Abstract:
We consider an information design problem in which the sender faces ambiguity regarding the probability distribution over the states of the world, the utility function, and the prior of the receiver. The solution concept is minimax loss (regret), that is, the sender minimizes the difference in payoffs from the Bayesian benchmark in the worst-case scenario. In the binary state and binary action setting the mechanism contains a continuum of messages, and admits a representation as a randomization over two-message mechanisms. A small level of uncertainty makes the sender more truthful, but larger uncertainty may result in the sender lying more often than the Bayesian benchmark. If the sender either knows the probability distribution over the states of the world, or knows that the receiver knows it, then the maximal loss is bounded from above by 1/ e . When admissible mechanisms are limited to cut-off strategies, this result generalizes to a multiple state model.
