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Handbook of the Shapley Value

Edited by: Encarnación Algaba , Vito Fragnelli , Joaquín Sánchez-Soriano

Print publication date:  December  2019
Online publication date:  December  2019

Print ISBN: 9780815374688
eBook ISBN: 9781351241410
Adobe ISBN:

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Book description

Handbook of the Shapley Value contains 24 chapters and a foreword written by Alvin E. Roth, who was awarded the Nobel Memorial Prize in Economic Sciences jointly with Lloyd Shapley in 2012. The purpose of the book is to highlight a range of relevant insights into the Shapley value. Every chapter has been written to honor Lloyd Shapley, who introduced this fascinating value in 1953.

The first chapter, by William Thomson, places the Shapley value in the broader context of the theory of cooperative games, and briefly introduces each of the individual contributions to the volume. This is followed by a further contribution from the editors of the volume, which serves to introduce the more significant features of the Shapley value. The rest of the chapters in the book deal with different theoretical or applied aspects inspired by this interesting value and have been contributed specifically for this volume by leading experts in the area of Game Theory.

Chapters 3 through to 10 are more focused on theoretical aspects of the Shapley value, Chapters 11 to 15 are related to both theoretical and applied areas. Finally, from Chapter 16 to Chapter 24, more attention is paid to applications of the Shapley value to different problems encountered across a diverse range of fields. As expressed by William Thomson in the Introduction to the book, "The chapters contribute to the subject in several dimensions: Mathematical foundations; axiomatic foundations; computations; applications to special classes of games; power indices; applications to enriched classes of games; applications to concretely specified allocation problems: an ever-widening range, mapping allocation problems into games or implementation."

Nowadays, the Shapley value continues to be as appealing as when it was first introduced in 1953, or perhaps even more so now that its potential is supported by the quantity and quality of the available results. This volume collects a large amount of work that definitively demonstrates that the Shapley value provides answers and solutions to a wide variety of problems.

Table of contents

Prelims Download PDF
Chapter  1:  The Shapley Value, a Crown Jewel of Cooperative Game Theory Download PDF
Chapter  2:  The Shapley Value, a Paradigm of Fairness Download PDF
Chapter  3:  An Index of Unfairness Download PDF
Chapter  4:  The Shapley Value and Games with Hierarchies Download PDF
Chapter  5:  Values, Nullifiers and Dummifiers Download PDF
Chapter  6:  Games with Identical Shapley Values Download PDF
Chapter  7:  Several Bases of a Game Space and an Application to the Shapley Value Download PDF
Chapter  8:  Extensions of the Shapley Value for Environments with Externalities Download PDF
Chapter  9:  The Shapley Value and other Values Download PDF
Chapter  10:  Power and the Shapley Value Download PDF
Chapter  11:  Cost Allocation with Variable Production and the Shapley Value Download PDF
Chapter  12:  Pure Bargaining Problems and the Shapley Rule: A Survey Download PDF
Chapter  13:  The Shapley Value as a Tool for Evaluating Groups: Axiomatization and Applications Download PDF
Chapter  14:  A Value for j-Cooperative Games: Some Theoretical Aspects and Applications Download PDF
Chapter  15:  The Shapley Value of Corporation Tax Games with Dual Benefactors Download PDF
Chapter  16:  The Shapley Value in Telecommunication Problems Download PDF
Chapter  17:  The Shapley Rule for Loss Allocation in Energy Transmission Networks Download PDF
Chapter  18:  On Some Applications of the Shapley-Shubik Index for Finance and Politics Download PDF
Chapter  19:  The Shapley Value in the Queueing Problem Download PDF
Chapter  20:  Sometimes the Computation of the Shapley Value Is Simple Download PDF
Chapter  21:  Analysing ISIS Zerkani Network Using the Shapley Value Download PDF
Chapter  22:  A Fuzzy Approach to Some Shapley Value Problems in Group Decision Making Download PDF
Chapter  23:  Shapley Values for Two-Sided Assignment Markets Download PDF
Chapter  24:  The Shapley Value in Minimum Cost Spanning Tree Problems Download PDF
Index Download PDF
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