The long run equilibrium in a game of "battle of the sexes"

Kandori,Mailath, and Rob (1993) considered a single, homogeneous population of agents playing a 2-player 2-action, coordination game and found that the risk-dominant equilibrium is the stochastically stable outcome. However, this robustness does not extend to the case where there are distinct populations of player 1's and player 2's. Here, with some restrictions on the adjustment dynamics other than the 'Darwinian property' we show that the risk-dominant equilibrium would be the stochastically stable outcome in the "battle of the sexes" game.