Game Theory Academic Discipline
A Game Theory Academic Discipline is an academic discipline that studies formal games among self-interested agents.
- See: Decision Making, Mathematical Model, Decision Theory, Zero-Sum Game, Brouwer Fixed-Point Theorem, Convex Set, Mathematical Economics, Utility Function.
References
2014
- (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/game_theory Retrieved:2014-9-19.
- Game theory is a study of strategic decision making. Specifically, it is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers". [1] An alternative term suggested "as a more descriptive name for the discipline" is interactive decision theory. [2] Game theory is mainly used in economics, political science, and psychology, as well as logic, computer science, and biology. The subject first addressed zero-sum games, such that one person's gains exactly equal net losses of the other participant or participants. Today, however, game theory applies to a wide range of behavioral relations, and has developed into an umbrella term for the logical side of decision science, including both humans and non-humans (e.g. computers, insects/animals).
Modern game theory began with the idea regarding the existence of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann. Von Neumann's original proof used 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 the 1944 book Theory of Games and Economic Behavior, co-written with Oskar Morgenstern, which considered cooperative games of several players. The second edition of this book provided an axiomatic theory of expected utility, which allowed mathematical statisticians and economists to treat decision-making under uncertainty.
This theory was developed extensively in the 1950s by many scholars. Game theory was later explicitly applied to biology 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. Ten game-theorists have won the Nobel Memorial Prize in Economic Sciences and John Maynard Smith was awarded the Crafoord Prize for his application of game theory to biology.
- Game theory is a study of strategic decision making. Specifically, it is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers". [1] An alternative term suggested "as a more descriptive name for the discipline" is interactive decision theory. [2] Game theory is mainly used in economics, political science, and psychology, as well as logic, computer science, and biology. The subject first addressed zero-sum games, such that one person's gains exactly equal net losses of the other participant or participants. Today, however, game theory applies to a wide range of behavioral relations, and has developed into an umbrella term for the logical side of decision science, including both humans and non-humans (e.g. computers, insects/animals).
- ↑ Roger B. Myerson (1991). Game Theory: Analysis of Conflict, Harvard University Press, p. 1. Chapter-preview links, pp. vii–xi.
- ↑ R. J. Aumann ([1987 2008). “game theory," Introduction, The New Palgrave Dictionary of Economics, 2nd Edition. Abstract.
- http://en.wikipedia.org/wiki/List_of_games_in_game_theory
- Game theory studies strategic interaction between individuals in situations called games. Classes of these games have been given names. This is a list of the most commonly studied games
2008
- (Brown & Shoham, 2008) ⇒ Kevin Leyton-Brown, and Yoav Shoham. (2008). “Essentials of Game Theory: A Concise Multidisciplinary Introduction." Synthesis Lectures on Artificial Intelligence and Machine Learning, 2(1). doi:10.2200/S00108ED1V01Y200802AIM003
- ABSTRACT: Game theory is the mathematical study of interaction among independent, self-interested agents. The audience for game theory has grown dramatically in recent years, and now spans disciplines as diverse as political science, biology, psychology, economics, linguistics, sociology, and computer science, among others. What has been missing is a relatively short introduction to the field covering the common basis that anyone with a professional interest in game theory is likely to require. Such a text would minimize notation, ruthlessly focus on essentials, and yet not sacrifice rigor. This Synthesis Lecture aims to fill this gap by providing a concise and accessible introduction to the field. It covers the main classes of games, their representations, and the main concepts used to analyze them.
1995
- Tamer Basar, Geert Jan Olsder, G. J. Clsder, T. Basar, T. Baser, and Geert Jan Olsder. (1995). “Dynamic noncooperative game theory." Academic press.