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Game Theoretical Foundations of Evolutionary Stability

  • Immanuel M. Bomze
  • Benedikt M. Pötscher

Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 324)

Table of contents

  1. Front Matter
    Pages N2-vi
  2. Immanuel M. Bomze, Benedikt M. Pötscher
    Pages 1-4
  3. Immanuel M. Bomze, Benedikt M. Pötscher
    Pages 5-23
  4. Immanuel M. Bomze, Benedikt M. Pötscher
    Pages 25-43
  5. Immanuel M. Bomze, Benedikt M. Pötscher
    Pages 45-59
  6. Immanuel M. Bomze, Benedikt M. Pötscher
    Pages 61-68
  7. Immanuel M. Bomze, Benedikt M. Pötscher
    Pages 69-82
  8. Immanuel M. Bomze, Benedikt M. Pötscher
    Pages 83-104
  9. Immanuel M. Bomze, Benedikt M. Pötscher
    Pages 105-116
  10. Back Matter
    Pages 117-148

About this book

Introduction

These Lecture Notes arose from discussions we had over a working paper written by the first author in fall 1987. We decided then to write a short paper about the basic structure of evolutionary stability and found ourselves ending up with a book manuscript. Parts of the material contained herein were presented in a seminar at the Department of Mathematics at the University of Vienna, as well as at a workshop on evolutionary game theory in Bielefeld. The final version of the manuscript has certainly benefitted from critical comments and suggestions by the participants of both the seminar and the workshop. Thanks are also due to S. Bomze-de Barba, R. Burger, G. Danninger, J. Hofbauer, R. Selten, K. Sigmund, G. Stiastny and F. Weising. The co-operation of W. Muller from Springer Verlag, Heidelberg, is gratefully acknowledged. Vienna, November 1988 Immanuel M. Bomze Benedikt M. Potscher III Contents 1. Introduction 1 2. Strategies and payoffs 5 2. 1. A general setting for evolutionary game theory 6 2. 2. Mixed strategies and population games 8 2. 3. Finite number of strategies . . . . . 13 2. 4. Infinitely many (pure) strategies 15 2. 5. Structured populations: asymmetric contests and multitype games 17 2. 6. Additional remarks . . . . . . . . . . . . . . . . . . . . . 21 3. Evolutionary stability 25 3. 1. Definition of evolutionary stability 25 3. 2. Evolutionary stability and solution concepts in classical game theory 30 3. 3. Conditions for evolutionary stability based on the normal cone 31 3. 4.

Keywords

dynamics foundation mathematics population stability strategy

Authors and affiliations

  • Immanuel M. Bomze
    • 1
  • Benedikt M. Pötscher
    • 2
  1. 1.Institut für Statistik und InformatikUniversität WienViennaAustria
  2. 2.Institut für Ökonometrie, Operations Research und SystemtheorieTU WienViennaAustria

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-45660-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 1989
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-50766-6
  • Online ISBN 978-3-642-45660-2
  • Series Print ISSN 0075-8442
  • Series Online ISSN 2196-9957
  • Buy this book on publisher's site
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