## Cooperative Extensions of the Bayesian GameThis 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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### Common terms and phrases

assume assumption Bayesian game Bayesian incentive compatibility Bayesian incentive-compatible core Bayesian incentive-compatible strong Bayesian pure exchange Bayesian society bundle xs center game chapter coarse core communication system conditional expected conditional probability consumer j's consumption set convex cooperative game core allocation plan core plan defined definition denote ex ante Bayesian ex ante probability example existence theorem feasible feasible-strategy correspondence finite framework Fs(x grand coalition incentive compatibility condition incomplete information initial endowment interim Bayesian incentive-compatible interim efficiency interim expected utility interim period interim probabilities K-S pure exchange large Bayesian pure lemma lower semicontinuous members of coalition Neumann-Morgenstern utility function non-side-payment game nonempty nonmarketed commodities Pareto optimal player j's postulate private measurable proposition pure exchange economy Radner satisfies social coalitional equilibrium solution concept strategy bundle subset supp trade plan true type profile Ts-measurable utility allocation utility function vector Vohra

### Popular passages

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.