Author: WILLIAM FRANKLIN LUCASPublisher:
ISBN:
Category : Games of strategy (Mathematics)
Languages : en
Pages : 108
Book Description
ON SOLUTIONS TO N-PERSON GAMES IN PARTITION FUNCTION FORM..
Author: WILLIAM FRANKLIN LUCASPublisher:
ISBN:
Category : Games of strategy (Mathematics)
Languages : en
Pages : 108
Book Description
Naval Research Logistics Quarterly
Author: Partition Function Form Games
Author: László Á. KóczyPublisher: Springer
ISBN: 3319698419
Category : Mathematics
Languages : en
Pages : 320
Book Description
This book presents a systematic overview on partition function form games: a game form in cooperative game theory to integrate externalities for various applications. Cooperative game theory has been immensely useful to study a wide range of issues, but the standard approaches ignore the side effects of cooperation. Recently interest shifted to problems where externalities play the main roles such as models of cooperation in market competition or the shared use of public resources. Such problems require richer models that can explicitly evaluate the side-effects of cooperation. In partition function form games the value of cooperation depends on the outsiders' actions. A recent surge of interest driven by applications has made results very fragmented. This book offers an accessible, yet comprehensive and systematic study of properties, solutions and applications of partition function games surveying both theoretical results and their applications. It assembles a survey of existing research and smaller original results as well as original interpretations and comparisons. The book is self-contained and accessible for readers with little or no knowledge of cooperative game theory.
Technical Abstract Bulletin
Author: N-Person Game Theory
Author: Anatol RapoportPublisher: Courier Corporation
ISBN: 0486143678
Category : Mathematics
Languages : en
Pages : 337
Book Description
DIVSequel to Two-Person Game Theory introduces necessary mathematical notation (mainly set theory), presents basic concepts and models, and provides applications to social situations. /div
Game Theory and Its Applications
Author: William F. LucasPublisher: American Mathematical Soc.
ISBN: 9780821867334
Category : Mathematics
Languages : en
Pages : 138
Book Description
Handbook of the Shapley Value
Author: Encarnación AlgabaPublisher: CRC Press
ISBN: 1351241397
Category : Business & Economics
Languages : en
Pages : 507
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.
NAVAL RESEARCH LOGISTICS QUARTERLY VOL. 13 NO. 1
Author: Collected Papers
Author: Robert J. AumannPublisher: MIT Press
ISBN: 9780262011556
Category : Business & Economics
Languages : en
Pages : 818
Book Description
Robert Aumann's career in game theory has spanned over research - from his doctoral dissertation in 1956 to papers as recent as January 1995. Threaded through all of Aumann's work (symbolized in his thesis on knots) is the study of relationships between different ideas, between different phenomena, and between ideas and phenomena. "When you look closely at one scientific idea", writes Aumann, "you find it hitched to all others. It is these hitches that I have tried to study". The papers are organized in several categories: general, knot theory, decision theory (utility and subjective probability), strategic games, coalitional games, and mathematical methods. Aumann has written an introduction to each of these groups that briefly describes the content and background of each paper, including the motivation and the research process, and relates it to other work in the collection and to work by others. There is also a citation index that allows readers to trace the considerable body of literature which cites Aumann's own work.
Mathematical Methods of Game and Economic Theory
Author: J.-P. AubinPublisher: Newnes
ISBN: 0080875289
Category : Mathematics
Languages : en
Pages : 653
Book Description
This book presents a unified treatment of optimization theory, game theory and a general equilibrium theory in economics in the framework of nonlinear functional analysis. It not only provides powerful and versatile tools for solving specific problems in economics and the social sciences but also serves as a unifying theme in the mathematical theory of these subjects as well as in pure mathematics itself.