Publication Date: January 2019
Revision Date: February 2019March 2021
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.
Keywords: Counterfactuals, Bayes correlated equilibrium, information structure, linear program
JEL Classification Codes: C72, D44, D82, D83CFDP 2162CFDP 2162RCFDP 2162R3