Effectivity Functions in Social Choice

1. Introduction.- 1. Collective decisions and power structure.- 2. Social choice.- 3. Games and game forms.- 4. The effectivity functions of a game form.- 5. Effectivity functions and cooperative games.- 6. An overview of the book.- 7. Notes.- 2. The structure of effectivity functions.- 1. Introduction.- 2. Fundamental concepts.- 3. Polarity.- 4. Selected families of effectivity functions.- 5. Topological effectivity functions.- 6. Notes.- 3. Stability.- 1. Introduction.- 2. The core of an effectivity function.- 3. Stable effectivity functions.- 4. Stability of convex effectivity functions.- 5. Acyclicity and stability.- 6. Stable veto functions.- 7. Notes.- 4. Implementation.- 1. Introduction.- 2. Implementation of social choice correspondences by game forms.- 3. Monotonic social choice functions.- 4. Notes.- 5. Implementation in strong Nash equilibrium.- 1. Strong Nash equilibrium.- 2. The effectivity functions of a strongly Nash implementable social choice correspondence.- 3. The fundamental theorem.- 4. The nucleus.- 5. The supernucleus.- 6. The subcore.- 7. A characterization of strong Nash implementable social choice correspondences.- 8. Notes.- 6. Exact and strong consistency.- 1. Self-implementation.- 2. Successive elimination and exact and.- consistency.- 3. The Holzman conditions.- 4. Notes.- 7. Implementation in coalition proof Nash equilibrium.- 1. Coalition proof Nash equilibrium.- 2. Implementation in coalition proof Nash equilibrium.- 3. Uniform domination.- 4. U-effectiveness and indirect u-domination.- 5. Notes.- 8. Other effectivity functions.- 1. Introduction.- 2. The ?-effectivity function.- 3. Cooperative equilibria of type 1.- 4. Equilibria of type 2 and 3.- 5. Notes.- 9. Value of effectivity functions.- 1. Introduction.- 2. Effectivity functions with convex feasible sets.- 3. Correlated strategies and effectivity functions.- 4. Effectivity functions of repeated games.- 5. Notes.- References.