1st Edition
Handbook of the Shapley Value
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 1: The Shapley Value, a Crown Jewel of Cooperative Game Theory
William Thomson
Chapter 2: The Shapley Value, a Paradigm of Fairness
Encarnación Algaba, Vito Fragnelli, and Joaquin Sanchez-Soriano
Chapter 3: An Index of Unfairness
Victor H. Aguiar, Roland Pongou, Roberto Serrano, and Jean-Baptiste Tondji
Chapter 4: The Shapley Value and Games with Hierarchies
Encarnación Algaba and René van den Brink
Chapter 5: Values, Nullifiers and Dummifiers
J.M. Alonso-Meijide, J. Costa, and I. García-Jurado
Chapter 6: Games with Identical Shapley Values
Sylvain Béal, Mihai Manea, Eric Rémila, and Philippe Solal
Chapter 7: Several Bases of a Game Space and an Application to the
Shapley Value
Yukihiko Funaki and Koji Yokote
Chapter 8: Extensions of the Shapley value for Environments with Externalities
Inés Macho-Stadler, David Pérez-Castrillo, and David Wettstein
Chapter 9: The Shapley value and other values
Giulia Bernardi and Roberto Lucchetti
Chapter 10: Power and the Shapley Value
Hans Peters
Chapter 11: Cost Allocation with Variable Production and the Shapley Value
M. J. Albizuri, J. C. Santos, and J. M. Zarzuelo
Chapter 12: Pure Bargaining Problems and the Shapley Rule: A Survey
Francesc Carreras and Guillermo Owen
Chapter 13: The Shapley Value as a tool for evaluating groups: axiomatization and applications
Ramón Flores, Elisenda Molina, and Juan Tejada
Chapter 14: A value for j-cooperative games: some theoretical aspects and applications
Josep Freixas
Chapter 15: The Shapley value of corporation tax games with dual benefactors
Ana Meca, José A. García-Martínez, and Antonio J. Mayor-Serra
Chapter 16: The Shapley value in Telecommunication Problems
Joaquin Sanchez-Soriano
Chapter 17: The Shapley rule for loss allocation in energy transmission networks
Gustavo Bergantiños, Julio González-Díaz, and Ángel M. González-Rueda
Chapter 18: On Some Applications of the Shapley-Shubik Index for Finance and Politics
Cesarino Bertini, Gianfranco Gambarelli, Izabella Stach, and Maurizio Zola
Chapter 19: The Shapley Value in the Queueing Problem
Youngsub Chun
Chapter 20: Sometimes the Computation of the Shapley Value is Simple
Marco Dall’Aglio, Vito Fragnelli, and Stefano Moretti
Chapter 21: Analysing ISIS Zerkani Network using the Shapley Value
Herbert Hamers, Bart Husslage, and Roy Lindelauf
Chapter 22: A fuzzy approach to some Shapley value problems in group
decision making
Barbara Gladysz, Jacek Mercik, and David Ramsey
Chapter 23: Shapley values for two-sided assignment markets
Marina Núñez and Carles Rafels
Chapter 24: The Shapley value in minimum cost spanning tree problems
Christian Trudeau and Juan Vidal-Puga
Biography
Encarnación Algaba is Full Professor in the Department of Applied Mathematics II of the Advanced Engineering School at the University of Seville and research member in the Mathematics Research Institute of Seville University (IMUS). She also received her Ph.D. degree in Mathematical Sciences from the University of Seville. Her main research line is about Cooperative Games on Combinatorial Structures and their applications, with relevant contributions in the area. She is in the Editorial Board of Journal of Dynamics & Games. She has served as evaluator of projects at national and European level. She has organized diverse Streams in International Conferences and workshops on Game Theory. She has been invited speaker and guest researcher in various leading universities.
Vito Fragnelli is Associate Professor of Game Theory at University of Eastern Piedmont. His scientific contributions are on Cost allocation problems, Operations Research games, Bankruptcy games, Fair division, Electoral systems, Co-insurance games, Emergency management with more than 130 papers, more than 90 of which with international diffusion. He is in the Editorial Board of Operations Research and Decisions; he edited two books and five special issues related to different fields of Game Theory and Operations Research. He was Italian representative in the SING committee; he was responsible of several research projects; he organized several International Meetings and Workshops; he was invited speaker at various Workshops. He organizes and directs the series of Summer Schools "Game Theory and ..." from 2012 and was involved in several other Schools. He was visiting professor at several universities.
Joaquín Sánchez-Soriano is Full Professor of the Department of Statistics, Mathematics and Computer Science at the University Miguel Hernandez of Elche (UMH). He is a senior researcher of the Research Institute "Center of Operations Research (CIO)" of the UMH of which he was among the founders and was its director from 2004 to 2007. He received his Ph.D. degree in Mathematics from the University of Murcia. He has more than 80 scientific papers published in journals, books and proceedings. He is in the Editorial Board of the journals TOP and Journal of Dynamics & Games. His research interests are focused on game theory and its applications, scarce resource management, bankruptcy problems, cost/profit sharing in joint logistic projects and optimization of complex systems.
"This volume belongs to the series in Operations Research, and is devoted to the modern development and applications of the Shapley value—one of the most famous tools of the cooperative (non-antagonistic) game theory. [. . .] The book is innovative even for specialists in game theory and operations research, decision making and applied socio-economics research in various fields."
—Stan Lipovetsky, Technometrics, USA
"A nice contribution, offering researchers an up-to-date view of the many roads along which the interest for the Shapley value continues to develop, both in theory and in practice"
—Professor Fioravante Patrone, University of Genoa
"This handbook, written by the most prominent scientists in the field, offers an up-to-date survey on the Shapley value, a fundamental concept of game theory which have seen many applications in economics, operations research and artificial intelligence. A reference for both researchers and practitioners."
—Professor Michel Grabisch, Pantheon-Sorbonne University
"The Shapley value is alive and kicking: this book tells it all, from new axiomatic, mathematical, and computational insights, to applications in energy transmission, optimal queuing and terrorist networks."
—Professor Herve Moulin, University of Glasgow
"The Shapley Value is one of the most important contributions to Game Theory – a contribution that turned into a field of research and influenced multiple disciplines, including Economics, Business Administration, Political Science, Operations Research and Computer Science. Almost 70 years after its appearance, the field is still thriving.
The outstanding Handbook of the Shapley Value brings together a collection of contributions by leading experts from the field, with fresh and brilliant results about the tool and its applications. An essential reference for any researcher or student at advanced level, from any of the above mentioned disciplines, who wishes to be informed about this broadly applied concept and be inspired by it."
—Professor Eyal Winter, Lancaster University, Management School and Hebrew University, Center of the Study of Rationality
"Co-operative game theory - particularly its crown jewel, the Shapley value - is alive and kicking, as this remarkable collection of recent contributions shows."
—Professor Robert J. Aumann, The Hebrew University of Jerusalem
