  Discrete-time replicator map is a prototype of evolutionary selection game
dynamical models that have been very successful across disciplines in rendering
insights into the attainment of the equilibrium outcomes, like the Nash
equilibrium and the evolutionarily stable strategy. By construction, only the
fixed point solutions of the dynamics can possibly be interpreted as the
aforementioned game-theoretic solution concepts. Although more complex outcomes
like chaos are omnipresent in the nature, it is not known to which
game-theoretic solutions they correspond. Here we construct a game-theoretic
solution that is realized as the chaotic outcomes in the selection monotone
game dynamic. To this end, we invoke the idea that in a population game having
two-player--two-strategy one-shot interactions, it is the product of the
fitness and the heterogeneity (the probability of finding two individuals
playing different strategies in the infinitely large population) that is
optimized over the generations of the evolutionary process.
