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This advanced textbook covers the central topics in game theory and provides a strong basis from which readers can go on to more advanced topics. The subject matter is approached in a mathematically rigorous, yet lively and interesting way. New definitions and topics are motivated as thoroughly as possible. Coverage includes the idea of iterated Prisoner's Dilemma (super games) and challenging game-playing computer programs.
Games in Extensive Form.
Trees.
Game Trees.
Choice Functions and Strategies.
Games with Chance Moves.
Equilibrium N-tuples of Strategies.
Normal Forms.
Two-Person Zero-Sum Games.
Saddle Points.
Mixed Strategies.
Small Games.
Symmetric Games.
Linear Programming.
Primal and Dual Problems.
Basic Forms and Pivots.
The Simplex Algorithm.
Avoiding Cycles and Achieving Feasibility.
Duality.
Solving Matrix Games.
The Minimax Theorem.
Some Examples.
Non-Zero-Sum Games.
Noncooperative Games.
Solution Concepts for Noncooperative Games.
Cooperative Games.
N-Person Cooperative Games.
Coalitions.
Imputations.
Strategic Equivalence.
Two Solution Concepts.
Game-Playing Programs.
Three Algorithms.
Evaluation Functions.
Appendix. Solutions