Publication Date: January 2019
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. A counterfactual prediction is desired about behavior in another strategic setting, under the hypothesis that the distribution of 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 type space, is inﬁnite dimensional.
Keywords: Counterfactuals, Bayes correlated equilibrium, Information structure, Type space, Linear program
JEL Classification Codes: C72, D44, D82, D83