  We propose a new evolutionary dynamics for population games with a discrete
strategy set, inspired by the theory of optimal transport and Mean field games.
The dynamics can be described as a Fokker-Planck equation on a discrete
strategy set. The derived dynamics is the gradient flow of a free energy and
the transition density equation of a Markov process. Such process provides
models for the behavior of the individual players in population, which is
myopic, greedy and irrational. The stability of the dynamics is governed by
optimal transport metric, entropy and Fisher information.
