Adversarial coordination and public information design

We study flexible public information design in global games. In addition to receiving public information from the designer, agents are endowed with exogenous private information and must decide between two actions (invest and not invest), the profitability of which depends on unknown fundamentals and the agents’ aggregate action. The designer does not trust the agents to play favorably to her and evaluates any policy under the “worst-case scenario.” First, we show that the optimal policy removes any strategic uncertainty by inducing all agents to take the same action, but without permitting them to perfectly learn the fundamentals and/or the beliefs that rationalize other agents’ actions. Second, we identify conditions under which the optimal policy is a simple “pass/fail” test. Finally, we show that when the designer cares only about the probability the aggregate investment is successful, the optimal policy need not be monotone in fundamentals but then identify conditions on payoffs and exogenous beliefs under which the optimal policy is monotone.