Abstract
We study the impact of exogenous news on the classic Bayesian persuasion problem. The sender supplies information over multiple periods, but is unable to commit at the onset to the information that she will supply in periods ahead. A tension then emerges between the sender and her future self. We show that by resolving this tension, more informative news can make the sender better off.
Highlights
The classic Bayesian persuasion problem has found numerous applications, and recently received a lot of attention
To illustrate the main idea of our paper, consider the example in Kamenica and Gentzkow (2011) of a lobbyist trying to convince a politician to take a certain action A. Instead of modelling this situation as a static problem, imagine that we let the process unfold over multiple periods, thereby enabling the politician to accumulate information beyond the lobbyist’s control. We think of this information as exogenous news, and ask how this affects the problem of the lobbyist
We focus on Perfect Bayesian Equilibrium (PBE) such that: (1) whenever the sender is indifferent between two splittings ordered by Blackwell’s criterion, she chooses the least informative of the two; (2) whenever indifferent between two decisions, the receiver makes the decision preferred by the sender
Summary
The classic Bayesian persuasion problem has found numerous applications, and recently received a lot of attention. The purpose of the present paper is to draw attention to the subtle effects of exogenous news on the Bayesian persuasion problem. Instead of modelling this situation as a static problem, imagine that we let the process unfold over multiple periods, thereby enabling the politician to accumulate information beyond the lobbyist’s control. We think of this information as exogenous news, and ask how this affects the problem of the lobbyist
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