Two-sided uncertainty in persuasion games.

Abstract

I study a communication game between a listener and a speaker in which the speaker sends costless but verifiable messages in order to persuade the listener to take an action that is favorable for the speaker. Because of its practical relevance for many economic, legal, and political matters, this problem has been well studied in economics literature, usually under the assumption that the speaker knows the preferences of the listener. This assumption is restrictive, as in many persuasion problems the speaker might not know the preferences of the listener, possibly because either the listener is not able to communicate her preferences or wants to deliberately keep the speaker uncertain about her preferences. I explore two possible tools that can be used for information extraction in such a game. The first tool is the uncertainty about the listener's preferences (type) that may be maintained or removed. Another tool is to change the ``scale of actions"-for example, increasing or decreasing legal punishment. First, in a persuasion game in which the listener has two possible types and two actions to choose from, I show that when one of the listener's types is more likely, the equilibrium speaker strategies are a subset of those that arise when the speaker knows the listener's type. Further, I show that among the equilibria that deliver the highest expected utility to the more likely type when there is certainty, there is always one that remains in the set of equilibria under uncertainty. These results imply that maintaining uncertainty can be a useful tool only for the less likely type. To analyze the effect of the second tool, I study a legal application of persuasion games with two-sided uncertainty. A defendant (speaker) is trying to persuade a judge by presenting evidence to take a favorable legal action rather than less favorable ones on his case. I show that the equilibrium disclosure of the defendant is not affected by a change in the scale of legal actions when there is no uncertainty on how the judge evaluates evidence. With uncertainty, however, the defendant can be induced to disclose more information by decreasing the severity of the most unfavorable legal action relative to the favorable one.