Sophisticated play by idiosyncratic agents

Agents are drawn from a large population and matched to play a symmetric 2 times; 2 coordination game, the payoffs of which are perturbed by agent-specific heterogeneity. Individuals observe a (possibly sampled) history of play, which forms the initial hypothesis for an opponent's behaviour. Using this hypothesis as a starting point, the agents iteratively reason toward a Bayesian Nash equilibrium. When sampling is complete and the noise becomes vanishingly small, a single equilibrium is played almost all the time. A necessary and sufficient condition for selection, shown to be closely related (but not identical) to risk-dominance, is derived. When sampling is sufficiently incomplete, the risk-dominant equilibrium is played irrespective of the history observed.