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 twoperson 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
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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