Game theory

By: James Parsons

• Mathematics • Game Theory

What is Game Theory?

 Game Theory is the study of strategic decision making.

 Another definition would be the analysis of various games

History of Game Theory

    Early 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 1713 He provided a minimax mixed strategy solution to a two person version of a cared game Le Her.

The first mathematical discussion of the Prisoner’s Dilemma appeared in 1950.

Prisoner’s Dilemma

 Two 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 a Faustian bargain. Here's how it goes:    If A and B both confess the crime, each of them serves 2 years in prison If A confess but B denies the crime, A will be set free whereas B will serve 3 years If A and B both deny the crime, both of them will only serve 1 year in prison

Various types of Games

            Cooperative or non-cooperative Symmetric and asymmetric Zero-sum and Non-Zero-Sum Simultaneous and Sequential Perfect Information and Imperfect Information Combinatorial Infinitely Long Discrete and Continuous Differential Many-Player and Population Stochastic Outcomes Metagames

Combinatorial Games

 This is when the difficulty of finding an optimal strategy stems from the multiplicity of possible moves.  Ex: Chess, Checkers and Go

Perfect Information

 This 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 Theory

 Political 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  Philosophy

Sources

 http://mathworld.wolfram.com/PerfectInformation.html

 http://en.wikipedia.org/wiki/Game_theory  http://mathworld.wolfram.com/CombinatorialGameTheor y.html