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Game Theoretical Foundations of Evolutionary Stability Immanuel M. Bomze

Game Theoretical Foundations of Evolutionary Stability By Immanuel M. Bomze

Game Theoretical Foundations of Evolutionary Stability by Immanuel M. Bomze


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Summary

A general setting for evolutionary game theory 6 2. Finite number of strategies . . . . . Additional remarks . . . . . . . . . . . . . . . . . . . . . Evolutionary stability and solution concepts in classical game theory 30 3. Conditions for evolutionary stability based on the normal cone 31 3.

Game Theoretical Foundations of Evolutionary Stability Summary

Game Theoretical Foundations of Evolutionary Stability by Immanuel M. Bomze

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.

Table of Contents

Contents: Introduction.- Strategies and payoffs.- Evolutionary stability.- Global invasion barriers.- Games with bilinear average mean payoff.- Mixed strategies.- Population games.- Replicator dynamics.- Appendix.- References.- List of symbols.

Additional information

NLS9783540507666
9783540507666
3540507663
Game Theoretical Foundations of Evolutionary Stability by Immanuel M. Bomze
New
Paperback
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
1989-02-22
145
N/A
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