Game Theory

Thomas S. Ferguson
Mathematics Department, UCLA

Introduction.

Part I: Impartial Combinatorial Games.

1. Take-Away Games.
2. The Game of Nim.
3. Graph Games.
4. Sums of Combinatorial Games.
5. Coin Turning Games.
6. Green Hackenbush.

Part II: Two-Person Zero-Sum Games.

1. The Strategic Form of a Game.
2. Matrix Games. Domination.
3. The Principle of Indifference.
4. Solving Finite Games.
5. The Extensive Form of a Game.
6. Recursive and Stochastic Games.
7. Continuous Poker Models.

Part III: Two-Person General-Sum Games.

1. Bimatrix Games -- Safety Levels.
2. Noncooperative Games -- Equilibria.
3. Models of Duopoly.
4. Cooperative Games.

Part IV: Games in Coalitional Form.

1. Many-Person TU Games.
2. Imputations and the Core.
3. The Shapley Value.
4. The Nucleolus.

Appendix.

1. Utility Theory.
2. Contraction Maps and Fixed Points.
3. Existence of Equilibria in Finite Games.