Strategic Communication with Minimal Verification
A receiver wants to learn multidimensional information from a sender, but she has capacity to verify only one dimension. The sender's payoff depends on the belief he induces, via an exogenously given monotone function. We show that by using a randomized verification strategy, the receiver can learn the sender's information fully if the exogenous payoff function is submodular. If it is (strictly) supermodular, then full learning is not possible. In a variant of the model that allows for severe punishments when the sender is found to have lied, we can give a complete characterization of when full learning is possible. Our full learning result does not critically rely on perfect verifiability of one dimension: in an example with noisy verification, the receiver's ex-post perceived distribution of information converges in distribution to the true value as the noise vanishes.
Gabriel Carroll, Georgy Egorov
Carroll, Gabriel, and Georgy Egorov. 2018. Strategic Communication with Minimal Verification.