Synopses & Reviews
Eminently suited to classroom use as well as individual study, Roger Myerson's introductory text provides a clear and thorough examination of the models, solution concepts, results, andmethodological principles of noncooperative and cooperative game theory. Myerson introduces, clarifies, and synthesizes the extraordinary advances made in the subject over the past fifteen years, presents an overview of decision theory,and comprehensively reviews the development of the fundamental models: games in extensive form and strategic form, and Bayesian games with incomplete information.
GameTheorywill be useful for students at the graduate level in economics, political science, operations research, and applied mathematics. Everyone who uses game theory in research will find this book essential.
Review
In a clear, Myersonian writing style, this book systematically describes our state-of-the-art knowledge of game theory. Written as an introductory text, it looks at the subject from the viewpoint of a newcomer tothe field, beginning with utility theory and arriving at the most sophisticated ideas discussed today. Myerson not only gives complete mathematical statements and proofs, but also supplies the intuitive arguments that motivatethem...Because of its comprehensiveness, researchers and users of game theory can find descriptions of almost all special game theoretic topics and issues presented in "user friendly" style...It is very likely that Myerson'sGame Theorywill remain the main introductory text for many years to come.
Review
Exposing an applied mathematics field on a basic level poses a challenge to an author, namely, to find the proper mix of displaying the models, providing the motivation and presenting the mathematical results andderivations. This is even more true in a field like game theory, where the models are not universally acceptable as adequately depicting real applications. The author, in the text under review, is doing remarkably well. The models aredisplayed with enough details and explanations to generate motivation even in newcomers to the field...All in all, it is a very good elaborate introduction to game theory.
Review
Myerson provides a good introduction to game theory, focusing on the 'generality and unity of game theory' rather than on its extensive applications. After a brief overview of Bayesian decision theory,noncooperative and cooperative models of games are explored in the context of their solutions, results, and guiding methodological principles. The relative merits of the extensive form and the strategic form of a game are illustrated,which lead naturally into an analysis of equilibria for each representation. Special extensions are discussed, including games with communication, repeated games, and noncooperative games that introduce the elements of bargaining andcoalitions...The book has interesting and challenging problem sets for each chapter as well as a bibliography for students who want to study in more depth specific topics in game theory.
Review
A very well-written introduction to game theory.
About the Author
Table of Contents
Preface
1. Decision-Theoretic Foundations
1.1 Game Theory, Rationality, and Intelligence
1.2 Basic Concepts of Decision Theory
1.3 Axioms
1.4 The Expected-Utility Maximization Theorem
1.5 Equivalent Representations
1.6 Bayesian Conditional-Probability Systems
1.7 Limitations of the Bayesian Model
1.8 Domination
1.9 Proofs of the Domination Theorems
Exercises
2. Basic Models
2.1 Games in Extensive Form
2.2 Strategic Form and the Normal Representation
2.3 Equivalence of Strategic-Form Games
2.4 Reduced Normal Representations
2.5 Elimination of Dominated Strategies
2.6 Multiagent Representations
2.7 Common Knowledge
2.8 Bayesian Games
2.9 Modeling Games with Incomplete Information
Exercises
3. Equilibria of Strategic-Form Games
3.1 Domination and Rationalizability
3.2 Nash Equilibrium
3.5 Computing Nash Equilibria
3.4 Significance of Nash Equilibria
3.5 The Focal-Point Effect
3.6 The Decision-Analytic Approach to Games
3.7 Evolution, Resistance, and Risk Dominance
3.8 Two-Person Zero-Sum Games
3.9 Bayesian Equilibria
3.10 Purification of Randomized Strategies in Equilibria
3.11 Auctions
3.12 Proof of Existence of Equilibrium
3.13 Infinite Strategy Sets
Exercises
4. Sequential Equilibria of Extensive-Form Games
4.1 Mixed Strategies and Behavioral Strategies
4.2 Equilibria in Behavioral Strategies
4.3 Sequential Rationality at Information States with Positive Probability
4.4 Consistent Beliefs and Sequential Rationality at All Information States
4.5 Computing Sequential Equilibria
4.6 Subgame-Perfect Equilibria
4.7 Games with Perfect Information
4.8 Adding Chance Events with Small Probability
4.9 Forward Induction
4.10 Voting and Binary Agendas
4.11 Technical Proofs
Exercises
5. Refinements of Equilibrium in Strategic Form
5.1 Introduction
5.2 Perfect Equilibria
5.3 Existence of Perfect and Sequential Equilibria
5.4 Proper Equilibria
5.5 Persistent Equilibria
5.6 Stable Sets of Equilibria
5.7 Generic Properties
5.8 Conclusions
Exercises
6. Games with Communication
6.1 Contracts and Correlated Strategies
6.2 Correlated Equilibria
6.3 Bayesian Games with Communication
6.4 Bayesian Collective-Choice Problems and Bayesian Bargaining Problems
6.5 Trading Problems with Linear Utility
6.6 General Participation Constraints for Bayesian Games with Contracts
6.7 Sender-Receiver Games
6.8 Acceptable and Predominant Correlated Equilibria
6.9 Communication in Extensive-Form and Multistage Games
Exercises
Bibliographic Note
7. Repeated Games
7.1 The Repeated Prisoners' Dilemma
7.2 A General Model of Repeated Games
7.3 Stationary Equilibria of Repeated Games with Complete State Information and Discounting
7.4 Repeated Games with Standard Information: Examples
7.5 General Feasibility Theorems for Standard Repeated Games
7.6 Finitely Repeated Games and the Role of Initial Doubt
7.7 Imperfect Observability of Moves
7.8 Repeated Games in Large Decentralized Groups
7.9 Repeated Games with Incomplete Information
7.10 Continuous Time
7.11 Evolutionary Simulation of Repeated Games
Exercises
8. Bargaining and Cooperation in Two-Person Games
8.1 Noncooperative Foundations of Cooperative Game Theory
8.2 Two-Person Bargaining Problems and the Nash Bargaining Solution
8.3 Interpersonal Comparisons of Weighted Utility
8.4 Transferable Utility
8.5 Rational Threats
8.6 Other Bargaining Solutions
8.7 An Alternating-Offer Bargaining Game
8.8 An Alternating-Offer Game with Incomplete information
8.9 A Discrete Alternating-Offer Game8.10 Renegotiation
Exercises
9. Coalitions in Cooperative Games
9.1 Introduction to Coalitional Analysis
9.2 Characteristic Functions with Transferable Utility
9.3 The Core
9.4 The Shapley Value
9.5 Values with Cooperation Structures
9.6 Other Solution Concepts
9.7 Coalitional Games with Nontransferable Utility
9.8 Cores without Transferable Utility
9.9 Values without Transferable UtilityExercises
Bibliographic Note
10. Cooperation Under Uncertainty
10.1 Introduction
10.2 Concepts of Efficiency
10.3 An Example
10.4 Ex Post Inefficiency and Subsequent Offers
10.5 Computing Incentive-Efficient Mechanisms
10.6 Inscrutability and Durability
10.7 Mechanism Selection by an Informed Principal
10.8 Neutral Bargaining Solutions
10.9 Dynamic Matching Processes with Incomplete Information
Exercises
Bibliography Index