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Game Theoretical Foundations of Evolutionary Stability

  • Book
  • © 1989

Overview

Authors:
  1. Immanuel M. Bomze

    1. Institut für Statistik und Informatik, Universität Wien, Vienna, Austria

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  2. Benedikt M. Pötscher

    1. Institut für Ökonometrie, Operations Research und Systemtheorie, TU Wien, Vienna, Austria

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    You can also search for this author in PubMed   Google Scholar

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

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Table of contents (8 chapters)

  1. Front Matter

    Pages N2-vi
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  2. Introduction

    • Immanuel M. Bomze, Benedikt M. Pötscher
    Pages 1-4

  3. Strategies and payoffs

    • Immanuel M. Bomze, Benedikt M. Pötscher
    Pages 5-23

  4. Evolutionary stability

    • Immanuel M. Bomze, Benedikt M. Pötscher
    Pages 25-43

  5. Global invasion barriers

    • Immanuel M. Bomze, Benedikt M. Pötscher
    Pages 45-59

  6. Games with bilinear average mean payoff

    • Immanuel M. Bomze, Benedikt M. Pötscher
    Pages 61-68

  7. Mixed strategies

    • Immanuel M. Bomze, Benedikt M. Pötscher
    Pages 69-82

  8. Population games

    • Immanuel M. Bomze, Benedikt M. Pötscher
    Pages 83-104

  9. Replicator dynamics

    • Immanuel M. Bomze, Benedikt M. Pötscher
    Pages 105-116

  10. Back Matter

    Pages 117-148
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Keywords

About this book

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.

Authors and Affiliations

  • Institut für Statistik und Informatik, Universität Wien, Vienna, Austria

    Immanuel M. Bomze

  • Institut für Ökonometrie, Operations Research und Systemtheorie, TU Wien, Vienna, Austria

    Benedikt M. Pötscher

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