Abstract
This paper analyzes optimal policy in setups where both the leader and the follower have doubts about the probability model of uncertainty. I illustrate the methodology in two environments: a) an industry populated with a large firm and many small firms in a competitive fringe, where both types of firms doubt the probability model of demand shocks, and b) a general equilibrium economy, where a policymaker taxes linearly the labor income of a representative household in order to finance an exogenous stream of stochastic spending shocks. The policymaker can distrust the probability model of spending shocks more, the same, or less than the household. Whenever there are doubts about the model, cautious agents form endogenous worstcase beliefs by assigning high probability on low profitability or low-utility events. There are two forces that shape optimal policy results: the manipulation of the endogenous beliefs of the follower to the benefit of the leader, and the discrepancy (if any) in the pessimistic beliefs between the leader and the follower. Depending on the application, the leader may amplify or mitigate the worst-case beliefs of the follower.