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A Game-Theoretic Perspective on Coalition Formation$

Debraj Ray

Print publication date: 2007

Print ISBN-13: 9780199207954

Published to Oxford Scholarship Online: January 2008

DOI: 10.1093/acprof:oso/9780199207954.001.0001

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(p.vii) Preface

(p.vii) Preface

A Game-Theoretic Perspective on Coalition Formation
Oxford University Press

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 (p.viii) 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 (p.ix) tried to provide a self-contained and rigorous account, emphasizing the conceptual issues involved but without skimping on the necessary 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 (p.x) appearance in this book. Kyle Hyndman (as a graduate student at NYU) and I worked on another paper that plays a role in this book. I'm very grateful to both Kyle and Hideo for allowing me to use their research.

I want to record my gratitude to some of the other individuals whose research has (indirectly or directly) shaped my own interests. My somewhat narcissistic focus notwithstanding, several of them are mentioned in this book. It couldn't be otherwise. I especially have in mind Francis Bloch, Doug Bernheim, Joan Esteban, Armando Gomes, Peter Hammond, Matt Jackson, William Lucas, Roger Myerson, Ariel Rubinstein, David Schmeidler, Lloyd Shapley, Robert Wilson and John von Neumann. (I haven't met all these individuals, at least one of them for demographic reasons, but that doesn't matter.)

I thank Anja Sautmann for her careful reading of the manuscript and suggestions for better exposition. I am grateful to the London School of Economics, STICERD in particular, for hosting me during a wonderful sabbatical year in which the writing of this book began. I thank Luis Cabral and the Stern School at New York University for providing me with a hideaway: an office to retreat to once in a while to think about this book. And I warmly thank Sarah Caro and Carol Bestley at Oxford University Press: Sarah for her encouragement and good cheer through the inevitable delays in writing, Carol for her help with typesetting. While on this last subject, salaams are due to the great Donald Knuth. How would one write this book (or any book) without TEX?

No words suffice to thank my wife Nilita and my two children, Riyaaz and Zayira. All I can say is I've never believed you can write a good book when you're happy. I hope I'm wrong.