Learning from Others' Outcomes

June 2017
Alexander Wolitzky

I develop a simple model of social learning in which players observe others' outcomes but not their actions. There is a continuum of players, and each player chooses once-and-for-all between a safe action (which succeeds with known probability) and a risky action (which succeeds with fixed but unknown probability, depending on the state of the world). The actions also differ in their costs. Before choosing, a player observes the outcomes of K others. There is always an equilibrium in which success is more likely in the good state, and this regularity property holds whenever the initial generation of players is not well-informed about the state. In the case of an outcome-improving innovation (where the risky action may yield a higher probability of suceess), players take the correct action as K approaches infinity. In the case of a cost-saving innovation (where the risky action invles saving a cost but accepting a lower probability of sucess), inefficiency persists as K approaches infinity in any regular equilibrium. Whether inefficiency takes the form of under-adoption or over-adoption also depends on the nature of the innovation. Convergence of the population to equilibrium may be non-monotone.

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