Equilibria of Replicator Dynamics in Quantum Games

Abstract

An evolutionarily stable strategy (ESS) was originally defined as a static concept but later given a dynamic characterization. A well known theorem in evolutionary game theory says that an ESS is an attractor of replicator dynamics but not every attractor is an ESS. We search for a dynamic characterization of ESSs in quantum games and find that in certain asymmetric bi-matrix games evolutionary stability of attractors can change as the game switches between its two forms, one classical and the other quantum.