Unique Solutions for Strategic Games

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.