Game theory and evolution: finite size and absolute fitness measures

This article is concerned with the characterization and existence of evolutionarily stable strategies (ESS) in Games against Nature, a class of models described by finite size populations and absolute fitness measures. We address these problems in terms of a new formalism which revolves around the concept evolutionary entropy, a measure of the diversity of options associated with a strategy – pure strategies have zero entropy, mixed strategies positive entropy. We invoke this formalism to show that ESS are characterized by extremal states of entropy. We illustrate this characterization of ESS by an analysis of the evolution of the sex ratio and the evolution of seed size.