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.
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The game of chess
Behavior strategies and Kuhns Theorem
Games with incomplete information and common priors
the general model
Coalitional games with transferable utility
The Shapley value
The bargaining set
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afﬁne alternatives ascribes probability Aumann model average payoff bargaining game behavior strategy belief hierarchy belief space belief subspace buyer chance move choose coalitional game coalitional structure contains convex set core deduce deﬁned Deﬁnition Denote dominated strategies efﬁciency Equation equilibrium payoff example Exercise exists expected payoff extensive-form game Figure ﬁnd ﬁnite ﬂow game tree game with incomplete II’s imputation incomplete information inﬁnite information set knows lottery mixed strategy model of incomplete monotonic Nash equilibrium nonempty nucleolus ofplayer outcome pair partition payoff function Player 11 player i G N Player I’s preference relation private value probability distribution proﬁt proof Prove pure strategies repeated game satisﬁes satisfying sealed-bid second-price auction set of players Shapley value simplex solution concept stable matching strategic-form game strategy of Player strategy vector strict preference subgame perfect equilibrium symmetric symmetric equilibrium Theorem two-player zero-sum game utility function vertex vertices winning