Unique Solutions for Strategic Games: Equilibrium Selection Based on Resistance Avoidance

ISBN-13: 9783540509745 / Angielski / Miękka / 1989 / 200 str.

Werner Guth;Brigitte Kalkofen

Opis

This book develops a general solution concept for strategic games which resolves strategic uncertainty completely. The concept is described by a mathematically formulated solution procedure and illustrated by applying it to many interesting examples. A long nontechnical introduction tries to survey and to discuss the more technical parts of the book. The book and especially the introduction provide firm and consistent guidance for scholars of game theory. There are many open problems which could inspire further research efforts.

Spis treści

Introduction: On equilibrium selection.- 1. The equilibrium concept.- 2. Examples of games with multiple equilibria.- 3. Refinement concepts versus equilibrium selection theory.- 4. The state of the art in equilibrium selection.- 4.1 NASH’s selection approach for unanimity bargaining games.- 4.2 The Harsanyi-Selten theory of equilibrium selection.- 4.2.1 Uniformly perturbed games in standard form.- 4.2.2 The tracing procedure.- 4.2.3 The method of how to solve a game.- 4.2.4 Properties of the Harsanyi-Selten theory.- 4.2.5 The solution procedure.- 5. Equilibrium selection based on resistance avoidance (ESBORA).- 5.1 The general motivation.- 5.2 The idea of resistance avoidance.- 5.3 The selection procedure.- 5.4 Possible modifications of the ESBORA-concept.- I: The concept of resistance avoidance.- 1. Modelling finite noncooperative games.- 2. The definition of resistance dominance.- 3. General properties of resistance dominance.- 4. Applying the principle of resistance avoidance.- 4.1 Games with complete information.- 4.1.1 A simple 2-person game with three strict equilibrium points.- 4.1.2 A 3-person game with two solution candidates.- 4.1.3 A 3-person game with an unbiased threat.- 4.1.4 An extensive game with chance moves.- 4.2 Games with incomplete information.- 4.2.1 Unanimity bargaining games with incomplete information.- 4.2.2 Wage bargaining with incomplete information.- 4.2.3 An art forgery situation.- II: Generating complete (agent) normal forms and candidate sets.- 1. Uniformly perturbed (agent) normal forms.- 2. Cell composition.- 3. Completing cell games and the residual game.- 4. Generating irreducible games.- 5. Generating candidate sets for irreducible games.- 6. The limit solution for the unperturbed game.- 7. Simplifications of the solution procedure in nondegenerate games.- 8. Examples.- 8.1 A degenerate unanimity bargaining game.- 8.2 An extensive game.- 8.3 The Condorcet Paradox.- 8.4 A 2-person bargaining game with a nonbargaining strategy on one side.- 8.4.1 The case of simultaneous decisions.- 8.4.2 Sequential agent splitting.- 8.5 A 2-person bargaining game with a nonbargaining strategy on both sides.- III: Generalizing the weights for normalized individual resistances.- 1. The ‘one seller and n-1 buyers’-problem.- 2. The generalized ESBORA-concept.- 3. Examples.- 3.1 The ‘one seller and n-1 buyers’-problem reconsidered.- 3.2 A class of 3-person games with three solution candidates.- 3.3 Decentralized or centralized bargaining?.- 3.4 Market entry games.- IV: Further perspectives for improving the ESBORA-concept.- 1. Continuous weights.- 1.1 New weights.- 1.2 Alternative weights.- 1.3 A 3-person game in the light of the various weighting approaches.- 1.4 The ‘one seller and n-1 buyers’-problem once again.- 1.5 A 3-person bargaining game with an unbiased threat reconsidered.- 2. Defining restricted games by the formation structure.- 3. Mixed strategy equilibria as solution candidates.- 3.1 On mixed strategy solutions.- 3.2 Changing the definition of solution candidates.- Final Remarks.- Notations.- References.