  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.
