A Game-Theoretic Perspective on Coalition

The formation of coalitions to achieve both collaborative and competitive goals is a phenomenon we see all around us. The list is long and varied: production cartels, political lobbies, customs unions, environmental coalitions, and ethnic alliances are just a few everyday instances. Drawingupon and extending his inaugural Lipsey Lectures at the University of Essex, Debraj Ray looks at coalition formation from the perspective of game theory. How are agreements determined? Which coalitions will form? And are such agreements invariably efficient from a social perspective?Ray brings together developments in both cooperative and noncooperative game theory to study the analytics of coalition formation and binding agreements. This book concentrates on pure theory, but discusses several potential applications, such as oligopoly and the provision of public goods.

Preface	p. vii
Introduction	p. 1
The Setting	p. 7
Ingredients for a Theory of Agreements	p. 9
Introduction	p. 9
Characteristic Functions and Cooperative Games	p. 10
Two Approaches to Coalition Formation	p. 14
Farsightedness	p. 15
Two Examples	p. 16
Negotiations: One-Time or Continuing?	p. 20
Coalitions, Cooperation and Noncooperation	p. 23
Definitions and Notation	p. 23
Coalitional Equilibrium	p. 24
Partition Functions	p. 27
Extensions	p. 32
Summary	p. 33
A Bargaining Approach To Coalition Formation	p. 35
Irreversible Agreements	p. 37
Introduction	p. 37
A Model	p. 38
Equilibrium	p. 41
Rubinstein-Stahl Bargaining	p. 41
Baron-Ferejohn Bargaining	p. 46
Summary	p. 47
Irreversible Agreements: Symmetric Games	p. 53
Symmetric Partition Functions	p. 54
An Algorithm	p. 55
Connecting the Algorithm to Equilibria	p. 56
A Remark on Nontransferable Payoffs	p. 67
Proofs	p. 68
Summary	p. 80
Applications	p. 83
Cournot Oligopoly	p. 83
Public Goods	p. 87
Proofs	p. 93
Summary	p. 102
Irreversible Agreements: The General Case	p. 105
Characteristic Functions and the Core	p. 106
Equilibrium Response Vectors	p. 108
No-Delay Equilibrium	p. 111
Condition M, Payoffs and Coalition Structure	p. 113
More on Efficiency	p. 125
Externalities Revisited	p. 130
Alternative Protocols	p. 140
Proofs	p. 145
Summary	p. 152
A Framework for Reversible Agreements	p. 155
An Example	p. 156
A Proposal-Based Model of Coalition Formation	p. 158
Binding Agreements	p. 161
Strategies and Equilibrium	p. 164
Absorption and Efficiency	p. 166
Summary	p. 167
Reversible Agreements Without Externalities	p. 169
Two Examples	p. 170
Benignness	p. 172
Absorption and Efficiency	p. 173
Proofs	p. 178
Summary	p. 181
Reversible Agreements With Externalities	p. 183
The Baseline Model for Three-Player Games	p. 184
The Baseline Model for Four or More Players	p. 187
Superadditive Games	p. 192
Upfront Transfers and the Failure of Efficiency	p. 194
Summary	p. 198
A Blocking Approach to Coalition Formation	p. 211
Blocking	p. 213
The Core Revisited	p. 213
Farsightedness in Blocking	p. 215
A First Pass at Farsightedness	p. 215
Externalities and Farsightedness	p. 219
Summary	p. 220
Irreversible Commitments	p. 221
Equilibrium Binding Agreements	p. 222
Farsightedness and Prediction	p. 224
Inefficiency	p. 227
An Application to Political Party Formation	p. 230
Beyond Nested Deviations	p. 236
Summary	p. 241
The Blocking Approach in Real Time	p. 243
Introduction	p. 243
An Informal Description	p. 244
A Process of Coalition Formation	p. 246
Deterministic Equilibrium Processes	p. 250
Stochastic Equilibrium Processes	p. 261
Proofs	p. 271
Summary	p. 276
Directions	p. 287
Coalition Formation Without Unanimity	p. 288
Equity Within Coalitions	p. 289
Coalition Formation With Deliberate Exit	p. 292
Overlapping Coalitions	p. 294
Networks	p. 296
Coalition Formation With Nonbinding Agreements	p. 299
Incomplete Information	p. 301
Nontransferable Utility	p. 303
Axiomatic Approaches	p. 304
References	p. 307
Subject Index	p. 315
Author Index	p. 319
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A Game-Theoretic Perspective on Coalition Formation

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