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The Shapley Value
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 (ISBN-13: 9780511829727)

Composed in honour of the sixty-fifth birthday of Lloyd Shapley, this volume makes accessible the large body of work that has grown out of Shapley's seminal 1953 paper. Each of the twenty essays concerns some aspect of the Shapley value. Three of the chapters are reprints of the 'ancestral' papers: Chapter 2 is Shapley's original 1953 paper defining the value; Chapter 3 is the 1954 paper by Shapley and Shubik applying the value to voting models; and chapter 19 is Shapley's 1969 paper defining a value for games without transferable utility. The other seventeen chapters were contributed especially for this volume. The first chapter introduces the subject and the other essays in the volume, and contains a brief account of a few of Shapley's other major contributions to game theory. The other chapters cover the reformulations, interpretations and generalizations that have been inspired by the Shapley value, and its applications to the study of coalition formulation, to the organization of large markets, to problems of cost allocation, and to the study of games in which utility is not transferable.

Contents

Preface; 1. Introduction to the Shapley value Alvin E. Roth; Part I. Ancestral Papers: 2. A value for n-person games Lloyd S. Shapley; 3. A method for evaluating the distribution of power in a committee system Lloyd S. Shapley and Martin Shubik; Part II. Reformulation and Generalizations: 4. The expected utility of playing a game Alvin E. Roth; 5. The Shapley-Shubik and Banzhaf power indices as probabilities Philip D. Straffin, Jr.; 6. Weighted Shapley values Ehud Kalai and Dov Samet; 7. Probabilistic values for games Robert James Weber; 8. Combinatorial representations of the Shapley value based on average relative payoffs Uriel G. Rothblum; 9. The potential of the Shapley value Sergiu Hart and Andreu Mas-Colell; 10. Multilinear extensions of games Guillermo Owen; Part III. Coalitions: 11. Coalitional value Mordecai Kurz; 12. Endogenous formation of links between players and the coalitions: an application of the Shapley value Robert J. Aumann and Roger B. Myerson; Part IV. Large Games: 13. Values of large finite games Myrna Holtz Wooders and William R. Zame; 14. Payoffs in nonatomic economics: an axiomatic approach Pradeep Dubley and Abraham Neyman; 15. Values of smooth nonatomic games: the method of multilinear approximation Dov Monderer and Abraham Neyman; 16. Nondifferentiable TU markets: the value Jean-Fran├žois Mertens; Part V. Cost Allocation and Fair Division: 17. Individual contribution and just compensation H. P. Young; 18. The Aumann-Shapley prices: a survey Yair Tauman; Part VI. NTU Games: 19. Utility comparison and the theory of games Lloyd S. Shapley; 20. Paths leading to the Nash set Michael Maschler, Guillermo Owen and Bezalel Peleg.

Contributors

Alvin E. Roth, Lloyd S. Shapley, Martin Shubik, Philip D. Straffin, Jr., Ehud Kalai, Dov Samet, Robert James Weber, Uriel G. Rothblum, Sergiu Hart, Andreu Mas-Colell, Guillermo Owen, Mordecai Kurz, Robert J. Aumann, Roger B. Myerson, Myrna Holtz Wooders, William R. Zame, Pradeep Dubley, Abraham Neyman, Dov Monderer, Jean-Fran├žois Mertens, H. P. Young, Yair Tauman, Michael Maschler, Guillermo Owen, Bezalel Peleg

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