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.
