Introduction to the Theory of Cooperative Games 2nd ed - B. Peleg, P. Sudholter (Springer, 2007) WW.pdf - Najnowsze ksiazki(28) - walbo48

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VOLUME 34

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Bezalel Peleg · Peter Sudhölter

Introduction

to the Theory

of Cooperative

Games

Second Edition

123

Professor Bezalel Peleg

The Hebrew University of Jerusalem

Institute of Mathematics and

Center for the Study of Rationality

Givat-Ram, Feldman Building

91904 Jerusalem

Israel

pelegba@math.huji.ac.il

Professor Peter Sudhölter

University of Southern Denmark

Department of Business and Economics

Campusvej 55

5230 Odense M

Denmark

psu@sam.sdu.dk

Library of Congress Control Number: 2007931451

ISSN 0924-6126

ISBN 978-3-540-72944-0 Springer Berlin Heidelberg New York

ISBN 978-1-4020-7410-3 1st Edition Springer Berlin Heidelberg New York

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Preface to the Second Edition

The main purpose of the second edition is to enhance and expand the treat-

ment of games with nontransferable utility. The main changes are:

(1) Chapter 13 is devoted entirely to the Shapley value and the Harsanyi so-

lution. Section 13.4 is new and contains an axiomatization of the Harsanyi

solution.

(2) Chapter 14 deals exclusively with the consistent Shapley value. Sections

14.2 and 14.3 are new and present an existence proof for the consistent

value and an axiomatization of the consistent value respectively. Section

14.1, which was part of the old Chapter 13, deals with the consistent value

of polyhedral games.

(3) Chapter 15 is almost entirely new. It is mainly devoted to an investigation

of the Mas-Colell bargaining set of majority voting games. The existence of

the Mas-Colell set is investigated and various limit theorems are proved for

majority voting games. As a corollary of our results we show the existence

of a four-person super-additive and non-levelled (NTU) game whose Mas-

Colell bargaining set is empty.

(4) The treatment of the ordinal bargaining set was moved to the ﬁnal chap-

ter 16.

We also have used this opportunity to remove typos and inaccuracies from

Chapters 2 – 12 which otherwise remained intact.

We are indebted to all our readers who pointed out some typo. In particular we

thank Michael Maschler for his comments and Martina Bihn who personally

supported this edition.

June 2007

Bezalel Peleg and Peter Sudholter

Introduction to the Theory of Cooperative Games 2nd ed - B. Peleg, P. Sudholter (Springer, 2007) WW.pdf

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