Game theory

Game theory

By: James ParsonsGame theoryMathematics Game TheoryWhat is Game Theory?Game Theory is the study of strategic decision making.

Another definition would be the analysis of various gamesHistory of Game TheoryEarly discussions of examples of two-person games occurred long before the rise of modern, mathematical game theory.The first known discussion of Game Theory occurred in a letter written by James Waldegrave in 1713He provided a minimax mixed strategy solution to a two-person version of a cared game Le Her.The first mathematical discussion of the Prisoners Dilemma appeared in 1950.Prisoners DilemmaTwo members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of speaking to or exchanging messages with the other. The police admit they don't have enough evidence to convict the pair on the principal charge. They plan to sentence both to a year in prison on a lesser charge. Simultaneously, the police offer each prisoner aFaustian bargain. Here's how it goes:

If A and B both confess the crime, each of them serves 2 years in prisonIf A confess but B denies the crime, A will be set free whereas B will serve 3 yearsIf A and B both deny the crime, both of them will only serve 1 year in prisonVarious types of GamesCooperative or non-cooperativeSymmetric and asymmetricZero-sum and Non-Zero-SumSimultaneous and SequentialPerfect Information and Imperfect InformationCombinatorial Infinitely LongDiscrete and ContinuousDifferentialMany-Player and PopulationStochastic OutcomesMetagamesCombinatorial GamesThis is when the difficulty of finding an optimal strategy stems from the multiplicity of possible moves.

Ex: Chess, Checkers and Go

Perfect InformationThis is a type of game in which players move alternately and each player is aware of the previous move. An optimal strategy may be difficult to compute as to be effectively impossible to find.

Ex: Checkers and Chess

Other applications for Game TheoryPolitical Science 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.

In each of these areas, researchers have developed game-theoretic models in which players are often voters, states, special interest groups, and politicians. Other Applications (cont)Biology

Computer Science

PhilosophySourceshttp://mathworld.wolfram.com/PerfectInformation.html

http://en.wikipedia.org/wiki/Game_theory

http://mathworld.wolfram.com/CombinatorialGameTheory.html