Cooperative Decision-Making Under Risk
In cooperative games, one generally assumes that the agents know exactly the joint (monetary) gains that can be achieved by any possible coalition of cooperating agents. In reality, however, only little is known with certainty. This does not necessarily i
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THEORY AND DECISION LIBRARY
General Editors: W. Leinfellner (Vienna) and G. Eberlein (Munich) Series A: Philosophy and Methodology of the Social Sciences Series B: Mathematical and Statistical Methods Series C: Game Theory, Mathematical Programming and Operations Research
SERIES C: GAME THEORY, MATHEMATICAL PROGRAMMING AND OPERATIONS RESEARCH VOLUME 24
Editor: S. H. Tijs (University of Tilburg); Editorial Board: E.E.C. van Damme (Tilburg), H. Keiding (Copenhagen), I.-F. Mertens (Louvain-la-Neuve), H. Moulin (Durham), S. Muto (Tokyo University), T. Parthasarathy (New Delhi), B. Peleg (Jerusalem), H. Peters (Maastricht), T. E. S. Raghavan (Chicago), 1. RosenmUller (Bielefeld), A. Roth (pittsburgh), D. Schmeidler (Tel-Aviv), R. Selten (Bonn), W. Thomson (Rochester, NY). Scope: Particular attention is paid in this series to game theory and operations research, their formal aspects and their applications to economic, political and social sciences as well as to socia-biology. It will encourage high standards in the application of game-theoretical methods to individual and social decision making.
The titles published in this series are listed at the end of this volume.
COOPERATIVE DECISION-MAKING UNDERRISK
by
JEROEN SUIJS Tilburg University
" ~.
SPRINGER SCIENCE+BUSINESS MEDIA, LLC
ISBN 978-1-4613-7097-0 ISBN 978-1-4615-4637-5 (eBook) DOI 10.1007/978-1-4615-4637-5
Library of Congress Cataloging-in-Publication Data A C.I.P. Catalogue record for this book is available from the Library ofCongress. LC# 99047429 Copyright © 2000 Springer Science+Business Media New York Originally published by Kluwer Academic Publishers in 2000 Softcover reprint ofthe hardcover Ist edition 2000 AII rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher, Springer Science+Business Media, LLC.
Printed on acid-free paper.
Contents
Acknowledgements
vii
Notations
ix
1 Introduction
1
2 Cooperative Game Theory 2.1 Cooperative Decision-Making Problems 2.2 Transferable and Non-transferable Utility 2.3 Cooperative Games with Transferable Utility 2.4 Cooperative Games with Non-Transferable Utility 2.5 Chance-Constrained Games
7 7 11 20
29 36
3 Stochastic Cooperative Games 3.1 The Model 3.2 Preferences on Stochastic Payoffs 3.2.1 Weakly Continuous Preferences 3.2.2 Certainty Equivalents
43 43
4 The Core, Superadditivity, and Convexity 4.1 The Core of a Stochastic Cooperative Game 4.2 Superadditive Games 4.3 Convex Games 4.4 Ftemarks
57 57
5 Nucleoli for Stochastic Cooperative Games 5.1 NucleolusNl 5.2 Nucleolus N2 5.2.1 Preliminary Definitions 5.2.2 Definition of the Excess Function and Nucleolus
63 65 69
47 50 53
59 59 61
71
73
vi
5.3 Nucleoli, Core, and Certainty Equivalents 5.4 Appendix: Proofs
74 77
6 Risk Sharing and Insurance 6.1 Insurance Games 6.1.1 Pareto Optimal Distributions of Risk 6.1.2 The Zero Utility Premium Calculati
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