Game Theory Text

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The Wayback Machine - https://web.archive.org/web/20050301121109/http://www.math.ucla.edu:80/~tom/Game_Theory/Contents.html

Game Theory Text

Thomas S. Ferguson

Mathematics Department, UCLA

Introduction.

Part I: Impartial Combinatorial Games.

Take-Away Games.<br>The Game of Nim.<br>Graph Games.<br>Sums of Combinatorial Games.<br>Coin Turning Games.<br>Green Hackenbush.

Part II: Two-Person Zero-Sum Games.

The Strategic Form of a Game.<br>Matrix Games. Domination.<br>The Principle of Indifference.<br>Solving Finite Games.<br>The Extensive Form of a Game.<br>Recursive and Stochastic Games.<br>Continuous Poker Models.

Part III: Two-Person General-Sum Games.

Bimatrix Games -- Safety Levels.<br>Noncooperative Games -- Equilibria.<br>Models of Duopoly.<br>Cooperative Games.

Part IV: Games in Coalitional Form.

Many-Person TU Games.<br>Imputations and the Core.<br>The Shapley Value.<br>The Nucleolus.

Appendix.

Utility Theory.<br>Contraction Maps and Fixed Points.<br>Existence of Equilibria in Finite Games.