Learning from Others' Outcomes

I develop a simple model of social learning in which players observe others' outcomes but not their actions. A continuum of players arrives continuously over time, 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 earlier players. There is always an equilibrium in which success is more likely in the good state, and this alignment 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 success), players take the correct action as K → ∞. In the case of a cost-saving innovation (where the risky action involves saving a cost but accepting a lower probability of success), inefficiency persists as K → ∞ in any aligned 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.