The Shapley Value: Essays in Honor of Lloyd S. Shapley

doi:10.1017/CBO9780511528446

The Shapley Value

Essays in Honor of Lloyd S. Shapley

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Edited by Alvin E. Roth

Publisher:: Cambridge University Press
Online publication date:: October 2009
Print publication year:: 1988
Online ISBN:: 9780511528446
DOI:: https://doi.org/10.1017/CBO9780511528446

Subjects:: Economics, Microeconomics, Econometrics and Mathematical Methods

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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.

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The Shapley Value

Essays in Honor of Lloyd S. Shapley

This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-viii

1 - Introduction to the Shapley value
pp 1-28

I - Ancestral papers
pp 29-30

2 - A value for n-person games
pp 31-40

3 - A method for evaluating the distribution of power in a committee system
pp 41-48

II - Reformulations and generalizations
pp 49-50

4 - The expected utility of playing a game
pp 51-70

5 - The Shapley—Shubik and Banzhaf power indices as probabilities
pp 71-82

6 - Weighted Shapley values
pp 83-100

7 - Probabilistic values for games
pp 101-120

8 - Combinatorial representations of the Shapley value based on average relative payoffs
pp 121-126

9 - The potential of the Shapley value
pp 127-138

10 - Multilinear extensions of games
pp 139-152

III - Coalitions
pp 153-154

11 - Coalitional value
pp 155-174

12 - Endogenous formation of links between players and of coalitions: an application of the Shapley value
pp 175-192

IV - Large games
pp 193-194

13 - Values of large finite games
pp 195-206

14 - Payoffs in nonatomic economies: an axiomatic approach
pp 207-216

15 - Values of smooth nonatomic games: the method of multilinear approximation
pp 217-234

16 - Nondifferentiable TU markets: the value
pp 235-264

V - Cost allocation and fair division
pp 265-266

17 - Individual contribution and just compensation
pp 267-278

18 - The Aumann-Shapley prices: a survey
pp 279-304

VI - NTU games
pp 305-306

19 - Utility comparison and the theory of games
pp 307-320

20 - Paths leading to the Nash set
pp 321-330

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The Shapley Value

Essays in Honor of Lloyd S. Shapley

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