Cheap talk with two-sided private information

Abstract

This paper studies how the transmission of information from a biased expert to a decision maker is affected when the latter has access to an unbiased symmetric private signal. The extra information has two distinct effects on the expert's incentives to communicate. First, there is an information effect that allows the decision maker to choose a better action on expectation. This reduces the implicit cost of transmitting coarse messages and hence hampers communication. Second, there is a risk effect that arises because the extra information introduces uncertainty to the expert. For risk averse experts, this effect increases the cost of sending coarse messages and hence favours communication. I show that the information effect dominates the risk effect, and for any symmetric signal structure there are always sufficiently biased experts for which communication is no longer possible in equilibrium. Moreover, for any bias of the expert, no communication is possible if the signal structure is sufficiently precise. For the uniform signal structure I show that communication decreases with the precision of the signal. Finally, I provide non degenerate examples for which the decision maker's private information cannot make up for the loss of communication implying that the welfare of both agents decreases.