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Author: Lloyd S. Shapley
Publisher:
Published: 1952
Total Pages: 14
ISBN-13:
DOWNLOAD EBOOKIn the finite theory of von Neumann and Morgenstern difficulty in evaluation persists for the essential games, and for only those. In this paper a value is deduced for the essential case and a number of its elementary properties are examined. A set of three axioms, having simple intuitive interpretations, which suffice to determine the value uniquely serves as a starting point.
Author: Harold William Kuhn
Publisher: Princeton University Press
Published: 2016-03-02
Total Pages: 408
ISBN-13: 1400881978
DOWNLOAD EBOOKThese two new collections, numbers 28 and 29 respectively in the Annals of Mathematics Studies, continue the high standard set by the earlier Annals Studies 20 and 24 by bringing together important contributions to the theories of games and of nonlinear differential equations.
Author: Alvin E. Roth
Publisher: Cambridge University Press
Published: 1988-10-28
Total Pages: 342
ISBN-13: 1107717213
DOWNLOAD EBOOKComposed 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.
Author: Anatol Rapoport
Publisher: Courier Corporation
Published: 2013-06-17
Total Pages: 337
ISBN-13: 0486143678
DOWNLOAD EBOOKDIVSequel to Two-Person Game Theory introduces necessary mathematical notation (mainly set theory), presents basic concepts and models, and provides applications to social situations. /div
Author: Harold William Kuhn
Publisher: Princeton University Press
Published: 2020-11-10
Total Pages: 328
ISBN-13: 1400829151
DOWNLOAD EBOOKClassics in Game Theory assembles in one sourcebook the basic contributions to the field that followed on the publication of Theory of Games and Economic Behavior by John von Neumann and Oskar Morgenstern (Princeton, 1944). The theory of games, first given a rigorous formulation by von Neumann in a in 1928, is a subfield of mathematics and economics that models situations in which individuals compete and cooperate with each other. In the "heroic era" of research that began in the late 1940s, the foundations of the current theory were laid; it is these fundamental contributions that are collected in this volume. In the last fifteen years, game theory has become the dominant model in economic theory and has made significant contributions to political science, biology, and international security studies. The central role of game theory in economic theory was recognized by the award of the Nobel Memorial Prize in Economic Science in 1994 to the pioneering game theorists John C. Harsanyi, John Nash, and Reinhard Selten. The fundamental works for which they were honored are all included in this volume. Harold Kuhn, himself a major contributor to game theory for his reformulation of extensive games, has chosen eighteen essays that constitute the core of game theory as it exists today. Drawn from a variety of sources, they will be an invaluable tool for researchers in game theory and for a broad group of students of economics, political science, and biology.
Author: R. Henn
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 714
ISBN-13: 3642454941
DOWNLOAD EBOOKAuthor: Encarnación Algaba
Publisher: CRC Press
Published: 2019-12-06
Total Pages: 472
ISBN-13: 1351241397
DOWNLOAD EBOOKHandbook 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.
Author: Frank C. Zagare
Publisher: SAGE
Published: 1984-07
Total Pages: 100
ISBN-13: 9780803920507
DOWNLOAD EBOOKProfessor Zagare provides methods for analysing the structure of the game; considers zero and nonzero-sum games and the fundamental 'minimax theorem'; and investigates games with more than two players, including the possibility of coalitions between players.
Author: Robert J. Aumann
Publisher: Princeton University Press
Published: 2015-03-08
Total Pages: 348
ISBN-13: 1400867088
DOWNLOAD EBOOKThe "Shapley value" of a finite multi- person game associates to each player the amount he should be willing to pay to participate. This book extends the value concept to certain classes of non-atomic games, which are infinite-person games in which no individual player has significance. It is primarily a book of mathematics—a study of non-additive set functions and associated linear operators. Originally published in 1974. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author: Lloyd S. Shapley
Publisher:
Published: 1951
Total Pages:
ISBN-13:
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