papers for evidence on the accuracy of forecasts from game theory and other methods Archived 15 September 2019 at the Wayback Machine.

Conflict Forecasting

McKelvey, Richard D., McLennan, Andrew M., and Turocy, Theodore L. (2007) .

Gambit: Software Tools for Game Theory

Benjamin Polak: Archived 3 August 2010 at the Wayback Machine videos of the course

Open Course on Game Theory at Yale

Benjamin Moritz, Bernhard Könsgen, Danny Bures, Ronni Wiersch, (2007) .

Spieltheorie-Software.de: An application for Game Theory implemented in JAVA

Antonin Kucera: .

Stochastic Two-Player Games