A shared feature of communication games with verifiable evidence is that the receiver is skeptical following any non-disclosure: he will believe that the message comes from an informed sender who is withholding unfavorable evidence. It then follows that when the receiver is more skeptical he will choose a less preferable action for the sender. This paper seeks to characterize when a change in the distribution of evidence induces any receiver to be more skeptical, i.e. take an action that is less favorable to the sender following any message. We introduce the ”more evidence” relation on prior distributions over types: a distribution has more evidence than another if sender types with larger available message sets are more probable in a monotone likelihood ratio sense. Our main result shows that the sender having more evidence is equivalent to an increase in receiver skepticism. We first show that this equivalence unifies many seemingly different comparative statics results from the verifiable disclosure literature. We then apply our analysis to a dynamic disclosure environment in which the sender obtains and discloses evidence gradually. Our result reveals when the receiver does not "benefit from dynamic disclosure" relative to the case in which evidence is disclosed only in the final period.
Single-Crossing Differences on Distributions, with Navin Kartik and SangMok Lee;
Revise and Resubmit at Econometrica
We characterize when choices among lotteries over arbitrary allocations are monotonic in an expected-utility agent’s type. Our necessary and sufficient condition is on the von Neumann-Morgenstern utility function; we identify an order over lotteries that generates the choice monotonicity when the condition holds. We discuss applications to cheap-talk games, costly signaling games, and collective choice problems. Our characterization requires some new results on monotone comparative statics and aggregating single-crossing functions, a by-product of which is a characterization of the monotone likelihood ratio property.
We study a principal who hires an agent to acquire costly information that will influence the decision of a third party. While the realized piece of information is observable and contractible, the experimental process is not. Assuming a general family of information cost functions (inclusive of Shannon’s mutual information), we show that the first best is achievable when the agent has limited liability or when he is risk averse, in contrast to standard moral hazard models. However, when the agent is both risk averse and has limited liability, efficiency losses arise generically. Specifically, we show that the principal obtains his first best outcome if and only if he intends to implement a ”symmetric” experiment, i.e. one in which the cost of generating each piece of evidence is the same. On the other hand, ”asymmetric” experiments that are uninformative with high probability but occasionally produce conclusive evidence will bear large agency costs.