Papers in Game Theory

This volume contains twelve of my game-theoretical papers, published in the period of 1956-80. It complements my Essays on Ethics, Social Behavior, and Scientific Explanation, Reidel, 1976, and my Rational Behavior and Bargaining Equilibrium in Games and Social Situations, Cambridge University Press, 1977. These twelve papers deal with a wide range of game-theoretical problems. But there is a common intellectual thread going though all of them: they are all parts of an attempt to generalize and combine various game-theoretical solution concepts into a unified solution theory yielding one-point solutions for both cooperative and noncooperative games, and covering even such 'non-classical' games as games with incomplete information. SECTION A The first three papers deal with bargaining models. The first one discusses Nash's two-person bargaining solution and shows its equivalence with Zeuthen's bargaining theory. The second considers the rationality postulates underlying the Nash-Zeuthen theory and defends it against Schelling's objections. The third extends the Shapley value to games without transferable utility and proposes a solution concept that is at the same time a generaliza tion of the Shapley value and of the Nash bargaining solution.

Inhalt

1. Approaches to the Bargaining Problem Before and After the Theory of Games: A Critical Discussion of Zeuthen's, Hicks', and Nash's Theories.- 2. On the Rationality Postulates Underlying the Theory of Cooperative Games.- 3. A Simplified Bargaining Model for the n-Person Cooperative Game.- 4. Games with Randomly Disturbed Payoffs: A New Rationale for Mixed-Strategy Equilibrium Points.- 5. Oddness of the Number of Equilibrium Points: A New Proof.- 6. Games with Incomplete Information Played by Bayesian Players. Part I: The Basic Model.- 7. Games with Incomplete Information Played by Bayesian Players. Part II: Bayesian Equilibrium Points.- 8. Games with Incomplete Information Played by Bayesian Players. Part III: The Basic Probability Distribution of the Game.- 9. Uses of Bayesian Probability Models in Game Theory.- 10. An Equilibrium-Point Interpretation of Stable Sets and a Proposed Alternative Definition.- 11. A New General Solution Concept for Both Cooperative and Noncooperative Games.- 12. Rule Utilitarianism, Rights, Obligations and the Theory of Rational Behavior.