Competitive disclosure of correlated information

  • Pak Hung Au
  • Keiichi Kawai
Research Article


We analyze a model of competition in Bayesian persuasion in which two senders vie for the patronage of a receiver by disclosing information about the qualities of their respective proposals, which are positively correlated. The information externality—the news disclosed by one sender contains information about the other sender’s proposal—generates two effects on the incentives for information disclosure. The first effect, which we call the underdog-handicap effect, arises because the receiver is endogenously biased toward choosing the ex ante stronger sender. The second effect, which we call the good-news curse, arises because a sender’s favorable signal realization implies that the rival is more likely to generate a strong competing signal realization. While the underdog-handicap effect encourages more aggressive disclosure, the good-news curse can lower disclosure incentives. If the senders’ ex ante expected qualities are different, and the qualities of their two proposals are highly correlated, then the underdog-handicap effect dominates. Furthermore, as the correlation approaches its maximum possible value, the competition becomes so intense that both senders engage in full disclosure in the unique limit equilibrium.


Bayesian persuasion Multiple senders Correlated information Disclosure 

JEL Classification




  1. Au, P.H.: Dynamic information disclosure. RAND J. Econ. 46(4), 791–823 (2015)CrossRefGoogle Scholar
  2. Au, P.H., Kawai, K.: Competitive information disclosure by multiple senders. Working Paper, UNSW (2018)Google Scholar
  3. Battaglini, M.: Multiple referrals and multidimensional cheap talk. Econometrica 70, 1379–1401 (2002)CrossRefGoogle Scholar
  4. Board, S., Lu, J.: Competitive information disclosure in search markets. J. Polit. Econ. 126(5), 1965–2010 (2018)CrossRefGoogle Scholar
  5. Boleslavsky, R., Cotton, C.: Grading standards and education quality. Am. Econ. J. Microecon. 7(2), 248–79 (2015). CrossRefGoogle Scholar
  6. Boleslavsky, R., Cotton, C.: Limited capacity in project selection: competition through evidence production. Econ. Theory 65(2), 385–421 (2018). CrossRefGoogle Scholar
  7. Crawford, V.P., Sobel, J.: Strategic information transmission. Econometrica 50(6), 1431–1451 (1982)CrossRefGoogle Scholar
  8. Gentzkow, M., Kamenica, E.: Bayesian persuasion with multiple senders and rich signal spaces. Games Econ. Behav. 104, 411–429 (2017a). CrossRefGoogle Scholar
  9. Gentzkow, M., Kamenica, E.: Competition in persuasion. Rev. Econ. Stud. 84(1), 300–322 (2017b). CrossRefGoogle Scholar
  10. Hoffmann, F., Inderst, R., Ottaviani, M.: Persuasion through selective disclosure: implications for marketing, campaigning, and privacy regulation. Working Paper, University of Bonn (2014)Google Scholar
  11. Kamenica, E., Gentzkow, M.: Bayesian persuasion. Am. Econ. Rev. 101(6), 2590–2615 (2011). CrossRefGoogle Scholar
  12. Kawai, K.: Sequential cheap talks. Games Econ. Behav. 90, 128–133 (2015)CrossRefGoogle Scholar
  13. Kolotilin, A.: Optimal information disclosure: a linear programming approach. Theor. Econ. 13(2), 607–635 (2018)CrossRefGoogle Scholar
  14. Krishna, V., Morgan, J.: A model of expertise. Q. J. Econ. 116(2), 747–75 (2001)CrossRefGoogle Scholar
  15. Li, F., Norman, P.: Sequential persuasion. Working Paper, UNC Chapel-Hill (2017)Google Scholar
  16. Li, F., Norman, P.: On Bayesian persuasion with multiple senders. Econ. Lett. 170, 66–70 (2018)CrossRefGoogle Scholar
  17. Milgrom, P., Roberts, J.: Relying on the information of interested parties. RAND J. Econ. 17(1), 18–32 (1986)CrossRefGoogle Scholar
  18. Ostrovsky, M., Schwarz, M.: Information disclosure and unraveling in matching markets. Am. Econ. J. Microecon. 2(2), 34–63 (2010). CrossRefGoogle Scholar
  19. Perloff, J.M., Salop, S.C.: Equilibrium with product differentiation. Rev. Econ. Stud. 52(1), 107–120 (1985)CrossRefGoogle Scholar
  20. Reny, P.J.: On the existence of pure and mixed strategy Nash equilibria in discontinuous games. Econometrica 67(5), 1029–1056 (1999)CrossRefGoogle Scholar
  21. Simon, L.K., Zame, W.R.: Discontinuous games and endogenous sharing rules. Econometrica 58(4), 861–872 (1990)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Division of Economics, School of Social SciencesNanyang Technological UniversitySingaporeSingapore
  2. 2.Department of EconomicsThe Hong Kong University of Science and TechnologyKowloonHong Kong
  3. 3.School of EconomicsUNSW Business SchoolSydneyAustralia

Personalised recommendations