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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References
Alonso, R., Câmara, O.: On the value of persuasion by experts. J. Econ. Theory 174, 103–123 (2018)
Ash, E., Morelli, M., Van Weelden, R.: Elections and divisiveness: theory and evidence. J. Polit. 79(4), 1268–1285 (2017)
Au, P.H., Kawai, K.: Competitive disclosure of correlated information. Econ. Theory 1–33 (2019)
Banks, J.S., Sobel, J.: Equilibrium selection in signaling games. Econometrica 55(3), 647–61 (1987)
Boleslavsky, R., Cotton, C.: Limited capacity in project selection: competition through evidence production. Econ. Theory 65(2), 385–421 (2018)
Boleslavsky, R., Cotton, C.S., Gurnani, H.: Demonstrations and price competition in new product release. Manag. Sci 63(6), 2016–2026 (2016)
Chakraborty, A., Harbaugh, R.: Persuasion by cheap talk. Am. Econ. Rev. 100(5), 2361–2382 (2010)
Che, Y.K., Kartik, N.: Opinions as incentives. J. Polit. Econ. 117(5), 815–860 (2009)
Che, Y.K., Dessein, W., Kartik, N.: Pandering to persuade. Am. Econ. Rev. 103(1), 47–79 (2013)
Chen, Y., Zhang, J.: Signalling by Bayesian persuasion and pricing strategy. Econ. J. 130(628), 976–1007 (2020)
Cho, I.K., Kreps, D.M.: Signaling games and stable equilibria. Q. J. Econ. 102(2), 179–221 (1987)
Cho, I.K., Sobel, J.: Strategic stability and uniqueness in signaling games. J. Econ. Theory 50(2), 381–413 (1990)
Chung, K.S., Eső, P.: Persuasion and learning by countersignaling. Econ. Lett. 121(3), 487–491 (2013)
Daley, B., Green, B.: Market signaling with grades. J. Econ. Theory 151, 114–145 (2014)
DeGroot, M.H.: Optimal Statistical Decisions. McGraw-Hill, New York (1970)
Espinosa, F., Ray, D.: Noisy agents, p. w24627. Technical report, National Bureau of Economic Research, No (2018)
Feltovich, N., Harbaugh, R., To, T.: Too cool for school? Signalling and countersignalling. RAND J. Econ. 33(4), 630–649 (2002)
Ferris, D.G., Samakoses, R., Block, S.L., Lazcano-Ponce, E., Restrepo, J.A., Mehlsen, J., Chatterjee, A., Iversen, O.E., Joshi, A., Chu, J.L., et al.: 4-Valent human papillomavirus (4vHPV) vaccine in preadolescents and adolescents after 10 years. Pediatrics 140(6), e20163,947 (2017)
Fox, J., Van Weelden, R.: Partisanship and the effectiveness of oversight. J. Public Econ. 94(9–10), 674–687 (2010). https://doi.org/10.1016/j.jpubeco.2010.05.003
Fu, Q., Li, M.: Reputation-concerned policy makers and institutional status quo bias. J. Public Econ. 110, 15–25 (2014)
Fudenberg, D., Tirole, J.: Game Theory. MIT Press, Cambridge, MA, translated into Chinese by Renmin University Press, Bejing: China (1991a)
Fudenberg, D., Tirole, J.: Perfect Bayesian equilibrium and sequential equilibrium. J. Econ. Theory 53(2), 236–260 (1991b)
Gentzkow, M., Kamenica, E.: Costly persuasion. Am. Econ. Rev. 104(5), 457–62 (2014)
Gentzkow, M., Kamenica, E.: Competition in persuasion. Rev. Econ. Stud. 84(1), 300–322 (2016)
Gill, D., Sgroi, D.: Sequential decisions with tests. Games Econ. Behav. 63(2), 663–678 (2008)
Gill, D., Sgroi, D.: The optimal choice of pre-launch reviewer. J. Econ. Theory 147(3), 1247–1260 (2012)
Gratton, G., Holden, R., Kolotilin, A.: When to drop a bombshell. Rev. Econ. Stud. 85(4), 2139–2172 (2017)
Grossman, S.J.: The informational role of warranties and private disclosure about product quality. J. Law Econ. 24(3), 461–483 (1981)
Hedlund, J.: Persuasion with communication costs. Games Econ. Behav. 92, 28–40 (2015). https://doi.org/10.1016/j.geb.2015.04.004
Hedlund, J.: Bayesian persuasion by a privately informed sender. J. Econ. Theory 167, 229–268 (2017). https://doi.org/10.1016/j.jet.2016.11.003
Heufer, J.: In Vino Veritas: The Economics of Drinking, p. 158. Technical report, Ruhr Economic Paper No (2010)
Kamenica, E., Gentzkow, M.: Bayesian persuasion. Am. Econ. Rev. 101(6), 2590–2615 (2011). https://doi.org/10.1257/aer.101.6.2590
Kolotilin, A., Mylovanov, T., Zapechelnyuk, A., Li, M.: Persuasion of a privately informed receiver. Econometrica 85(6), 1949–1964 (2017)
Kosenko, A.: Bayesian persuasion with private information. Available at SSRN 3236191 (2018)
Li, H., Li, W.: Misinformation. Int. Econ. Rev. 54(1), 253–277 (2013)
Medical College of Georgia at Augusta University: HPV vaccine is effective, safe 10 years after it’s given, study shows. Science Daily (2017). www.sciencedaily.com/releases/2017/11/171129131400.htm. Accessed 14 Jan 2019
Milgrom, P.: Good news and bad news: representation theorems and applications. Bell J. Econ. 12(2), 380–391 (1981)
Milgrom, P.: What the seller won’t tell you: Persuasion and disclosure in markets. J Econ. Perspect. 22(2), 115–131 (2008)
Milgrom, P., Roberts, J.: Relying on the information of interested parties. RAND J. Econ. 17(1), 18–32 (1986)
Nilsen, E.: Cynthia Nixon: democrats need to be more than a “gentler, more diverse version” of the GOP. Vox https://www.vox.com/policy-and-politics/2018/9/11/17845396/cynthia-nixon-new-york-governors-race-democratic-primary-andrew-cuomo-midterms (2018). Accepted 25 Feb 2021
Perez-Richet, E.: Interim Bayesian Persuasion: first steps. Am. Econ. Rev. 104(5), 469–74 (2014)
Perez-Richet, E., Prady, D.: Complicating to persuade. Available at SSRN 1868066 (2011)
Rayo, L.: Monopolistic signal provision. B. E. J. Theor. Econ. Adv. 13(1), 27–58 (2013)
Rayo, L., Segal, I.: Optimal information disclosure. J. Polit. Econ. 118(5), 949–987 (2010)
Riley, J.G.: Informational equilibrium. Econometrica 47(3), 331–359 (1979)
Rosenthal, E.: Drug makers’ push leads to cancer vaccines’ rise. New York Times (2008)
Sobel, J.: Signaling games. In: Meyers, R. (ed.) Encyclopedia of Complexity and System Science. Springer, New York (2009)
Spence, A.M.: Job market signaling. Q. J. Econ. 87(3), 355–374 (1973)
Spence, A.M.: Market Signalling: Informational Transfers in Hiring and Related Screening Processes. Harvard University Press, Cambrige (1974)
Taneva, I.: Information design. Am. Econ. J. Microecon. 11(4), 151–85 (2019)
Wang, Y.: Bayesian persuasion with multiple receivers. mimeo (2013). http://ssrn.com/abstract=2625399. Accepted 25 Feb 2021
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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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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DOI: https://doi.org/10.1007/s00199-021-01346-9
Keywords
- Persuasion
- Costly signals
- Precision
- Signalling
- D1 equilibrium
- Strategic communication
- Optimal information provision