A comprehensive introduction to game theory, incorporating exercises, examples and advanced topics.
Covering both noncooperative and cooperative games, this comprehensive introduction to game theory also includes some advanced chapters on auctions, games with incomplete information, games with vector payoffs, stable matchings and the bargaining set. Mathematically oriented, the book presents every theorem alongside a proof. The material is presented clearly and every concept is illustrated with concrete examples from a broad range of disciplines. With numerous exercises the book is a thorough and extensive guide to game theory from undergraduate through graduate courses in economics, mathematics, computer science, engineering and life sciences to being an authoritative reference for researchers.
Introduction; 1. The game of chess; 2. Utility theory; 3. Extensive-form games; 4. Strategic-form games; 5. Mixed strategies; 6. Behavior strategies and Kuhn\'s theorem; 7. Equilibrium refinements; 8. Correlated equilibria; 9. Games with incomplete information and common priors; 10. Games with incomplete information: the general model; 11. The universal belief space; 12. Auctions; 13. Repeated games; 14. Repeated games with vector payoffs; 15. Bargaining games; 16. Coalitional games with transferable utility; 17. The core; 18. The Shapley value; 19. The bargaining set; 20. The nucleolus; 21. Social choice; 22. Stable matching; 23. Appendices; Index.
\'This is the book for which the world has been waiting for decades: a definitive, comprehensive account of the mathematical theory of games, by three of the world\'s biggest experts on the subject. Rigorous yet eminently readable, deep yet comprehensible, replete with a large variety of important real-world applications, it will remain the standard reference in game theory for a very long time.\' Robert Aumann, Nobel Laureate in Economics, The Hebrew University of Jerusalem