An Introduction to Game Theory – Part I

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214 pages

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English

Part I of An Introduction to Game Theory gives a thorough presentation of the non-cooperative theory. Knowledge of Mathematics corresponding to one semester of university studies is required.

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Part I of An Introduction to Game Theory gives a thorough presentation of the non-cooperative theory at a level suitable for undergraduate students. The book contains classical results of strategic games and extensive games with and without perfect information and in addition also a brief introduction to utility theory. Precise definitions and full proofs of all results are given. The book also contains plenty of exercises with answers and hints. Knowl- edge of Mathematics corresponding to one semester of university studies is required.

Lars-Åke Lindahl obtained his mathematical education at Uppsala University and Institut Mittag-Leffler and got a Ph.D. in Mathematics in 1971 with a thesis on Harmonic Analysis. Shortly thereafter he was employed as senior lecturer in Mathematics at Uppsala University, where he remained until his retirement in 2010 and for more than 20 years served as chairman of the Math. Department.

He has given lectures in a variety of mathematical subjects such as Calculus, Linear Algebra, Fourier Analysis, Complex Analysis, Convex Optimization, Game Theory and Probability Theory, and he has also written several textbooks and compendia. After his retirement, he has been a consultant to Al Baha University, Saudi Arabia, with a mission to assist in the development of their master's program in Mathematics.

- Preface
- Notation
- Utility Theory
- Preference relations and utility functions
- Continuous preference relations
- Lotteries
- Expected utility
- Von Neumann-Morgenstern preferences

- Preference relations and utility functions
- Strategic Games
- Definition and examples
- Nash equilibrium
- Existence of Nash equilibria
- Maxminimization
- Strictly competitive games

- Definition and examples
- Two Models of Oligopoly
- Cournot’s model of oligopoly
- Bertrand’s model of oligopoly

- Cournot’s model of oligopoly
- Congestion Games and Potential Games
- Congestion games
- Potential games

- Congestion games
- Mixed Strategies
- Mixed strategies
- The mixed extension of a game
- The indifference principle
- Dominance
- Maxminimizing strategies

- Mixed strategies
- Two-person Zero-sum Games
- Optimal strategies and the value
- Two-person zero-sum games and linear programming

- Optimal strategies and the value
- Rationalizability
- Beliefs
- Rationalizability

- Beliefs
- Extensive Games with Perfect Information
- Game trees
- Extensive form games
- Subgame perfect equilibria
- Stackelberg duopoly
- Chance moves

- Game trees
- Extensive Games with Imperfect Information
- Basic Endgame
- Extensive games with incomplete information
- Mixed strategies and behavior strategies

- Basic Endgame
- Answers and hints for the exercises
- Index