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Sven von Widekind

Evolution of Non-Expected Utility Preferences

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Dr. Sven von Widekind Institute of Mathematical Economics Bielefeld University Universitätsstraße 25 33615 Bielefeld Germany sven.von [email protected]

ISBN 978-3-540-76841-8

e-ISBN 978-3-540-76845-6

DOI 10.1007/978-3-540-76845-6 Lecture Notes in Economics and Mathematical Systems ISSN 0075-8442 Library of Congress Control Number: 2007941068 © 2008 Springer-Verlag Berlin Heidelberg 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. Production: LE-TEX Jelonek, Schmidt & Vöckler GbR, Leipzig Cover design: WMX Design GmbH, Heidelberg Printed on acid-free paper 987654321 springer.com

“It is clear that Economics if it is to be a science at all, must be a mathematical one.” (W. St. Jevons, 1871)

Preface

This monograph has been prepared as my doctoral thesis in Economics at the Institute of Mathematical Economics (IMW), Bielefeld University, Germany. The dissertation has been accepted by the Department of Business Administration and Economics (Examiners: Prof. Dr. Walter Trockel and Prof. em. Dr. Joachim Rosenm¨ uller). It has successfully been defended on June 13, 2007. With this work I strive to complement the recent literature on the evolution of preferences by investigating the non-expected utility case. I have divided the book into seven chapters. An introduction to the topic is given in Chap. 1. In the following Chap. 2 the main model is presented, followed by an analysis of existence issues concerning stable populations. This chapter is preceded by a section reviewing some basic concepts from the theory of choice and game theory. Although I assume that most readers are familiar with these ideas they are recalled primarily in order to assure a common understanding of the terminology. Chap. 3 discusses the results from the previous chapter by means of some examples. A study of the performance of non-expected utility preferences compared to expected utility ones is the subject of Chap. 4. The impact of an important variant of the type space is investigated in Chap. 5. After this, in Chap. 6, I provide an outlook to further possible modifications of the model. Eventually, I summarize and discuss all main findings in Chap. 7. The preparation of