DiscoverScroll article

Game theory is the study of mathematical models of strategic interactions.

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. 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. 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. 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.

In 1913, Ernst Zermelo published Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels (On an Application of Set Theory to the Theory of the Game of Chess), which proved that the optimal chess strategy is strictly determined.

The work of John von Neumann established game theory as its own independent field in the early-to-mid 20th century, with von Neumann publishing his paper On the Theory of Games of Strategy in 1928. Von Neumann's work in game theory culminated in his 1944 book Theory of Games and Economic Behavior, co-authored with Oskar Morgenstern. Game theory experienced a flurry of activity in the 1950s, during which the concepts of the core, the extensive form game, fictitious play, repeated games, and the Shapley value were developed.

Cooperative game theory provides a high-level approach as it describes only the structure and payoffs of coalitions, whereas non-cooperative game theory also looks at how strategic interaction will affect the distribution of payoffs. As non-cooperative game theory is more general, cooperative games can be analyzed through the approach of non-cooperative game theory (the converse does not hold) provided that sufficient assumptions are made to encompass all the possible strategies available to players due to the possibility of external enforcement of cooperation.

A game with perfect information means that all players, at every move in the game, know the previous history of the game and the moves previously made by all other players.

The use of game theory in the social sciences has expanded, and game theory has been applied to political, sociological, and psychological behaviors as well.

Game theorists usually assume players act rationally, but in practice, human rationality and/or behavior often deviates from the model of rationality as used in game theory.

The application of game theory to political science is focused in the overlapping areas of fair division, political economy, public choice, war bargaining, positive political theory, and social choice theory.

According to Maynard Smith, in the preface to Evolution and the Theory of Games, "paradoxically, it has turned out that game theory is more readily applied to biology than to the field of economic behaviour for which it was originally designed".

Core (game theory) – Set in game theory

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

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

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

Yu-Chi Ho: What is Mathematical Game Theory; What is Mathematical Game Theory (#2); What is Mathematical Game Theory (#3); What is Mathematical Game Theory (#4)-Many person game theory; What is Mathematical Game Theory ?( #5) – Finale, summing up, and my own view

Quick Facts

• Core (game theory) – Set in game theory
• 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.
• 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 work in game theory culminated in his 1944 book Theory of Games and Economic Behavior, co-authored with Oskar Morgenstern.
• Adam Kalai: Game Theory and Computer Science — Lecture notes on Game Theory and Computer Science

Source material: Wikipedia - "Game theory". Adapted and summarized for DiscoverScroll. Original contributors are credited through the linked Wikipedia article. Read original on Wikipedia. CC BY-SA 4.0. Changes were made from the original.