Set Functions, Games and Capacities in Decision Making
Michel Grabisch has fully succeeded in transforming his deep knowledge of the field into a very rich and quite readable text.Professor Denis Bouyssou, Université Paris DauphineThis monograph provides a much-needed perspective on a rich collection of struc
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Michel Grabisch
Set Functions, Games and Capacities in Decision Making
Theory and Decision Library C
Game Theory, Social Choice, Decision Theory, and Optimization
Volume 46 Editors-in-Chief Hervé Moulin, Glasgow, Scotland, United Kingdom Hans Peters, Maastricht, The Netherlands Honorary Editor Stef H. Tijs, Tilburg, The Netherlands Editorial Board Jean-Jacques Herings, Maastricht, The Netherlands Matthew O. Jackson, Stanford, CA, USA Mamuro Kaneko, Tokyo, Japan Hans Keiding, Copenhagen, Denmark Bezalel Peleg, Jerusalem, Israel Clemens Puppe, Karlsruhe, Germany Alvin E. Roth, Stanford, CA, USA David Schmeidler, Tel Aviv, Israel Reinhard Selten, Bonn, Germany William Thomson, Rochester, NJ, USA Rakesh Vohra, Evanston, IL, USA Peter Wakker, Rotterdam, The Netherlands
More information about this series at http://www.springer.com/series/6618
Michel Grabisch
Set Functions, Games and Capacities in Decision Making
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Michel Grabisch Paris School of Economics Université Paris I Panthéon-Sorbonne Paris, France
ISSN 0924-6126 Theory and Decision Library C ISBN 978-3-319-30688-9 DOI 10.1007/978-3-319-30690-2
ISSN 2194-3044 (electronic) ISBN 978-3-319-30690-2 (eBook)
Library of Congress Control Number: 2016941938 © Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland
Foreword
The book by Michel Grabisch is about a fascinating mathematical object that has received different names and has been studied by different communities: set functions, capacities, pseudo-Boolean functions, and cooperative games, to mention just a few. Results on these objects were often proven several times, often under slightly different forms, in different communities. The book has two main parts. The first one is devoted to a detailed presentation of this mathematical object and its main properti
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