Cooperative Extensions of the Bayesian Game

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World Scientific, 2006 - Mathematics - 243 pages
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This is the very first comprehensive monograph in a burgeoning, new research area — the theory of cooperative game with incomplete information with emphasis on the solution concept of Bayesian incentive compatible strong equilibrium that encompasses the concept of the Bayesian incentive compatible core. Built upon the concepts and techniques in the classical static cooperative game theory and in the non-cooperative Bayesian game theory, the theory constructs and analyzes in part the powerful n-person game-theoretical model characterized by coordinated strategy-choice with individualistic incentives, the influence of outsiders' strategy choice upon the feasibility and implications of coalitional attainability, and incomplete information. The book presents the basic results of this theory. It also presents the research results to date on the simple, but central economic model of Bayesian pure exchange economy, and also on an alternative approach, anonymous coalition formation.The theory presented here points to an important future research direction in economics. In particular, it has the potential to provide game-theoretical foundations of organizational analysis in which organizations (coalitions) as corporations institute a non-market resource allocation mechanism while using the market resource allocation mechanism at the same time.The book provides appraisals of the various concepts, setups and results established to date as well as many discussions on philosophical issues on different approaches in the area, thereby clarifying the applicability and limitations of the current theory. It also contains numerous examples illustrating various concepts and points of discussions.Cooperative Extensions of the Bayesian Game is an essential reference in strategic cooperative game theory, and serves as an informative textbook for PhD courses in advanced economic theory, mathematical economics, game theory, and industrial organization.
 

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Contents

Measurability as Feasibility of Individual Actions
21
SOLUTIONS INFORMATION REVELATION
43
Comparisons of Several Core Concepts
65
Existence
91
A Appendix to Chapter 8
98
Approaches to Information Revelation
109
A Appendix to Chapter 9
149
Existence
167
Large Economy
195
Core ConvergenceEquivalence Theorems
207
SelfSelection in Anonymous Environments
219
Glossary
235
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Page 231 - Games with incomplete information played by 'Bayesian' players," Management Science: Theory 14, 159-182 (Part I), 320-334 (Part II), 486-502 (Part III). Hildenbrand, W. (1968): "On the core of an economy with a measure space of economic agents," Review of Economic Studies 35, 443-452.
Page 227 - Shitovitz, B.: Rational expectations equilibria and the ex-post core of an economy with asymmetric Information, Journal of Mathematical Economics 34 (2000) 527-535.
Page 230 - Communication, credible improvements and the core of an economy with asymmetric information, International Journal of Game Theory 29 (2000) 63-79.
Page 228 - Cooperative processing of information via choice at an information set," International Journal of Game Theory 23, 145-165.
Page 228 - Incentives and the core of an exchange economy: a survey, " Journal of Mathematical Economics 38, 1-41.

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