Inferring Beliefs from Actions

We address the question to which degree the private information of a decision maker is revealed through his action, in an environment with compact metrizable state and action space. We show that the decision maker's optimal action reveals his posterior distribution for a generic set of continuous utility functions if and only if the set of actions contains no isolated points. We apply the generic result to fully strategic, repeated interaction in social networks without payoff externalities. We establish that if the action set contains no isolated points, then perfect information aggregation holds in equilibrium for generic continuous utility functions, in any strongly connected social network