This is an extract from the 4-volume dictionary of economics, a reference book which aims to define the subject of economics today. 1300 subject entries in the complete work cover the broad themes of economic theory. It concentrates on the topic of game theory.
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.
Game Theory has been an essential tool in analyzing national security, international trade, and the global environment since Neumann and Morgenstern introduced it more than 45 years ago. Chamberlin examines the work of these two authors, focusing on the relationship between rationality and morality as it arises in strategic interactions among players in a game based on three essential features: rational behavior, consequentialism, and the self-interest of players. The author concludes that due to the egoistic nature of actors, political dilemmas cannot easily be solved through the use of Game Theory. Nonetheless, he insists on its validity in contributing to our thinking about the place of ethics in international affairs and in clarifying both the dangers and potential areas of cooperation inherent in many international relationships.
Historical notes and references for the Foreword and Introduction -- 1 Noncooperative games -- 1 Noncooperative games and their components -- 2 Optimality principles in noncooperative games -- 3 Realizability of A-optimality principles -- 4 Realizability of A-principles in metastrategies -- 5 Realizability of equilibrium situations in mixed strategies -- 6 Natural topology in games -- Notes and references for Chapter 1 -- 2 Finite noncooperative games -- 1 Finite noncooperative games -- 2 Dyadic games -- 3 Solution of general finite noncooperative games -- 4 On the structure of the set of equilibria in finite noncooperative games -- 5 The complexity of solution of finite noncooperative games -- 6 Reduction to three-person games -- Notes and references for Chapter 3 -- 3 Two-person zero-sum games -- 1 Optimality in two-person zero-sum games -- 2 Basis of the maximin principle -- 3 Minimax theorems -- 4 Finitely additive strategies -- 5 Analytic games on the unit square -- 6 Separable games -- 7 Convex games -- 8 Games with a simple payoff function -- 9 Games of timing -- Notes and references for Chapter 3 -- 4 Matrix games -- 1 Basic concepts and propositions -- 2 Solution of matrix games of small format -- 3 Matrix games and linear programming -- 4 Description of all equilibrium situations in matrix and bimatrix games -- 5 Solution of matrix games with matrix payoffs of a special form -- 6 Approximate methods for solving matrix games -- 7 Structure of the set of a matrix game -- Notes and references for Chapter 4 -- References -- Collections -- List of Joint Authors -- Index of Notations.