Now in its second edition, this popular textbook on game theory is unrivalled in the breadth of its coverage, the thoroughness of technical explanations and the number of worked examples included. Covering non-cooperative and cooperative games, this introduction to game theory includes advanced chapters on auctions, games with incomplete information, games with vector payoffs, stable matchings and the bargaining set. This edition contains new material on stochastic games, rationalizability, and the continuity of the set of equilibrium points with respect to the data of the game. The material is presented clearly and every concept is illustrated with concrete examples from a range of disciplines. With numerous exercises, and the addition of a solution manual for instructors with this edition, the book is an extensive guide to game theory for undergraduate through graduate courses in economics, mathematics, computer science, engineering and life sciences, and will also serve as useful reference for researchers.
Author(s): Michael Maschler, Eilon Solan, Shmuel Zamir
Edition: 2
Publisher: Cambridge University Press
Year: 2020
Language: English
Pages: 1050
Front Cover
CONTENTS
Acknowledgments
Notations
Introduction
1 The game of chess
1.1 Schematic description of the game
1.2 Analysis and results
1.3 Remarks
1.4 Exercises
2 Utility theory
2.1 Preference relations and their representation
2.2 Preference relations over uncertain outcomes: the model
2.3 The axioms of utility theory
2.4 The characterization theorem for utility functions
2.5 Utility functions and afï¬ne transformations
2.6 Infinite outcome set
2.7 Attitude towards risk
2.8 Subjective probability
2.9 Discussion
2.10 Remarks
2.11 Exercises
3 Extensive-form games
3.1 An example
3.2 Graphs and trees
3.3 Game trees
3.4 Chomp: David Gale's game
3.5 Games with chance moves
3.6 Games with imperfect information
3.7 Exercises
4 Strategic-form games
4.1 Examples and definition of strategic-form games
4.2 The relationship between the extensive form and the strategic form
4.3 Strategic-form games: solution concepts
4.4 Notation
4.5 Domination
4.6 Second-price auctions
4.7 The order of elimination of dominated strategies
4.8 Stability: Nash equilibrium
4.9 Properties of the Nash equilibrium
4.10 Security: the maxmin concept
4.11 The effect of elimination of dominated strategies
4.12 Two-player zero-sum games
4.13 Games with perfect information
4.14 Games on the unit square
4.15 Remarks
4.16 Exercises
5 Mixed strategies
5.1 The mixed extension of a strategic-form game
5.2 Computing equilibria in mixed strategies
5.3 The proof of Nash's Theorem
5.4 Generalizing Nash's Theorem
5.5 Utility theory and mixed strategies
5.6 The maxmin and the minmax in n-player games
5.7 Imperfect information: the value of information
5.8 Rationalizability
5.9 Evolutionarily stable strategies
5.10 The dependence of Nash equilibria on the payoffs of the game
5.11 Remarks
5.12 Exercises
6 Behavior strategies and Kuhn's Theorem
6.1 Behavior strategies
6.2 Kuhn's Theorem
6.3 Equilibria in behavior strategies
6.4 Kuhn's Theorem for infinite games
6.5 Remarks
6.6 Exercises
7 Equilibrium reï¬nements
7.1 Subgame perfect equilibrium
7.2 Rationality, backward induction, and forward induction
7.3 Perfect equilibrium
7.4 Sequential equilibrium
7.5 Remarks
7.6 Exercises
8 Correlated equilibria
8.1 Examples
8.2 Definition and properties of correlated equilibrium
8.3 Remarks
8.4 Exercises
9 Games with incomplete information and common priors
9.1 The Aumann model of incomplete information and the concept of knowledge
9.2 The Aumann model of incomplete information with beliefs
9.3 An infinite set of states of the world
9.4 The Harsanyi model of games with incomplete information
9.5 Incomplete information as a possible interpretation of mixed strategies
9.6 The common prior assumption: inconsistent beliefs
9.7 Remarks
9.8 Exercises
10 Games with incomplete information: the general model
10.1 Belief spaces
10.2 Belief and knowledge
10.3 Examples of belief spaces
10.4 Belief subspaces
10.5 Games with incomplete information
10.6 The concept of consistency
10.7 Remarks
10.8 Exercises
11 The universal belief space
11.1 Belief hierarchies
11.2 Types
11.3 Definition of the universal belief space
11.4 Remarks
11.5 Exercises
12 Auctions
12.1 Notation
12.2 Common auction methods
12.3 Definition of a sealed-bid auction with private values
12.4 Equilibrium
12.5 The symmetric model with independent private values
12.6 The Envelope Theorem
12.7 Risk aversion
12.8 Mechanism design
12.9 Individually rational mechanisms
12.10 Finding the optimal mechanism
12.11 Remarks
12.12 Exercises
13 Repeated games
13.1 The model
13.2 Examples
13.3 The T-stage repeated game
13.4 Characterization of the set of equilibrium payoffs of the T-stage repeated game
13.5 Inï¬nitely repeated games
13.6 The discounted game
13.7 Subgame perfectness
13.8 Uniform equilibrium
13.9 Discussion
13.10 Remarks
13.11 Exercises
14 Repeated games with vector payoffs
14.1 Notation
14.2 The model
14.3 Examples
14.4 Connections between approachable and excludable sets
14.5 A geometric condition for the approachability of a set
14.6 Characterizations of convex approachable sets
14.7 Application 1: Repeated games with incomplete information
14.8 Application 2: Challenge the expert
14.9 Discussion
14.10 Remarks
14.11 Exercises
15 Stochastic games
15.1 The model
15.2 The T-stage stochastic game
15.3 The inïfinite discounted game
15.4 Remarks
15.5 Exercises
16 Bargaining games
16.1 Notation
16.2 The model
16.3 Properties of the Nash solution
16.4 Existence and uniqueness of the Nash solution
16.5 Another characterization of the Nash solution
16.6 The minimality of the properties of the Nash solution
16.7 Critiques of the properties of the Nash solution
16.8 Monotonicity properties
16.9 Bargaining games with more than two players
16.10 Remarks
16.11 Exercises
17 Coalitional games with transferable utility
17.1 Examples
17.2 Strategic equivalence
17.3 A game as a vector in a Euclidean space
17.4 Special families of games
17.5 Solution concepts
17.6 Geometric representation of the set of imputations
17.7 Remarks
17.8 Exercises
18 The core
18.1 Definition of the core
18.2 Balanced collections of coalitions
18.3 The Bondareva-Shapley Theorem
18.4 Market games
18.5 Additive games
18.6 The consistency property of the core
18.7 Convex games
18.8 Spanning tree games
18.9 Flow games
18.10 The core for general coalitional structures
18.11 Remarks
18.12 Exercises
19 The Shapley value
19.1 The Shapley properties
19.2 Solutions satisfying some of the Shapley properties
19.3 The definition and characterization of the Shapley value
19.4 Examples
19.5 An alternative characterization of the Shapley value
19.6 Application: the Shapley-Shubik power index
19.7 Convex games
19.8 The consistency of the Shapley value
19.9 Remarks
19.10 Exercises
20 The bargaining set
20.1 Definition of the bargaining set
20.2 The bargaining set in two-player games
20.3 The bargaining set in three-player games
20.4 The bargaining set in convex games
20.5 Discussion
20.6 Remarks
20.7 Exercises
21 The nucleolus
21.1 Definition of the nucleolus
21.2 Nonemptiness and uniqueness of the nucleolus
21.3 Properties of the nucleolus
21.4 Computing the nucleolus
21.5 Characterizing the prenucleolus
21.6 The consistency of the nucleolus
21.7 Weighted majority games
21.8 The bankruptcy problem
21.9 Discussion
21.10 Remarks
21.11 Exercises
22 Social choice
22.1 Social welfare functions
22.2 Social choice functions
22.3 Non-manipulability
22.4 Discussion
22.5 Remarks
22.6 Exercises
23 Stable matching
23.1 The model
23.2 Existence of stable matching: the men's courtship algorithm
23.3 The women's courtship algorithm
23.4 Comparing matchings
23.5 Extensions
23.6 Remarks
23.7 Exercises
24 Appendices
24.1 Fixed point theorems
24.2 The Separating Hyperplane Theorem
24.3 Linear programming
24.4 Remarks
24.5 Exercises
References
Index
Back Cover
