Game Theoretical Foundations of Evolutionary Stability

This book provides a systematic treatment of the mathematical aspects of evolutionary stability, which has become a central concept in theoretical biology and biomathematics in recent years. The purpose of the book is to create a general mathematical theory for evolutionary stability, which allows a unified treatment of the seemingly unrelated case by case studies currently dominating the literature on this subject. This goal is achieved by laying out the framework for a general game theoretical model containing the models considered in the literature as special cases. Furthermore, conditions for evolutionary stability and for a stricter stability concept are explored. Apart from the general discussion, these stability concepts are studied extensively in some important classes of evolutionary games, which have been investigated in the literature. The relation between evolutionary stability and the replicator dynamics is also discussed