Can a better informed listener be easier to persuade?
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Can a better informed listener be easier to persuade? Jacopo Bizzotto1 · Adrien Vigier2 Received: 22 May 2020 / Accepted: 10 October 2020 © The Author(s) 2020
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. Keywords Bayesian Persuasion · Dynamic Games · Information Provision JEL classification C70 · D72 · D80
1 Introduction The by now classic Bayesian persuasion problem has found numerous applications, and therefore recently received a lot of attention. Yet one aspect of the problem that is still not well understood concerns the impact of exogenous news. The purpose of the present paper is to draw attention to the subtle effects of exogenous news on the Bayesian persuasion problem. 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. However, 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.
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00199020-01321-w) contains supplementary material, which is available to authorized users.
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Jacopo Bizzotto [email protected]
1
Oslo Business School, Oslo Metropolitan University, Pilestredet 35, 0563 Oslo, Norway
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School of Economics, University of Nottingham, Sir Clive Granger Building, University Park, Nottingham NG7 2RD, UK
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J. Bizzotto, A. Vigier
Suppose that the lobbyist gets to meet the politician twice. In this setting, the politician can either choose an action after the first meeting, or wait until the second meeting in order to observe whatever news comes up in the time interval between the two meetings. The lobbyist is worse off in this setting as compared to the static setting, since to obtain action A after the first meeting the lobbyist must now additionally persuade the politician not to wait. In particular, in sharp contrast with the static setting, to obtain action A in the first period the lobbyist here supplies information that –from the politician’s perspective– creates positive value. Now suppose that the lobbyist gets to meet the politician thrice. The previous remarks concerning the value of information provided by the sender in the two-period setting imply that, with three periods, seen from period one, the lobbyist’s current self is effectively playing against the lobbyist’s future self. Indeed, with three periods, the reason for which the politician is tempted to wait m
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