Game TheoryCambridge University Press, 21.03.2013 - 979 Seiten 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. |
Inhalt
Utility theory | 9 |
Extensiveform games | 39 |
Strategicform games | 75 |
Mixed strategies | 144 |
Behavior strategies and Kuhns Theorem | 219 |
Equilibrium refinements | 251 |
Correlated equilibria | 300 |
Games with incomplete information and common priors | 319 |
Bargaining games | 622 |
Coalitional games with transferable utility | 659 |
The core | 686 |
The Shapley value | 748 |
The bargaining set | 782 |
The nucleolus | 801 |
Social choice | 853 |
Stable matching | 884 |
the general model | 386 |
The universal belief space | 440 |
Auctions | 461 |
Repeated games | 519 |
Repeated games with vector payoffs | 569 |
Appendices | 916 |
| 958 | |
| 968 | |
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affine transformation alternatives ascribes probability Aumann model b₁ bargaining game behavior strategy belief hierarchy belief space belief subspace buyer choose coalitional game coalitional structure contains convex set core deduce defined Definition Denote dominated strategies Equation equilibrium payoff Example Exercise exists expected payoff extensive-form game Figure game tree game with incomplete imputation incomplete information information set knows lottery mixed strategy model of incomplete monotonic Nash equilibrium nonempty nucleolus outcome pair partition payoff function Player I's preference relation private value probability distribution proof Prove pure strategies repeated game s₁ satisfying sealed-bid second-price auction set of players Shapley value simplex solution concept stable matching stage strategic-form game strategy of Player strategy vector strict preference subgame perfect equilibrium symmetric symmetric equilibrium T₁ Theorem two-player zero-sum game utility function v₁ vertex vertices winning x₁ σ₁