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Game theory is the study of mathematical models of strategic interactions.[1] It has applications in many fields of social science, and is used extensively in economics, 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 1950s, it was extended to the study of non zero-sum games, and was eventually applied to a wide range of behavioral relations. It is now an umbrella term for the science of rational decision making in humans, animals, and computers.
Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum games 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.
- ^ Myerson, Roger B. (1991). Game Theory: Analysis of Conflict. Harvard University Press. ISBN 9780674341166.
- ^ Shapley, Lloyd S.; Shubik, Martin (1 January 1971). "Chapter 1, Introduction, The Use of Models". Game Theory in Economics. Archived from the original on 23 April 2023. Retrieved 23 April 2023.
- ^ Neumann, John von; Morgenstern, Oskar (8 April 2007). Theory of Games and Economic Behavior. Princeton University Press. ISBN 978-0-691-13061-3. Archived from the original on 28 March 2023. Retrieved 23 April 2023.
- ^ Nisan (2020). "Book report: Theory of Games and Economic Behavior (von Neumann & Morgenstern)". lesswrong.com.