ABSTRACT

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.

chapter Chapter 1|15 pages

The Shapley Value, a Crown Jewel of Cooperative Game Theory

ByWilliam Thomson

chapter Chapter 2|13 pages

The Shapley Value, a Paradigm of Fairness

ByEncarnación Algaba, Vito Fragnelli, Joaquín Sánchez-Soriano

chapter Chapter 3|18 pages

An Index of Unfairness

ByVictor H. Aguiar, Roland Pongou, Roberto Serrano, Jean-Baptiste Tondji

chapter Chapter 4|26 pages

The Shapley Value and Games with Hierarchies

ByEncarnación Algaba, René van den Brink

chapter Chapter 5|18 pages

Values, Nullifiers and Dummifiers

ByJosé María Alonso-Meijide, Julián Costa, Ignacio García-Jurado

chapter Chapter 6|17 pages

Games with Identical Shapley Values

BySylvain Béal, Mihai Manea, Eric Rémila, Philippe Solal

chapter Chapter 7|20 pages

Several Bases of a Game Space and an Application to the Shapley Value

ByYukihiko Funaki, Koji Yokote

chapter Chapter 8|25 pages

Extensions of the Shapley Value for Environments with Externalities

ByInés Macho-Stadler, David Pérez-Castrillo, David Wettstein

chapter Chapter 9|23 pages

The Shapley Value and other Values

ByGiulia Bernardi, Roberto Lucchetti

chapter Chapter 10|18 pages

Power and the Shapley Value

ByHans Peters

chapter Chapter 11|18 pages

Cost Allocation with Variable Production and the Shapley Value

ByMiren Josune Albizuri, Juan Carlos Santos, José Manuel Zarzuelo

chapter Chapter 12|36 pages

Pure Bargaining Problems and the Shapley Rule: A Survey

ByFrancesc Carreras, Guillermo Owen

chapter Chapter 13|25 pages

The Shapley Value as a Tool for Evaluating Groups: Axiomatization and Applications

ByRamón Flores, Elisenda Molina, Juan Tejada

chapter Chapter 14|31 pages

A Value for j-Cooperative Games: Some Theoretical Aspects and Applications

ByJosep Freixas

chapter Chapter 15|18 pages

The Shapley Value of Corporation Tax Games with Dual Benefactors

ByAna Meca, José Antonio García-Martínez, Antonio J. Mayor-Serra

chapter Chapter 16|37 pages

The Shapley Value in Telecommunication Problems

ByJoaquín Sánchez-Soriano

chapter Chapter 17|24 pages

The Shapley Rule for Loss Allocation in Energy Transmission Networks

ByGustavo Bergantiños, Julio González-Díaz, Ángel M. González-Rueda

chapter Chapter 18|26 pages

On Some Applications of the Shapley-Shubik Index for Finance and Politics

ByCesarino Bertini, Gianfranco Gambarelli, Izabella Stach, Maurizio Zola

chapter Chapter 19|23 pages

The Shapley Value in the Queueing Problem

ByYoungsub Chun

chapter Chapter 20|21 pages

Sometimes the Computation of the Shapley Value Is Simple

ByMarco Dall’Aglio, Vito Fragnelli, Stefano Moretti

chapter Chapter 21|18 pages

Analysing ISIS Zerkani Network Using the Shapley Value

ByHerbert Hamers, Bart Husslage, Roy Lindelauf

chapter Chapter 22|31 pages

A Fuzzy Approach to Some Shapley Value Problems in Group Decision Making

ByBarbara Gladysz, Jacek Mercik, David Ramsey

chapter Chapter 23|21 pages

Shapley Values for Two-Sided Assignment Markets

ByMarina Núñez, Carles Rafels

chapter Chapter 24|23 pages

The Shapley Value in Minimum Cost Spanning Tree Problems

ByChristian Trudeau, Juan Vidal-Puga