An Introduction to Allocation Rules
This book focuses on analyzing cost and surplus sharing problems in a systematic fashion. It offers an in-depth analysis of various types of rules for allocating a common monetary value (cost) between members of a group or network – e.g. individuals, firm
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Jens Leth Hougaard
An Introduction to Allocation Rules
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Prof. Dr. Jens Leth Hougaard Department of Food and Resource Economics University of Copenhagen Rolighedsvej 25 1958 Frederiksberg C Denmark [email protected]
ISBN 978-3-642-01827-5 e-ISBN 978-3-642-01828-2 DOI 10.1007/978-3-642-01828-2 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2009928107 c Springer-Verlag Berlin Heidelberg 2009 ° This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, 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. Cover design: WMXDesign GmbH Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To Pernille and Ida
Preface
This book contains a systematic analysis of allocation rules related to cost and surplus sharing problems. Broadly speaking, it examines various types of rules for allocating a common monetary value (cost) between individual members of a group (or network) when the characteristics of the problem are somehow objectively given. Without being an advanced text it offers a comprehensive mathematical analysis of a series of well-known allocation rules. The aim is to provide an overview and synthesis of current knowledge concerning cost and surplus sharing methods. The text is accompanied by a description of several practical cases and numerous examples designed to make the theoretical results easily comprehensible for both students and practitioners alike. The book is based on a series of lectures given at the University of Copenhagen and Copenhagen Business School for graduate students joining the math/econ program. I am indebted to numerous colleagues, conference participants and students who during the years have shaped my approach and interests through collaboration, comments and questions that were greatly inspiring. In particular, I would like to thank Hans Keiding, Maurice Koster, Tobias Markeprand, Juan D. Moreno-Ternero, Herv´e Moulin, Bezalel Peleg, Lars ThorlundPetersen, Jørgen Tind, Mich Tvede and Lars Peter Østerdal.
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Contents
1
Motivation and a Few Cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Motivation . . . . . .
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