Counterfactuals with Latent Information

We describe a methodology for making counterfactual predictions when the information held by strategic agents is a latent parameter. The analyst observes behavior which is rationalized by a Bayesian model, in which agents maximize expected utility, given partial and differential information about payoff-relevant states of the world, represented as an information structure. A counterfactual prediction is desired about behavior in another strategic setting, under the hypothesis that the distribution of the state and agents’ information about the state are held fixed. When the data and the desired counterfactual prediction pertain to environments with finitely many states, players, and actions, there is a finite dimensional description of the sharp counterfactual prediction, even though the latent parameter, the information structure, is infinite dimensional.