A Game-Theoretic Perspective on Coalition Formation the Lipsey Lectures

A Game-Theoretic Perspective on Coalition Formation The Lipsey Lectures The Lipsey Lectures, delivered every two years, offer a forum for leading scholars to reflect upon their research. Lipsey lecturers, cho- sen from among professional economists approaching the height of their careers, will have recently made key contributions at the frontier of any field of theoretical or applied economics. The em- phasis is on novelty, originality and relevance to an understanding of the modern world. It is expected, therefore, that each volume in the series will become a core source for graduate students and an inspiration for further research. The lecture series is named after Richard G. Lipsey, the founding professor of economics at the University of Essex. Professor Lipsey instilled at Essex a commitment to explore challenging issues in applied economics, grounded in formal economic theory, the predictions of which were to be subjected to rigorous testing, thereby illuminating important policy debates. This approach remains central to economic research at Essex and an inspiration for members of the Department of Economics. In recognition of Richard Lipsey’s early vision for the Department, and in continued pursuit of its mission of academic excellence, the Department of Economics is pleased to organize the lecture series, with support from Oxford University Press. A Game-Theoretic Perspective on Coalition Formation DEBRAJ RAY 1 3 Great Clarendon Street, Oxford, OX2 6DP, United Kingdom Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries © Debraj Ray2007 The moral rights of the author have been asserted First Edition published in 2007 Impression: 3 Some rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, for commercial purposes, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by licence or under terms agreed with the appropriate reprographics rights organization. This is an open access publication, available online and distributed under the terms of a Creative Commons Attribution – Non Commercial – No Derivatives 4.0 International licence (CC BY-NC-ND 4.0), a copy of which is available at http://creativecommons.org/licenses/by-nc-nd/4.0/. Enquiries concerning reproduction outside the scope of this licence should be sent to the Rights Department, Oxford University Press, at the address above. Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America British Library Cataloguing in Publication Data Data available Library of Congress Control Number: 2015939040 ISBN 978–0–19––4920795 Typeset by Author Using Printed in Great Britain on acid-free paper by Biddles Ltd., King+s Lynn, Norfolk Links to third party websites are provided by Oxford in good faith and for information only. Oxford disclaims any responsibility for the materials contained in any third party website referenced in this work. To Rahul Wahi (1956–2006) This page intentionally left blank Preface This monograph describes a theory of coalition formation. I would like it to serve as an open invitation for young theorists to enter this fascinating and important line of inquiry. My own account of this theory is naturally selective and largely based on research that I have conducted, so I cannot hope to have been comprehensive in any way. I am uneasily aware, for instance, of the vast stylistic and expositional differences between this work and my earlier book, Development Economics. Individuals seeking the same degree of coverage will certainly not find it here. Yet I hope that in some way this short book will have enough in it to attract, provoke, and even be occasionally useful. The basic objective of this book is easy enough to describe. I outline a theory of coalition formation, a process by which individual agents come together to achieve collaborative though occasionally compromised goals. The underlying premise of the theory is simple yet compelling. Left to their own devices, individuals will generally engage in actions that fail to adequately internalize the negative externalities imposed on one another. The explicit agreement to form a coalition may be viewed as an agreement to be jointly sensitive to those externalities, and to take actions to try and lower them. A theory of coalition formation that starts from this premise can proceed along one of two broad lines. First, the grouping of individuals into coalitions may simply represent a certain degree of consensus, with no binding agreements involved. In such a line of inquiry, the principal focus of attention would be the actual strategies that sustain such agreements, as well as the “best” agreements sustainable in nonbinding play. A leading framework viii Preface for such a study is the theory of dynamic games (especially repeated games). A second view, central to the tradition of cooperative game theory, is that an agreement, once made, is binding. Just how it is binding is not really up for discussion. It may be that there are enough strategic checks and balances (in repeated play, for instance) to keep the agreement together. Or perhaps social conventions and the threat of social sanctions uphold an agreement. Or perhaps an agreement can be legally enforced in ways that — while possibly fascinating to a lawyer — are not of great interest to the game theorist. The focus is on the agreements themselves, and especially on the process by which those agreements are reached, as opposed to the way in which those agreements are implemented. Obviously, the two views are complementary. They study two distinct aspects of the theory of coalition formation. This book is a contribution to the second view. In this sense, then, my questions belong to the old-fashioned, classical lineage of cooperative game theory. But the approach is very different. While agreements once written are presumed to be binding, the process of achieving those negotiations is assuredly not. Proposal and counterproposal, acceptance and rejection, objection and agreement, sidepayments and subcoalitions, all play a role in the strategic negotiations that precede the writing of agreements. Thus much of the material in this book represents a marriage of noncooperative game theory and its more traditional, cooperative counterpart, and I hope — as the title suggests — that it will provide a useful game- theoretic perspective on coalition formation. As we shall see, the process of arriving at an agreement is far from trouble-free, even in a world of perfect and complete information. While there are clear incentives for all parties to come together in the interests of minimizing externalities and thereby achieving efficiency, there is also room for subterfuge and sabotage, for the formation of intermediate coalitions that may profit from an inefficient situation. These possibilities influence a small set of questions that run through the book: What agreements will be written? Which coalitions will form? Are binding agreements invariably efficient? This book is a substantial outgrowth of the inaugural Richard Lipsey lectures given at the University of Essex in December 2004. I have Preface ix tried to provide a self-contained and rigorous account, emphasizing the conceptual issues involved but without skimping on the neces- sary formalism. With interest in economic theory at an all-time low (for good reason, some would say), I don’t expect the battle-scarred veteran economist to give the more difficult arguments more than a cursory once-over. But I do hope that the younger, more open, non-bottom-line oriented generation of economic theorists will read some of this material with interest, with an eye to taking the story much further, and in many more imaginative directions than I could ever expect to address. I am immensely grateful to Abhinay Muthoo, who — as Department Chair at the University of Essex — first invited me to give these lectures, and then (before I could react swiftly enough) talked me into writing this book. Thank you Abhinay, I would have never done it otherwise. I am also very grateful to Venkataraman Bhaskar and Sanjeev Goyal, now ex-Essex but certainly leading figures in the Economics Department when they were there, who offered constant encouragement and support when I dithered with the choice of subject matter for the Lectures. Yes, you can pull off a public lecture on game theory, they said. I hope they were right. My greatest intellectual debt is to Rajiv Vohra. He and I have been thinking together about the issues in this book since 1988. Half the book is based on my joint work with him and while he graciously encouraged me to write this monograph on my own, it is only right that I acknowledge, here in unambiguous print, that I view him as possessing the moral equivalent of full coauthorship rights (and obligations in case of any errors). I want to especially mention three other influences on this book: Kalyan Chatterjee, Bhaskar Dutta and Kunal Sengupta. Together we wrote a four-author paper that I am proud of and that served as foundation — implicit or explicit — for many of the ideas presented here. It was a great intellectual experience (and better yet, fun) to work on these ideas together at the Indian Statistical Institute in the 1980s, where Bhaskar, Kunal and I were at the time, with Kalyan a regular visitor. Two other coauthors figure prominently in this book: Hideo Konishi and Kyle Hyndman. I met Hideo when he visited Boston University in 1997. It didn’t take long to see that we had several interests in common, and we worked together on a paper that makes an x Preface appearance in this book.

Load more