Informed Information Design

Abstract

We study informed persuasion whereby a privately informed designer without ex ante commitment power chooses disclosure mechanisms to influence agents' actions. We characterize the subset of Bayes-correlated equilibria yielding every designer type a payoff higher than what they could get from any disclosure mechanism with credible beliefs. This set of interim optimal mechanisms is non-empty and tractable, and all its elements are perfect Bayesian equilibrium mechanisms of the informed-designer game. Interim optimal mechanisms are characterized via belief-based approaches in pure persuasion settings. We identify single-and multi-agent interactive environments in which ex ante optimal mechanisms are interim optimal.

On the Equivalence of Information Design by Uninformed and Informed Principals

“…Second, it shows why the assumption that tests cannot be perfectly accurate (Assumption (A 2 )) is crucial for this construction, and why relaxing this assumption (and thus enlarging the set of tests that the principal can deviate to) can destroy the pooling equilibrium. It also highlights the difference between Koessler and Skreta (2022) and this paper.…”

“…So the outcome of this optimal test is implementable by the uninformed principal. Koessler and Skreta (2022) argue that the outcome of the test t * is not implementable by the informed principal. The reason is that if it was implementable, the informed principal would have to choose t * in both states, H and L. But when the state was H, the principal would prefer to deviate by revealing the state.…”

“…In this section, we present an example borrowed from Koessler and Skreta (2022). The role of this example is twofold.…”

“…Perez-Richet (2014) and Koessler and Skreta (2022) deal with the above belief indeterminacy problem using to the principle of the preeminence of tests. They impose the constraint that every out-of-equilibrium posterior belief must assign probability one to each event that is revealed as certain by the test.…”

“…Related Literature. The closest paper in the literature to our paper is Koessler and Skreta (2022), thereafter, KS. Like our paper, KS compare the problems of uninformed and informed information designer, but they reach a different conclusion.…”