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Persuasion with costly precision

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Abstract

We study a sender’s optimal choice of precision when he selects from a class of random signals to persuade a receiver to accept his request, with higher costs associated with higher precision. The receiver observes both the precision and a random realization of the signal. We consider two situations: commitment, where the sender chooses the precision of his signal before observing any private information; and discretion, where the sender privately observes favourable or unfavourable information before choosing precision. We show that, under commitment, a positive level of precision is possible only when receiver is ex-ante neutral or slightly pessimistic about the sender. Under discretion, as long as the receiver is not convinced ex ante that he should accept the sender, there exists a unique plausible equilibrium, in which each type of sender’s payoff is independent of how pessimistic the receiver is about the sender. We then analyze optimal persuasion by comparing the sender’s payoff from discretion and that from commitment. We demonstrate that the more reluctant the receiver is to accept the sender, the more likely the sender prefers discretion to commitment. Finally, we show that whenever the sender prefers commitment to discretion, the receiver prefers the opposite.

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Acknowledgements

This paper supersedes the working paper titled “Persuasive signalling.” We thank the Associate Editor and an anonymous referee for valuable comments. We are grateful to Raphael Boleslavsky, Odilon Câmara, Chris Cotton, Brendan Daley, Rick Harbaugh, Navin Kartik, Ayca Kaya, Daniel Kselman, Frédéric Koessler, Ernest Lai, Wei Li, Meng-Yu Liang, Thomas Mariotti, Andrea Mattozzi, Eduardo Perez-Richet, Larry Samuelson, Joel Sobel, and Richard Van Weelden for their very helpful comments and suggestions. We also wish to thank audiences at Canadian Economics Association Meeting, Falset Workshop in Theoretical Political Science, Midwest Political Science Association Meetings, North American Summer Meetings of Econometric Society, Québec Political Economy Conference, Academia Sinica, Concordia University, Kytoto University, National Sun Yat-Sen University, National Taiwan University, National University of Singapore, Queen’s University, University of Alberta, University of Arizona, University of Miami, and Université du Québec à Montreal for their valuable inputs. Degan and Li acknowledge financial support from FRQSC-Equipe de Recherche, Grant Number 144617. Part of the research was completed while Li was a visiting researcher of RIHSS at National Taiwan University and he is grateful for the hospitality. All remaining errors are our own.

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Authors and Affiliations

  1. Département des Sciences Économiques, École des Sciences de la Gestion, Université du Québec à Montréal, Montréal, Québec, H3C 3P8, Canada

    Arianna Degan

  2. Department of Economics, Concordia University, Concordia University, 1455 Boulevard de Maisonneuve Ouest, Montréal, Québec, H3G 1M8, Canada

    Ming Li

  3. CIRANO, Montréal, Québec, H3G 1M8, Canada

    Ming Li

  4. CIREQ, Montréal, Québec, H3G 1M8, Canada

    Ming Li

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  1. Arianna Degan
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Correspondence to Ming Li.

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Degan, A., Li, M. Persuasion with costly precision. Econ Theory 72, 869–908 (2021). https://doi.org/10.1007/s00199-021-01346-9

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