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Series F: Computer and Systems Sciences, Vol. 155
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Cooperation:
Game-Theoretic Approaches
Edited by
Sergiu Hart
Department of Economics and Department of Mathematics
The Hebrew University ofJerusalem
Givat Ram, 91904 Jerusalem, Israel
Andreu Mas-Colell
Facultat de Ciencies Economiques i Empresarials
Universitat Pompeu Fabra
c/ Ramon Trias Fargas, 25-27, E-08005 Barcelona, Spain
Springer
Published in cooperation with NATO Scientific Affairs Division
Proceedings of the NATO Advanced Study Institute on Cooperation:
Game-Theoretic Approaches, held at SUNY, Stony Brook, New York,
July 18-29, 1994
Library of Congress Cataloging-in-Publication Data
Cooperation: game-theoretic approaches I edited by Sergiu Hart,
Andreu Mas-Colell,
p. em. -- (NATO ASI series. Series F, Computer and systems
sciences; no. 155)
"Proceedings of the Nato Advanced Study Institute on Cooperation:
Game-Theoretic Approaches.- held at SUNY, Stony Brook, New York, July
18-29, 1994"--T.p. verso.
Includes bibliographical references.
Additional material to tbis book can be downloaded from bttp:llextra.apringer.com.
ISBN-13:978-3-642-64413-9 e·ISBN-13:978-3-642-60454-6
DOl: 10.10071978-3-642·60454-6
1. Game theory--Congresses. I. Hart, Sergiu. II. Mas-Colell,
Andreu. III. Nato Advanced Study Institute on Cooperation: Game
-Theoretic Approaches (1994 : Stony Brook, N.Y.) IV. Series: NATO
ASI series. Series F, Computer and systems sciences; no. 155.
QA269.C66 1997
519.3--DC20 96-27102
CIP
CR Subject Classification (1991): H,1.1, J,4
ISBN -13: 978-3-642-64413-9
This work is subject to copyright. All rights are reserved, whether the whole or part of the
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the German Copyright Law.
© Springer-Verlag Berlin Heidelberg 1997
Softcover reprint of the hardcover 1st edition 1997
Typesetting: Camera-ready by editor
Printed on acid-free paper
SPIN: 10537423 45/3142 - 5 432 1 0
Preface
This volume includes the proceedings of the NATO Advance Study Institute on
"Cooperation: Game Theoretic Approaches", that took place at Stony Brook, NY,
USA, from July 18 to July 29, 1994.
The Institute was a success and it is already part of a well established biannual
Stony Brook tradition to which many researchers around the world look forward
to.
We thank the institute for Decision Sciences of the State University of New York
at Stony Brook for hosting this event. It is a particular pleasure to thank Colleen
Wallahora and Eileen Zapia, for the very successful organization of this AS!.
June 1996 Sergiu Hart and Andreu Mas-Colell
List of Authors
Prof. Beth Allen, University of Minnesota, Minneapolis
Prof. Robert J. Aumann, The Hebrew University of Jerusalem
Prof. Joseph Greenberg, McGill University, Montreal
Prof. Sergiu Hart, The Hebrew University of Jerusalem
Prof. Vijay Krishna, Pennsylvania State University at University Park
Prof. Andreu Mas-Colell, Harvard University,
and Universitat Pompeu Fabra, Barcelona
Prof. Abraham Neyman, The Hebrew University of Jerusalem,
and State University of New York at Stony Brook
Prof. Philip J. Reny, University ofPitlsburgh
Prof. Reinhard Selten, Universitat Bonn
Prof. Tomas Sjostrom, Harvard University
Prof. Sylvain Sorin, Universite de Paris X, Nanterre,
and Ecole Normale Superieure, Paris
Prof. William Thomson, University of Rochester
Prof. Rajiv Vohra, Brown University, Providence
Table of Contents
Preface v
List of Authors ......................................... VI
Introduction .......................................... .
Sergiu Hart and Andreu Mas-Colell
Introductory Remarks 5
Robert J. Aumann
Part A Classical Cooperative Theory
Cooperative Theory of Bargaining I: Classical 9
William Thomson
Cooperative Theory of Bargaining II: Modem Development ........... 25
William Thomson
Classical Cooperative Theory I: Core-Like Concepts ................ 35
SergiuHart
Classical Cooperative Theory II: Value-Like Concepts ............... 43
Sergiu Hart
Cooperative Theory with Incomplete Information .................. 51
Beth Allen
Part B Non-Cooperative Approaches
Bargaining Games ....................................... 69
Andreu Mas-Colell
Two Lectures on Implementation Under Complete Information:
General Results and the Core ................................ 91
Philip J. Reny
VIII
Implementation Theory with Incomplete Information ................ 115
Beth Al/en
Coalitional Non-Cooperative Approaches to Cooperation ............. 127
Rajiv Vohra
Situation Approach to Cooperation ............................ 143
Joseph Greenberg
Part C Dynamic Models
Cooperation Through Repetition: Complete Information .............. 169
Sylvain Sorin
Communication, Correlation and Cooperation ..................... 199
Sylvain Sorin
Rationality and Bounded Rationality ........................... 219
Robert J. Aumann
Cooperation, Repetition, and Automata ......................... 233
Abraham Neyman
Learning in Games: Fictitious Play Dynamics ..................... 257
Vijay Krishna and Thomas Sjostrom
Evolution and Games: Replicator Dynamics ...................... 275
Vijay Krishna and Thomas Sjostrom
Part D Descriptive Theory
Descriptive Approaches to Cooperation ......................... 289
Reinhard Selten
Introduction
Sergiu Hart a and Andreu Mas-Colell b
a The Hebrew University of Jerusalem
b Harvard University and Universitat Pompeu Fabra, Barcelona
This book constitutes a systematic exposition of the various game theoretic
approaches to the issue of cooperation.
Game Theory is the study of decision making in multi-person situations, where
the outcome depends on everyone's choice. The goal of each participant is to
maximize his own utility, while taking into account that the other participants are
doing the same. In such interactive situations, cooperation between the agents
may lead to results that are better, for everyone, that the non-cooperative
outcomes. A simple - but extensively studied - example is the so-called
"Prisoners' Dilemma": Assume each on of the two players can ask a generous
donor either to give him I million dollars, or to give 4 million dollars to the other
player, the donor will carry out the instructions of both players (thus, for example,
if player I asks for $IM to himself and player 2 asks for $4M to the other, then
player I gets $5M and payer 2 gets nothing). Clearly, whatever the other player
does, it is strictly better for each player to ask for $IM to himself (more precisely,
it will always lead to an additional" 1M). This yields $IM for each; cooperation,
whereby each one asks for $4M to the other, would have yielded each $4M
instead! The Prisoner's Dilemma is by no means an artificial example. The
economic competition between firms exhibits similar phenomena: keeping a
commodity in short supply may be to the advantage of all producers; at the same
time, it may be better for any single producer to unilaterally increase his own
production.
The problems that need to be addressed are, first, whether cooperation can be
reached at all; second, by what procedures are agreements reached; and third,
which ones will be indeed attained. This volume will survey some of the
contributions of game theory to these questions, from its early traditional theories
to its current approaches.
Game theoretical approaches are usually classified as either "cooperative" or
" non-cooperative" . This should not be viewed as an exclusive division; these are
2
two ways of looking at the same problem. The Introductory Remarks of R. J.
Aumann that follow this Introduction address this point in some detail.
Part A, which opens this volume, surveys the classical cooperative approach.
This starts by assuming that binding agreements are possible, and it abstracts
away from the detailed bargaining procedures. The selection of the appropriate
cooperative outcome is usually based on a set of desired postulates or axioms,
which, when applied to a class of problems, characterize one or another solution
concept. Chapters 1 and 2 by W. Thomson cover the pure bargaining problems,
where only the grand coalition of all players can reach a beneficial agreement;
Chapter 1 deals with the classical approaches that originate with Nash's 1950
seminal paper, and Chapter 2 deals with recent axiomatizations based on internal
consistency properties (the" reduced game property"). Chapters 3 and 4, by S.
Hart, survey the general n-person problems where subcoalitions of players can
reach agreements as well, and this of course influences the final outcome. The
classical cooperative solution concepts that arise are grouped into "core-like"
notions and "value-like" notions. The former include the core, the stable sets of
von Neumann and Morgenstern, the bargaining set, the kernel and the nucleolus;
the latter include the Nash bargaining solution, the Shapley value and their many
extensions and generalizations. Chapter 5 by B. Allen deals with games of
incomplete information, i.e. , games where some of the participants may possess
private information not known to the others. Here, the questions of cooperation
are further complicated by the need to address the informational issues; how to
ensure that the players have incentive to reveal the appropriate information.
Part B is devoted to non-cooperative approaches, namely, non-cooperative
models that lead to cooperative solutions. One may start from a non-cooperative
bargaining model, like the Stahl-Rubinstein "alternating offers" procedure,
characterize its strategic equilibria, and relate the resulting outcomes to various
cooperative solutions. Or, one may start from a cooperative solution, and construct
games whose equilibria yield precisely this given solution. Either way, one
establishes connections between non-cooperative and cooperative setups, that
further strengthen and reinforce one another. In the literature, all this is usually
referred as "bargaining procedures", " non-cooperative foundations", or
"implementation" . The distinctions are not always clear , in particular since some
of the recent implementation literature is concerned with "natural" and "simple"
games. Chapter 6 by A. Mas-Colell covers bargaining procedures that lead to
value-like cooperative solutions, and the second part of Chapter 7 by P. Reny and
Chapter 8 by B. Allen, for the case of complete information and incomplete
information, respectively. Chapter 9 by R. Vohra discusses coalitional non
cooperative approaches -i.e., models where not only individuals, but also
coalitions may act strategically. Chapter 10 by J. Greenberg surveys the theory of
"social situations", which looks for a stable standards of behavior in general
coalitional interactions.
