We study stochastically stable behaviour in 2 x 2 coordination games where the risk-dominant equilibrium differs from the Pareto-efficient equilibrium. Individuals are randomly matched to another individual in the population (with full support) and they choose strategies by imitating the most successful individual they observe. So, while individuals interact globally, their observation, as determined by their social network, may be local. In the benchmark model, all individuals observe each other, and hence, an individual imitates the strategy of the most successful individual in the entire population; here, the stochastically stable outcome corresponds to the situation where everyone coordinates on the Pareto-efficient equilibrium. While this outcome is always stochastically stable even when observability is incomplete, the state where everyone plays the action of the risk-dominant equilibrium may be stochastically stable as well. Reasonably tight sufficient conditions for unique stochastic stability of the state where all individuals play the Pareto-efficient equilibrium strategy include each individual observing at least four other individuals or when each individual observes the same number of other individuals.
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