Sophisticated Play by Idiosyncratic Agents

The payoffs of a symmetric 2x2 coordination game are perturbed by agent-specific heterogeneity. Individuals observe a (possibly sampled) history of play, which forms the initial hypothesis for an opponents behaviour. Seeding beliefs in this manner, they iteratively reason toward a Bayesian Nash equilibrium. Realised actions augment history and context evolves. Both risk-dominance and generalised risk-dominance determine equilibrium selection as heterogeneity vanishes. When sampling is sufficiently incomplete, the risk-dominant equilibrium is played irrespective of the history observed.