Observational learning in large anonymous games

I present a model of observational learning with payoff interdependence. Agents, ordered in a sequence, receive private signals about an uncertain state of the world and sample previous actions. Unlike in standard models of observational learning, an agent's payoff depends both on the state and on the actions of others. Agents want both to learn the state and to anticipate others' play. As the sample of previous actions provides information on both dimensions, standard informational externalities are confounded with payoff externalities. I show that in spite of these confounding factors, when signals are of unbounded strength there is learning in a strong sense: agents' actions are ex-post optimal given both the state of the world and others' actions. With bounded signals, actions approach ex-post optimality as the signal structure becomes more informative.