Cooperative game theory deals with situations where objectives of participants of the game are partially cooperative and partially conflicting. It is in the interest of participants to cooperate in the sense of making binding agreements to achieve the maximum possible benefit. When it comes to distribution of benefit/payoffs, participants have conflicting interests. Such situations are usually modelled as cooperative games. While the book mainly discusses transferable utility games, there is also a brief analysis of non-transferable utility games. Alternative solution concepts to cooperative game theoretic problems are presented in chapters 1-9 and the next four chapters present issues related to computations of solutions discussed in the earlier chapters. The proofs of all results presented in the book are quite explicit. Additionally the mathematical techniques employed in demonstrating the results will be helpful to those who wish to learn application of mathematics for solving problems in game theory.
Daugiau informacijos
This book deals with situations where objectives of participants of the game are partially cooperative and partially conflicting.
| Preface |
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vii | |
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1 Introduction and Motivation |
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1.1 A brief historical sketch |
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2 | (4) |
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1.2 An overview of the chapters |
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6 | (13) |
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2 Basics and Preliminaries |
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19 | (1) |
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19 | (9) |
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2.3 Illustrative examples |
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28 | (3) |
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29 | (2) |
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3 The Core and Some Related Solutions |
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31 | (1) |
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3.2 Concepts and definitions |
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32 | (3) |
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3.3 The core and dominance core |
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35 | (4) |
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3.4 A condition for the core to be non-empty |
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39 | (4) |
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3.5 Reasonable set and core cover as core catchers |
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43 | (3) |
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3.6 Some variants of the core |
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46 | (2) |
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48 | (2) |
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50 | (7) |
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55 | (2) |
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4 The Bargaining Set, Kernel and Nucleolus |
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57 | (1) |
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58 | (4) |
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4.3 The kernel and pre-kernel |
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62 | (3) |
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4.4 The nucleolus, pre-nucleolus and proportional nucleolus |
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65 | (4) |
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69 | (5) |
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72 | (2) |
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74 | (1) |
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5.2 The formal framework: Definitions and axioms |
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75 | (3) |
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5.3 Characterization of the Shapley value |
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78 | (6) |
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5.4 A discussion on some alternative characterizations |
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84 | (1) |
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85 | (2) |
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87 | (5) |
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90 | (2) |
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6 The Core, Shapley Value and Weber Set |
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92 | (1) |
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6.2 The Weber set and core |
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93 | (2) |
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6.3 Some properties of a convex game |
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95 | (7) |
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6.4 Random order values and the random arrival rule |
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102 | (4) |
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105 | (1) |
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106 | (2) |
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108 | (6) |
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7.3 Measures of individual voting power |
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114 | (12) |
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7.4 Postulates for a measure of voting power |
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126 | (9) |
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7.5 Characterizations and interpretations |
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135 | (6) |
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7.6 Voting power with more than two alternatives |
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141 | (1) |
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7.7 Measures of power of collectivity |
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142 | (4) |
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146 | (4) |
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148 | (2) |
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150 | (1) |
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151 | (6) |
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8.3 The Gale---Shapley algorithm |
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157 | (1) |
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8.4 Many-to-one matchings |
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158 | (3) |
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8.5 Matchings when one side does not have preferences |
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161 | (6) |
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165 | (2) |
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9 Non-Transferable Utility Cooperative Games |
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167 | (1) |
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168 | (2) |
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9.3 Cooperative bargaining games |
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170 | (9) |
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179 | (5) |
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182 | (2) |
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184 | (1) |
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185 | (3) |
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10.3 Basic feasible solution |
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188 | (1) |
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10.4 Geometry of linear programs |
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189 | (2) |
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191 | (1) |
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10.6 The simplex algorithm |
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191 | (7) |
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198 | (1) |
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199 | (2) |
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201 | (5) |
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204 | (2) |
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11 Algorithmic Aspects of Cooperative Game Theory |
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206 | (6) |
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11.2 Computational intractibility |
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212 | (4) |
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11.3 Complexity of linear programming |
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216 | (2) |
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11.4 Computational issues in cooperative game theory |
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218 | (2) |
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11.5 The assignment problem |
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220 | (2) |
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11.6 Combinatorial optimization games |
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222 | (6) |
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226 | (2) |
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12 Weighted Majority Games |
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228 | (4) |
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12.2 Winning coalitions and swings for a player |
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232 | (2) |
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12.3 Dummy players and minimal winning coalitions |
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234 | (9) |
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13 Stable Matching Algorithm |
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13.1 Optimality considerations |
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243 | (2) |
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13.2 Stable matching polytope |
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245 | (2) |
| References |
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247 | (16) |
| Index |
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263 | |
Satya R. Chakravarty is a Professor of Economics at the Indian Statistical Institute, Kolkata. He received a bachelor degree in Statistics in 1976, a master degree in economics in 1977 and a doctorate in economics in 1981 from the Indian Statistical Institute. Professor Chakravarty worked as a Visiting Professor at the University of British Columbia, Canada (19845), the University of Karlsruhe, Germany (198890) with a grant from the German Research Foundation, the Bar Ilan University, Israel (1990, 2004, 2005, 2006 and 2010), the Kagawa University, Japan (19967 and 2000), the Paris School of Economics, Paris, France (19978) with a grant from the French Ministry of Education, the Chinese University of Hong Kong (1998), the Bocconi University, Milan, Italy (20023 and 20067) and the Yokohama National University, Japan (2009). Professor Chakravarty's main areas of interest are welfare economics, public economics, mathematical finance, industrial organization and game theory. His work spans theoretical, empirical and policy analysis. Manipushpak Mitra is a Professor of Economics at the Indian Statistical Institute, Kolkata, India. He has articles published in internationally known journals and edited books on cooperative game theory, mechanisms design in allocation problems and in market regulation problems, and industrial organization. Palash Sarkar is a computer scientist and is presently a Professor at the Indian Statistical Institute, Kolkata, India. He has published over one hundred articles in leading journals and conference proceedings. His research and teaching interests range over a wide variety of topics at the interface of computer science and mathematics.
