In this monograph, noncooperative games are studied. Since in a noncooperative game binding agreements are not possible, the solution of such a game has to be self enforcing, i. e. a Nash equilibrium (NASH [1950,1951J). In general, however, a game may possess many equilibria and so the problem arises which one of these should be chosen as the solution. It was first pointed out explicitly in SELTEN [1965J that I not all Nash equilibria of an extensive form game are qualified to be selected as the solution, since an equilibrium may prescribe irrational behavior at unreached parts of the game tree. Moreover, also for normal form games not all Nash equilibria are eligible, since an equilibrium need not be robust with respect to slight perturba tions in the data of the game. These observations lead to the conclusion that the Nash equilibrium concept has to be refined in order to obtain sensible solutions for every game. In the monograph, various refinements of the Nash equilibrium concept are studied. Some of these have been proposed in the literature, but others are presented here for the first time. The objective is to study the relations between these refine ments;to derive characterizations and to discuss the underlying assumptions. The greater part of the monograph (the chapters 2-5) is devoted to the study of normal form games. Extensive form games are considered in chapter 6.
|Publisher:||Springer Berlin Heidelberg|
|Series:||Lecture Notes in Economics and Mathematical Systems , #219|
|Product dimensions:||6.69(w) x 9.61(h) x 0.01(d)|
Table of Contents1. General 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 equilibria and proper equilibria.- 1.6. Essential equilibria and regular equilibria.- 1.7. Summary of the following chapters.- 1.8. Notational conventions.- 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. Stable 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 section 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.- References.- Survey.