We study (interim correlated) rationalizability in a game with incomplete information. We characterize the recursive set of possible rationalizable hierarchies through a finite automaton, and provide a revelation principle that characterizes the distributions over these hierarchies that arise from any common prior. We show that a simple and finitely parametrized class of information structures, Stationary Common Automaton Markov Priors (SCAMP), is sufficient to generate every outcome distribution induced by general common prior information structures. Using this result, we characterize the set of rationalizable distributions as a convex polyhedron.

A principal delegates a decision to an agent, who has the capacity to process the relevant information. The principal can jointly control the actions and the informa-
tion available to the agent. I provide sufficient conditions under which the optimal mechanism (i) attains a perfect alignment of incentives—subject to the constraints on
discretion and information, the agent plays exactly as the principal would want him to; and (ii) belongs to a simple class of delegation and disclosure rules, called monotone
partitional rules, which specify a finite set of allowable actions from which the agent chooses his preferred one, and moreover, partition the state space into finite intervals so that the agent only learns to which interval the true state belongs. I then turn to the uniform-quadratic case which permits an explicit characterization of optimal mechanisms and clear comparative statics. Finally, I discuss two applications: the regulation of a monopolist, and the self-control of a dynamically inconsistent individual.

We study a strict version of the Kajii and Morris (1997) notion of equilibrium robustness, that allows for a larger class of perturbations of a given complete-infomation game, where with a high probability, players believe that their payoffs are close enough to (but may be different from) those of the complete-information game. It
is shown that a strict monotone potential maximizer of a complete-information game is strictly robust if either the game or the associated strict monotone potential is supermodular, and that the converse also holds in all binary-action supermodular games.