Stability and Perfection of Nash Equilibria

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 -- 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 -- 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 -- 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 -- 5 Incomplete Information -- 5.1 Introduction -- 5.2 Disturbed Games -- 5.3 Firm Equilibria -- 5.4 Perfect Equilibria -- 5 Weakly Proper Equilibria -- 5.6 Strictly Proper Equilibria and Regular Equilibria -- 5.7 Proofs of the Theorems of Sect. 5.5 -- 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 -- 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 -- 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 -- 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 -- 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 -- References -- Survey Diagrams.