Hierarchical games under uncertainty

The two-players hierarchical game is considered. The payoff function of low-level player (agent) depends on a random variable. The low-lever player knows the value of this variable at the moment of decision making. And high-level player (principal) knows only probability distribution on the domain when making his decision. We obtain the optimal strategy for the principal under the assumption that she is trying to maximize the guaranteed payoff. This results are tightly coupled with some work in the theory of contracts.