Stability and Perfection of Nash Equilibria

ISBN-13: 9783540538004 / Angielski / Miękka / 1991 / 339 str.

Eric Van Damme

Opis

This book discusses the main shortcomings of the classical solution concept from noncooperative game theory (that of Nash equilibria) and provides a comprehensive study of the more refined concepts (such as sequential, perfect, proper and stable equilibria) that have been introduced to overcome these drawbacks. The plausibility of the assumptions underlying each such concept are discussed, desirable properties as well as deficiencies are illustrated, characterizations are derived and the relationships between the various concepts are studied. The first six chapters provide an informal discussion with many examples as well as a comprehensive overview for normal form games. The remaining chapters are devoted to specific applications, illustrating the strength (resp. weakness) of the various concepts.

Spis treści

1 Introduction.- 1.1 Informal Description of Games and Game Theory.- 1.2 Dynamic Programming.- 1.3 Subgame Perfect Equilibria.- 1.4 Sequential Equilibria and Perfect Equilibria.- 1.5 Perfect, Proper and Persistent Equilibria.- 1.6 Essential Equilibria and Regular Equilibria.- Notes.- 2 Games in Normal Form.- 2.1 Preliminaries.- 2.2 Perfect Equilibria.- 2.3 Proper Equilibria.- 2.4 Essential Equilibria.- 2.5 Regular Equilibria.- 2.6 An “Almost all” Theorem.- Notes.- 3 Matrix and Bimatrix Games.- 3.1 Preliminaries.- 3.2 Perfect Equilibria.- 3.3 Regular Equilibria.- 3.4 Characterizations of Regular Equilibria.- 3.5 Matrix Games.- Notes.- 4 Control Costs.- 4.1 Introduction.- 4.2 Games with Control Costs.- 4.3 Approachable Equilibria.- 4.4 Proper Equilibria.- 4.5 Perfect Equilibria.- 4.6 Regular Equilibria.- Notes.- 5 Incomplete Information.- 5.1 Introduction.- 5.2 Disturbed Games.- 5.3 Firm Equilibria.- 5.4 Perfect Equilibria.- 5.5 Weakly Proper Equilibria.- 5.6 Strictly Proper Equilibria and Regular Equilibria.- 5.7 Proofs of the Theorems of Sect. 5.5.- Notes.- 6 Extensive Form Games.- 6.1 Definitions.- 6.2 Equilibria and Subgame Perfectness.- 6.3 Sequential Equilibria.- 6.4 Perfect Equilibria.- 6.5 Proper Equilibria.- 6.6 Control Costs.- 6.7 Incomplete Information.- Notes.- 7 Bargaining and Fair Division.- 7.1 Introduction.- 7.2 Divide and Choose.- 7.3 Auction Methods.- 7.4 Bargaining Problems and Bargaining Solutions.- 7.5 The Nash Negotiation Game.- 7.6 The Rubinstein/Binmore Model.- 7.7 The Crawford/Moulin Model.- 7.8 Bargaining Games with Variable Threat Point.- Notes.- 8 Repeated Games.- 8.1 Introduction.- 8.2 Preliminaries.- 8.3 Infinitely Repeated Games Without Discounting.- 8.4 Infinitely Repeated Games with Discounting: Nash Equilibria.- 8.5 Infinitely Repeated Games with Discounting: Subgame Perfect Equilibria.- 8.6 Finitely Repeated Games: Nash Equilibria.- 8.7 Finitely Repeated Games: Subgame Perfect Equilibria.- 8.8 Renegotiation-Proof Equilibria.- Notes.- 9 Evolutionary Game Theory.- 9.1 Introduction.- 9.2 Evolutionarily Stable Strategies.- 9.3 Strategic Stability of ESS.- 9.4 Population Dynamics.- 9.5 Asymmetric Contests: Examples and the Model.- 9.6 Asymmetric Contests: Results.- 9.7 Contests in Extensive Form: Definitions.- 9.8 Contests in Extensive Form: Results.- Notes.- 10 Strategic Stability and Applications.- 10.1 Equivalence of Games.- 10.2 Requirements for Strategic Stability.- 10.3 Stable Equilibria.- 10.4 Signalling Games: Introduction.- 10.5 Signalling Games: Dominance, Intuitive Arguments and Stability.- 10.6 Spence’s Job Market Signalling Model.- 10.7 The Chain Store Paradox.- 10.8 Repeated Games.- Notes.- References.- Survey Diagrams.