Information AboutGame Theory |
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Game theory is a branch of Applied Mathematics that is often used in the context of Economics . It studies strategic interactions between Agents . In strategic games, agents choose Strategies which will maximize their return, given the strategies the other agents choose. The essential feature is that it provides a formal modelling approach to social situations in which decision makers interact with other agents. Game theory extends the simpler optimisation approach developed in Neoclassical Economics . The field of game theory came into being with the 1944 classic '' Theory Of Games And Economic Behavior '' by John Von Neumann and Oskar Morgenstern . A major center for the development of game theory was RAND Corporation where it helped to define Nuclear Strategies . Game theory has played, and continues to play a large role in the Social Sciences , and is now also used in many diverse academic fields. Beginning in the 1970s , game theory has been applied to animal behaviour, including Evolutionary Theory . Many games, especially the Prisoner's Dilemma , are used to illustrate ideas in Political Science and Ethics . Game theory has recently drawn attention from Computer Scientist s because of its use in Artificial Intelligence and Cybernetics . In addition to its academic interest, game theory has received attention in popular culture. A Nobel Prize –winning game theorist, John Nash , was the subject of the 1998 biography by Sylvia Nasar and the 2001 film '' A Beautiful Mind ''. Game theory was also a theme in the 1983 film '' WarGames ''. Several Game Show s have adopted game theoretic situations, including '' Friend Or Foe? '' and to some extent '' Survivor ''. The character Jack Bristow on the Television show '' Alias '' is one of the few fictional game theorists in popular culture. GameTheory.net has an extensive list of references to game theory in popular culture . Although some game theoretic analyses appear similar to Decision Theory , game theory studies decisions made in an environment in which players interact. In other words, game theory studies choice of optimal behavior when costs and benefits of each option depend upon the choices of other individuals. REPRESENTATION OF GAMES See Also: List of games in game theory The games studied by game theory are well-defined mathematical objects. A game consists of a set of Player s, a set of moves (or Strategies ) available to those players, and a specification of payoffs for each combination of strategies. Most cooperative games are presented in the characteristic function form, while the extensive and the normal forms are used to define noncooperative games. Extensive form See Also: Extensive form game The extensive form can be used to formalize games with some important order. Games here are often presented as Trees (as pictured to the left). Here each Vertex (or node) represents a point of choice for a player. The player is specified by a number listed by the vertex. The lines out of the vertex represent a possible action for that player. The payoffs are specified at the bottom of the tree. In the game pictured here, there are two players. ''Player 1'' moves first and chooses either ''F'' or ''U''. ''Player 2'' sees ''Player 1'''s move and then chooses ''A'' or ''R''. Suppose that ''Player 1'' chooses ''U'' and then ''Player 2'' chooses ''A'', then ''Player 1'' gets 8 and ''Player 2'' gets 2. The extensive form can also capture simultaneous-move games and games with incomplete information. To represent it, either a dotted line connects different vertices to represent them as being part of the same Information Set (i.e., the players do not know at which point they are), or a closed line is drawn around them. Normal form
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| {{Payoff Matrix Name | An asymmetric game |
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| {{Payoff Matrix Name | A zero-sum game |
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| {{Payoff Matrix Name | The Prisoner's Dilemma |
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| {{Payoff Matrix Name | The hawk-dove game |
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| {{Payoff Matrix Name | Stag hunt |
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