Game Theoretical Foundations of Evolutionary Stability

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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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.

• dynamics
• foundation
• mathematics
• population
• stability
• strategy

• 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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