Conformism across games

I study a population of conformist and rational players playing 2x2 games and calculate the locally stable fraction of conformists. I evaluate the fitness of each behavioral rule in all Nash Equilibria for each population share, discounting a cognitive cost to rational players. I find that conformists outperform rational players when in the minority because, in that case, the equilibrium is such that all strategies yield the same payoff. If the cognitive cost for rational players is sufficiently large, the only locally stable population composition is one in which each behavioral rule plays a different pure strategy in equilibrium.