Game Theory

games, theory of

theory of games, group of mathematical theories first developed by John Von Neumann and Oskar Morgenstern. A game consists of a set of rules governing a competitive situation in which from two to n individuals or groups of individuals choose strategies designed to maximize their own winnings or to minimize their opponent's winnings; the rules specify the possible actions for each player, the amount of information received by each as play progresses, and the amounts won or lost in various situations. Von Neumann and Morgenstern restricted their attention to zero-sum games, that is, to games in which no player can gain except at another's expense.

This restriction was overcome by the work of John F. Nash during the early 1950s. Nash mathematically clarified the distinction between cooperative and noncooperative games. In noncooperative games, unlike cooperative ones, no outside authority assures that players stick to the same predetermined rules, and binding agreements are not feasible. Further, he recognized that in noncooperative games there exist sets of optimal strategies (so-called Nash equilibria) used by the players in a game such that no player can benefit by unilaterally changing his or her strategy if the strategies of the other players remain unchanged. Because noncooperative games are common in the real world, the discovery revolutionized game theory. Nash also recognized that such an equilibrium solution would also be optimal in cooperative games. He suggested approaching the study of cooperative games via their reduction to noncooperative form and proposed a methodology, called the Nash program, for doing so. Nash also introduced the concept of bargaining, in which two or more players collude to produce a situation where failure to collude would make each of them worse off.

The theory of games applies statistical logic to the choice of strategies. It is applicable to many fields, including military problems and economics. The Nobel Memorial Prize in Economic Sciences was awarded to Nash, John Harsanyi, and Reinhard Selten (1994), to Robert J. Aumann and Thomas C. Schelling (2005), and to Lloyd Shapley and Alvin Roth (2012) for work in applying game theory to aspects of economics.

See J. Von Neumann and O. Morgenstern, Theory of Games and Economic Behavior (3d ed. 1953); D. Fudenberg and J. Tirole, Game Theory (1994); M. D. Davis, Game Theory: A Nontechnical Introduction (1997); R. B. Myerson, Game Theory: Analysis of Conflict (1997); J. F. Nash, Jr., Essays on Game Theory (1997); A. Rapoport, Two-Person Game Theory (1999).

The Columbia Encyclopedia, 6th ed. Copyright© 2013, The Columbia University Press.

Selected full-text books and articles on this topic

Playing for Real: A Text on Game Theory
Ken Binmore.
Oxford University Press, 2007
Game Theory: A Critical Introduction
Shaun P. Hargreaves Heap; Yanis Varoufakis.
Routledge, 1995
Schelling's Game Theory: How to Make Decisions
Robert V. Dodge.
Oxford University Press, 2012
Game Theory Evolving: A Problem-Centered Introduction to Modeling Strategic Interaction
Herbert Gintis.
Princeton University Press, 2009 (2nd edition)
A History of Game Theory
Mary Ann Dimand; Robert W. Dimand.
Routledge, vol.1, 1996
Game Theory and Economic Analysis
Christian Schmidt.
Routledge, 2002
Negotiation Games: Applying Game Theory to Bargaining and Arbitration
Steven J. Brams.
Routledge, 2003 (Revised edition)
Decision Making Using Game Theory: An Introduction for Managers
Anthony Kelly.
Cambridge University Press, 2003
Innovation Analysis and Game Theory: A Review
Baniak, Andrzej; Dubina, Igor.
Innovation : Management, Policy & Practice, Vol. 14, No. 2, June 2012
Open Innovation Modeling Using Game Theory
Asllani, Arben; Lari, Alireza.
Academy of Information and Management Sciences Journal, Vol. 14, No. 2, July 1, 2011
Economics and the Theory of Games
Fernando Vega-Redondo.
Cambridge University Press, 2003
Game Theory and the Environment
Nick Hanley; Henk Folmer.
Edward Elgar, 1998
State, Anarchy and Collective Decisions
Alex Talbot Coram.
Palgrave, 2000
Librarian’s tip: Chap. 1 "State, Anarchy, and Game Theory"
Political Science: The State of the Discipline II
Ada W. Finifter.
American Political Science Association, 1993
Librarian’s tip: "Prisoners' Dilemma: The Problem of Collective Action, and the Developments of Non-cooperative Game Theory" begins on p. 87
Search for more books and articles on game theory