Editing Game theory (section)

{{Short description|Mathematical models of strategic interactions}}
{{about|the mathematical study of strategic behavior|the mathematical study of sequential games|Combinatorial game theory|the study of playing games for entertainment|Game studies|the YouTube series|MatPat|other uses}}
{{Use American English|date=July 2018}}
{{Economics sidebar}}
{{Strategy}}
'''Game theory''' is the study of [[mathematical model]]s of strategic interactions.<ref name=Myerson>{{cite book|last=Myerson|first=Roger B.|author-link=Roger B. Myerson|year=1991|title=Game Theory: Analysis of Conflict|publisher=[[Harvard University Press]]|isbn=9780674341166}}</ref> It has applications in many fields of [[social science]], and is used extensively in [[economics]], [[logic]], [[systems science]] and [[computer science]].<ref>{{Cite book|last1=Shapley |first1=Lloyd S. |last2=Shubik |first2=Martin |date=1971-01-01 |title=Game Theory in Economics |chapter = Chapter 1, Introduction, The Use of Models |url=https://www.rand.org/pubs/reports/R0904z1.html |access-date=23 April 2023 |archive-date=23 April 2023 |archive-url=https://web.archive.org/web/20230423130243/https://www.rand.org/pubs/reports/R0904z1.html |url-status=live }}</ref> Initially, game theory addressed two-person [[zero-sum game]]s, 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 [[Human behavior|behavioral relations]]. It is now an [[umbrella term]] for the [[science]] of rational [[Decision-making|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 set]]s, 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 game theory|cooperative game]]s of several players.<ref>{{Cite book |url= https://press.princeton.edu/books/paperback/9780691130613/theory-of-games-and-economic-behavior |title=Theory of Games and Economic Behavior |date=2007-04-08 |isbn=978-0-691-13061-3 |last1=Neumann |first1=John von |last2=Morgenstern |first2=Oskar |publisher=Princeton University Press |access-date=23 April 2023 |archive-date=28 March 2023 |archive-url= https://web.archive.org/web/20230328004503/https://press.princeton.edu/books/paperback/9780691130613/theory-of-games-and-economic-behavior |url-status=live }}</ref> The second edition provided an [[Von Neumann–Morgenstern utility theorem|axiomatic theory]] of [[Expected utility hypothesis|expected utility]], which allowed mathematical statisticians and economists to treat decision-making under uncertainty.

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 Memorial Prize in Economic Sciences|Nobel Prize in economics]] as of 2020, including most recently [[Paul Milgrom]] and [[Robert B. Wilson]].

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