Abstract
This paper studies robust Bayesian persuasion of a privately informed receiver in a binary environment, where an ambiguity-averse sender with a maxmin expected utility function has limited knowledge about the receiver’s private information source. We develop a novel method to solve the sender’s information design problem. Our main result shows that the sender’s optimal information structure can be found within the class of linear-contingent-payoff information structures. We also fully characterize the sender’s optimal linear-contingent-payoff information structure and analyze the impact of ambiguity on the sender’s payoff.
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References
Albrecht, B.C.: Political Persuasion. working paper, University of Minnesota (2017)
Alonso, R., Câmara, O.: Bayesian persuasion with heterogeneous priors. J. Econ. Theory 165, 672–706 (2016)
Au, P.H., Kawai, K.: Competitive disclosure of correlated information. Econ. Theory (2019). https://doi.org/10.1007/s00199-018-01171-7
Au, P.H., Kawai, K.: Competitive information disclosure by multiple senders. Games Econ. Behav. 119, 56–78 (2020)
Beauchẽne, D., Li, J., Li, M.: Ambiguous persuasion. J. Econ. Theory 179, 312–365 (2019)
Bergemann, D., Schlag, K.: Pricing without priors. J. Eur. Econ. Assoc. 6, 560–569 (2008)
Bergemann, D., Schlag, K.: Robust monopoly pricing. J. Econ. Theory 146(6), 2527–2543 (2011)
Bergemann, D., Brooks, B., Morris, S.: Informationally Robust Optimal Auction Design. Working paper (2016)
Bergemann, D., Bonatti, A., Smolin, A.: The design and price of information. Am. Econ. Rev. 108(1), 1–48 (2018)
Blackwell, D.: Comparison of experiments. In: Neyman, J. (ed.) Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, pp. 93–102. University of California Press, Berkeley, California (1951)
Bodoh-Creed, A.L.: Ambiguous beliefs and mechanism design. Games Econ. Behav. 75(2), 518–537 (2012)
Bose, S., Renou, L.: Mechanism design with ambiguous communication devices. Econometrica 82, 1853–1872 (2014)
Bose, S., Ozdenoren, E., Pape, A.: Optimal auctions with ambiguity. Theor. Econ. 1, 411–438 (2006)
Carrasco, V., Luz, V.F., Kos, N., Messner, M., Monteiro, P., Moreira, H.: Optimal selling mechanism under moment conditions. J. Econ. Theory 177, 245–279 (2018)
Carroll, G.: Robustness and linear contracts. Am. Econ. Rev. 105(2), 536–563 (2015)
de Castro, L.I., Yannelis, N.C.: Uncertainty, efficiency and incentive compatibility: ambiguity solves the conflict between efficiency and incentive compatibility. J. Econ. Theory 177, 678–707 (2018)
de Castro, L.I., Pesce, M., Yannelis, N.C.: Core and equilibria under ambiguity. Econ. Theory 48(2–3), 519 (2011)
de Castro, L.I., Liu, Z., Yannelis, N.C.: Ambiguous implementation: the partition model. Econ. Theory 63(1), 233–261 (2017a)
de Castro, L.I., Liu, Z., Yannelis, N.C.: Implementation under ambiguity. Games Econ. Behav. 101, 20–33 (2017b)
Du, S.: Robust mechanisms under common valuation. Econometrica 86, 1569–1588 (2018)
Esponda, I., Pouzo, D.: Berk–Nash equilibrium: a framework for modeling agents with misspecified models. Econometrica 84(2), 1093–1130 (2016a)
Esponda, I., Pouzo, D.: Equilibrium in Misspecified Markov Decision Processes. Working paper (2016b)
Garrett, D.F.: Robustness of simple menus of contracts in cost-based procurement. Games Econ. Behav. 87, 631–641 (2014)
Gentzkow, M., Kamenica, E.: Bayesian persuasion with multiple senders and rich signal space. Games Econ. Behav. 104, 411–429 (2017a)
Gentzkow, M., Kamenica, E.: Competition in persuasion. Rev. Econ. Stud. 84(1), 300–322 (2017b)
Gilboa, I., Schmeidler, D.: Maxmin expected utility with non-unique prior. J. Math. Econ. 18(2), 141–153 (1989)
Guo, Y., Shmaya, E.: The interval structure of optimal disclosure. Econometrica 87, 653–675 (2019)
Hewitt, E., Stromberg, K.: Real and Abstract Analysis: A Modern Treatment of the Theory of Functions of a Real Variable. Springer, New York (1965)
Kamenica, E., Gentzkow, M.: Bayesian persuasion. Am. Econ. Rev. 101(6), 2590–2615 (2011)
Koessler, F., Laclau, M., Tomala, T.: Interactive Information Design. Tech. rep (2018)
Kolotilin, A.: Optimal information disclosure: a linear programming approach. Theor. Econ. 13(2), 607–636 (2018)
Kolotilin, A., Li, M., Mylovanov, T., Zapechelnyuk, A.: Persuasion of a privately informed receiver. Econometrica 85(6), 1949–1964 (2017)
Kosterina, S.: Persuasion with Unknown Beliefs. Working paper, University of Princeton (2018)
Li, F., Norman, P.: On Bayesian persuasion with multiple senders. Econ. Lett. 170, 66–70 (2018)
Rayo, L., Segal, I.: Optimal information disclosure. J. Polit. Econ. 118(5), 949–987 (2010)
Wolitzky, A.: Mechanism design with maxmin agents: theory and an application to bilateral trade. Theor. Econ. 11(3), 971–1004 (2016)
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Hu and Weng would like to acknowledge the financial support of the National Natural Science Foundation of China (Grant Nos. 71803004 and 71973002)
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Hu, J., Weng, X. Robust persuasion of a privately informed receiver. Econ Theory 72, 909–953 (2021). https://doi.org/10.1007/s00199-020-01299-5
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DOI: https://doi.org/10.1007/s00199-020-01299-5