Evolutionarily stable strategy in asymmetric games: Dynamical and information-theoretical perspectives

Various extensions of evolutionarily stable strategy (ESS)—the central concept in evolutionary game theory—defined for asymmetric games differ in how they correspond to fixed points of the replicator equation, which models evolutionary dynamics of frequencies of strategies in a population. Along with reporting interesting new results, this paper is partially intended as a contextual mini-review of some of the most important definitions of ESS in asymmetric games. We present the definitions coherently and scrutinize them closely while establishing equivalences—some of them hitherto unreported—between them. Since it is desirable that a definition of ESS should correspond to asymptotically stable fixed points of the replicator dynamics, we bring forward the connections between various definitions and their dynamical stabilities. Furthermore, in this context, we use the principle of relative entropy minimization to gain information-theoretic insights into the concept of ESS, thereby establishing a threefold connection between game theory, dynamical system theory, and information theory.