The Optimal Timing of Persuasion

Jacopo Bizzotto
University of Oslo – Department of Economics

Jesper Rudiger
University of Copenhagen – Department of Economics

Adrien Vigier
University of Oxford – Department of Economics

January 13, 2016

Abstract:

We study the effect of the arrival of exogenous news in dynamic games of Bayesian persuasion. A receiver chooses what action to take, and when to act. If Receiver waits, exogenous news may be observed. A sender chooses a first information structure that generates a signal before the news and, if Receiver waits, a second signal structure after the news. Receiver observes the signal structures, as well as the corresponding signal realized. We show that, in the sense of Blackwell, information provided by Sender before the news is non-monotonic in the quantity of exogenous news. For very small and very large quantities of exogenous news, Sender provides enough information for Receiver to act before the news with probability one. By contrast, for intermediate quantities of exogenous news, Sender curbs the information she provides, in a way that minimizes the chances of Receiver acting early against Sender’s interest. In this case, Sender may even communicate nothing before the news, and concentrate her persuasion effort after the news.

The Optimal Timing of Persuasion

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