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

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.