Game Theory Stochastics, Information, Strategies and Cooperation
Game Theory: Stochastics, Information, Strategies and Cooperation provides a discussion of some relevant topics in game theory. It is composed partially from material compiled by Professor Joachim Rosenmüller when lecturing at IMW, the Institute of Mathem
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THEORY AND DECISION LffiRARY 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 D: System Theory, Knowledge Engineering an Problem Solving
SERIES C: GAME THEORY, MATHEMATICAL PROGRAMMING AND OPERATIONS RESEARCH VOLUME 25
Editor: S. H. Tijs (University of Tilburg); Editorial Board: E.E.C. van Damme (Tilburg), H. Keiding (Copenhagen), J.-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), J. Rosenmiiller (Bielefeld), A. Roth (Pittsburgh), D. Schmeidler (TelAviv), 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 sociobiology. 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.
GAME THEORY Stochastics, Information, Strategies and Cooperation by
JOACHIM ROSENMULLER University of Bielefeld
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
A c.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-1-4419-5114-4 ISBN 978-1-4757-3212-2 (eBook) DOI 10.1007/978-1-4757-3212-2
Printed on acid-free paper
AII Rights Reserved © 2000 Springer Science+Business Media Dordrecht Origina11y published by Kluwer Academic Publishers, Boston in 2000 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permis sion from the copyright owner.
Contents IX
Preface . . . . . . 1 Prerequisites
1
1
Probability and Integration
4
2
Conditional Expectation . .
17
3
Products and Markovian Measures
28
4
Stochastic Kernels
44
5
Common Knowledge
49
2 Stochastic Games and Incomplete Information
61
1
Markovian Games and Behavioral Strategies
64
2
Mixed Strategies and Kuhn's Theorem
92
3
Stopping Times . . . . . . . . . . .
110
4
Imperfect Information: Tree Games
116
5
Incomplete Information: Stochastic Games
140
6
Sequential Equilibria
169
7
The Trembling Hand
193
3 Stochastic Games: Infinite Horizon
211
1
The Model . . . . . . . . . . . . . . .
· 213
2
The Stationary Case: Value Iteration
· 218
3
Remarks on Martingales and Equilibrium Strategies
.228
4
Discounted Payoffs . . ..
· 232
........... . V
*
VI
CONTENTS
*
5
Tauberian Theorems . . . . . .
.240
6
The Asymptotic Behavior of VO
· 251
7
The Big Match . . . . . . . . .
.268
8
Stochastic Games have a Value
.280
4 Folk Theorems
299
1
Supergames.........
