Game Theory
Publisher: imusti; Cambridge University Press
Published: May 06, 2013
Format: hardcover
Number of pages: 1003
ISBN-13: 9781107005488
Table of contents: title: Acknowledgments
pagenum: xiv; title: Notations
pagenum: xv; title: Introduction
pagenum: xxiii; label: 1
title: The Game of Chess
pagenum: 1; label: 1.1
title: Schematic Description of the Game
pagenum: 1; label: 1.2
title: Analysis and Results
pagenum: 2; label: 1.3
title: Remarks
pagenum: 7; label: 1.4
title: Exercises
pagenum: 7; label: 2
title: Utility Theory
pagenum: 9; label: 2.1
title: Preference Relations and Their Representation
pagenum: 9; label: 2.2
title: Preference Relations Over Uncertain Outcomes: The Model
pagenum: 12; label: 2.3
title: The Axioms of Utility Theory
pagenum: 14; label: 2.4
title: The Characterization Theorem for Utility Functions
pagenum: 19; label: 2.5
title: Utility Functions and Affine Transformations
pagenum: 22; label: 2.6
title: Infinite Outcome Set
pagenum: 23; label: 2.7
title: Attitude Towards Risk
pagenum: 23; label: 2.8
title: Subjective Probability
pagenum: 26; label: 2.9
title: Discussion
pagenum: 27; label: 2.10
title: Remarks
pagenum: 31; label: 2.11
title: Exercises
pagenum: 31; label: 3
title: Extensive-Form Games
pagenum: 39; label: 3.1
title: An Example
pagenum: 40; label: 3.2
title: Graphs and Trees
pagenum: 41; label: 3.3
title: Game Trees
pagenum: 42; label: 3.4
title: Chomp: David Gale's Game
pagenum: 47; label: 3.5
title: Games With Chance Moves
pagenum: 49; label: 3.6
title: Games With Imperfect Information
pagenum: 52; label: 3.7
title: Exercises
pagenum: 57; label: 4
title: Strategic-Form Games
pagenum: 75; label: 4.1
title: Examples and Definition of Strategic-Form Games
pagenum: 76; label: 4.2
title: The Relationship Between the Extensive Form and the Strategic Form
pagenum: 82; label: 4.3
title: Strategic-Form Games: Solution Concepts
pagenum: 84; label: 4.4
title: Notation
pagenum: 85; label: 4.5
title: Domination
pagenum: 85; label: 4.6
title: Second-Price Auctions
pagenum: 91; label: 4.7
title: The Order of Elimination of Dominated Strategies
pagenum: 95; label: 4.8
title: Stability: Nash Equilibrium
pagenum: 95; label: 4.9
title: Properties of the Nash Equilibrium
pagenum: 100; label: 4.10
title: Security: The Maxmin Concept
pagenum: 102; label: 4.11
title: The Effect of Elimination of Dominated Strategies
pagenum: 106; label: 4.12
title: Two-Player Zero-Sum Games
pagenum: 110; label: 4.13
title: Games With Perfect Information
pagenum: 118; label: 4.14
title: Games on the Unit Square
pagenum: 121; label: 4.15
title: Remarks
pagenum: 128; label: 4.16
title: Exercises
pagenum: 128; label: 5
title: Mixed Strategies
pagenum: 144; label: 5.1
title: The Mixed Extension of a Strategic-Form Game
pagenum: 145; label: 5.2
title: Computing Equilibria in Mixed Strategies
pagenum: 152; label: 5.3
title: The Proof of Nash's Theorem
pagenum: 166; label: 5.4
title: Generalizing Nash's Theorem
pagenum: 170; label: 5.5
title: Utility Theory and Mixed Strategies
pagenum: 172; label: 5.6
title: The Maxmin and the Minmax in n-Player Games
pagenum: 176; label: 5.7
title: Imperfect Information: The Value of Information
pagenum: 180; label: 5.8
title: Evolutionarily Stable Strategies
pagenum: 186; label: 5.9
title: Remarks
pagenum: 194; label: 5.10
title: Exercises
pagenum: 194; label: 6
title: Behavior Strategies and Kuhn's Theorem
pagenum: 219; label: 6.1
title: Behavior Strategies
pagenum: 221; label: 6.2
title: Kuhn's Theorem
pagenum: 226; label: 6.3
title: Equilibria in Behavior Strategies
pagenum: 235; label: 6.4
title: Kuhn's Theorem for Infinite Games
pagenum: 238; label: 6.5
title: Remarks
pagenum: 243; label: 6.6
title: Exercises
pagenum: 244; label: 7
title: Equilibrium Refinements
pagenum: 251; label: 7.1
title: Subgame Perfect Equilibrium
pagenum: 252; label: 7.2
title: Rationality, Backward Induction, and Forward Induction
pagenum: 260; label: 7.3
title: Perfect Equilibrium
pagenum: 262; label: 7.4
title: Sequential Equilibrium
pagenum: 271; label: 7.5
title: Remarks
pagenum: 284; label: 7.6
title: Exercises
pagenum: 284; label: 8
title: Correlated Equilibria
pagenum: 300; label: 8.1
title: Examples
pagenum: 301; label: 8.2
title: Definition and Properties of Correlated Equilibrium
pagenum: 305; label: 8.3
title: Remarks
pagenum: 313; label: 8.4
title: Exercises
pagenum: 313; label: 9
title: Games With Incomplete Information and Common Priors
pagenum: 319; label: 9.1
title: The Aumann Model of Incomplete Information and the Concept of Knowledge
pagenum: 322; label: 9.2
title: The Aumann Model of Incomplete Information With Beliefs
pagenum: 334; label: 9.3
title: An Infinite Set of States of the World
pagenum: 344; label: 9.4
title: The Harsanyi Model of Games With Incomplete Information
pagenum: 345; label: 9.5
title: Incomplete Information as a Possible Interpretation of Mixed Strategies
pagenum: 361; label: 9.6
title: The Common Prior Assumption: Inconsistent Beliefs
pagenum: 365; label: 9.7
title: Remarks
pagenum: 367; label: 9.8
title: Exercises
pagenum: 368; label: 10
title: Games With Incomplete Information: The General Model
pagenum: 386; label: 10.1
title: Belief Spaces
pagenum: 386; label: 10.2
title: Belief and Knowledge
pagenum: 391; label: 10.3
title: Examples of Belief Spaces
pagenum: 394; label: 10.4
title: Belief Subspaces
pagenum: 400; label: 10.5
title: Games With Incomplete Information
pagenum: 407; label: 10.6
title: The Concept of Consistency
pagenum: 415; label: 10.7
title: Remarks
pagenum: 423; label: 10.8
title: Exercises
pagenum: 423; label: 11
title: The Universal Belief Space
pagenum: 440; label: 11.1
title: Belief Hierarchies
pagenum: 442; label: 11.2
title: Types
pagenum: 450; label: 11.3
title: Definition of the Universal Belief Space
pagenum: 453; label: 11.4
title: Remarks
pagenum: 456; label: 11.5
title: Exercises
pagenum: 456; label: 12
title: Auctions
pagenum: 461; label: 12.1
title: Notation
pagenum: 464; label: 12.2
title: Common Auction Methods
pagenum: 464; label: 12.3
title: Definition of a Sealed-Bid Auction With Private Values
pagenum: 465; label: 12.4
title: Equilibrium
pagenum: 468; label: 12.5
title: The Symmetric Model With Independent Private Values
pagenum: 471; label: 12.6
title: The Envelope Theorem
pagenum: 484; label: 12.7
title: Risk Aversion
pagenum: 488; label: 12.8
title: Mechanism Design
pagenum: 492; label: 12.9
title: Individually Rational Mechanisms
pagenum: 500; label: 12.10
title: Finding the Optimal Mechanism
pagenum: 501; label: 12.11
title: Remarks
pagenum: 508; label: 12.12
title: Exercises
pagenum: 509; label: 13
title: Repeated Games
pagenum: 519; label: 13.1
title: The Model
pagenum: 520; label: 13.2
title: Examples
pagenum: 521; label: 13.3
title: The T-Stage Repeated Game
pagenum: 524; label: 13.4
title: Characterization of the Set of Equilibrium Payoffs of the T-Stage Repeated Game
pagenum: 530; label: 13.5
title: Infinitely Repeated Games
pagenum: 537; label: 13.6
title: The Discounted Game
pagenum: 542; label: 13.7
title: Uniform Equilibrium
pagenum: 546; label: 13.8
title: Discussion
pagenum: 554; label: 13.9
title: Remarks
pagenum: 555; label: 13.10
title: Exercises
pagenum: 555; label: 14
title: Repeated Games With Vector Payoffs
pagenum: 569; label: 14.1
title: Notation
pagenum: 570; label: 14.2
title: The Model
pagenum: 572; label: 14.3
title: Examples
pagenum: 573; label: 14.4
title: Connections Between Approachable and Excludable Sets
pagenum: 574; label: 14.5
title: A Geometric Condition for the Approachability of a Set
pagenum: 576; label: 14.6
title: Characterizations of Convex Approachable Sets
pagenum: 585; label: 14.7
title: Application 1: Repeated Games With Incomplete Information
pagenum: 590; label: 14.8
title: Application 2: Challenge the Expert
pagenum: 600; label: 14.9
title: Discussion
pagenum: 606; label: 14.10
title: Remarks
pagenum: 607; label: 14.11
title: Exercises
pagenum: 608; label: 15
title: Bargaining Games
pagenum: 622; label: 15.1
title: Notation
pagenum: 625; label: 15.2
title: The Model
pagenum: 625; label: 15.3
title: Properties of the Nash Solution
pagenum: 626; label: 15.4
title: Existence and Uniqueness of the Nash Solution
pagenum: 630; label: 15.5
title: Another Characterization of the Nash Solution
pagenum: 635; label: 15.6
title: The Minimality of the Properties of the Nash Solution
pagenum: 639; label: 15.7
title: Critiques of the Properties of the Nash Solution
pagenum: 641; label: 15.8
title: Monotonicity Properties
pagenum: 643; label: 15.9
title: Bargaining Games With More Than Two Players
pagenum: 650; label: 15.10
title: Remarks
pagenum: 653; label: 15.11
title: Exercises
pagenum: 653; label: 16
title: Coalitional Games With Transferable Utility
pagenum: 659; label: 16.1
title: Examples
pagenum: 661; label: 16.2
title: Strategic Equivalence
pagenum: 668; label: 16.3
title: A Game as a Vector in a Euclidean Space
pagenum: 670; label: 16.4
title: Special Families of Games
pagenum: 671; label: 16.5
title: Solution Concepts
pagenum: 672; label: 16.6
title: Geometric Representation of the Set of Imputations
pagenum: 676; label: 16.7
title: Remarks
pagenum: 678; label: 16.8
title: Exercises
pagenum: 678; label: 17
title: The Core
pagenum: 686; label: 17.1
title: Definition of the Core
pagenum: 687; label: 17.2
title: Balanced Collections of Coalitions
pagenum: 691; label: 17.3
title: The Bondareva-Shapley Theorem
pagenum: 695; label: 17.4
title: Market Games
pagenum: 702; label: 17.5
title: Additive Games
pagenum: 712; label: 17.6
title: The Consistency Property of the Core
pagenum: 715; label: 17.7
title: Convex Games
pagenum: 717; label: 17.8
title: Spanning Tree Games
pagenum: 722; label: 17.9
title: Flow Games
pagenum: 724; label: 17.10
title: The Core for General Coalitional Structures
pagenum: 732; label: 17.11
title: Remarks
pagenum: 735; label: 17.12
title: Exercises
pagenum: 735; label: 18
title: The Shapley Value
pagenum: 748; label: 18.1
title: The Shapley Properties
pagenum: 749; label: 18.2
title: Solutions Satisfying Some of the Shapley Properties
pagenum: 751; label: 18.3
title: The Definition and Characterization of the Shapley Value
pagenum: 754; label: 18.4
title: Examples
pagenum: 758; label: 18.5
title: An Alternative Characterization of the Shapley Value
pagenum: 760; label: 18.6
title: Application: The Shapley-Shubik Power Index
pagenum: 763; label: 18.7
title: Convex Games
pagenum: 767; label: 18.8
title: The Consistency of the Shapley Value
pagenum: 768; label: 18.9
title: Remarks
pagenum: 774; label: 18.10
title: Exercises
pagenum: 774; label: 19
title: The Bargaining Set
pagenum: 782; label: 19.1
title: Definition of the Bargaining Set
pagenum: 784; label: 19.2
title: The Bargaining Set in Two-Player Games
pagenum: 788; label: 19.3
title: The Bargaining Set in Three-Player Games
pagenum: 788; label: 19.4
title: The Bargaining Set in Convex Games
pagenum: 794; label: 19.5
title: Discussion
pagenum: 797; label: 19.6
title: Remarks
pagenum: 798; label: 19.7
title: Exercises
pagenum: 798; label: 20
title: The Nucleolus
pagenum: 801; label: 20.1
title: Definition of the Nucleolus
pagenum: 802; label: 20.2
title: Nonemptiness and Uniqueness of the Nucleolus
pagenum: 805; label: 20.3
title: Properties of the Nucleolus
pagenum: 809; label: 20.4
title: Computing the Nucleolus
pagenum: 815; label: 20.5
title: Characterizing the Prenucleolus
pagenum: 816; label: 20.6
title: The Consistency of the Nucleolus
pagenum: 823; label: 20.7
title: Weighted Majority Games
pagenum: 825; label: 20.8
title: The Bankruptcy Problem
pagenum: 831; label: 20.9
title: Discussion
pagenum: 842; label: 20.10
title: Remarks
pagenum: 843; label: 20.11
title: Exercises
pagenum: 844; label: 21
title: Social Choice
pagenum: 853; label: 21.1
title: Social Welfare Functions
pagenum: 856; label: 21.2
title: Social Choice Functions
pagenum: 864; label: 21.3
title: Non-Manipulability
pagenum: 871; label: 21.4
title: Discussion
pagenum: 873; label: 21.5
title: Remarks
pagenum: 874; label: 21.6
title: Exercises
pagenum: 874; label: 22
title: Stable Matching
pagenum: 884; label: 22.1
title: The Model
pagenum: 886; label: 22.2
title: Existence of Stable Matching: The Men's Courtship Algorithm
pagenum: 888; label: 22.3
title: The Women's Courtship Algorithm
pagenum: 890; label: 22.4
title: Comparing Matchings
pagenum: 892; label: 22.5
title: Extensions
pagenum: 898; label: 22.6
title: Remarks
pagenum: 905; label: 22.7
title: Exercises
pagenum: 905; label: 23
title: Appendices
pagenum: 916; label: 23.1
title: Fixed Point Theorems
pagenum: 916; label: 23.2
title: The Separating Hyperplane Theorem
pagenum: 943; label: 23.3
title: Linear Programming
pagenum: 945; label: 23.4
title: Remarks
pagenum: 950; label: 23.5
title: Exercises
pagenum: 950; title: References
pagenum: 958; title: Index
pagenum: 968