Abstract
I describe a Bayesian persuasion problem where Receiver has a private type representing a cutoff for choosing Sender’s preferred action, and Sender has maxmin preferences over all Receiver type distributions with known mean and bounds. This problem can be represented as a zero-sum game where Sender chooses a distribution of posterior mean beliefs that is a mean-preserving contraction of the prior over states, and an adversarial Nature chooses a Receiver type distribution with the known mean; the player with the higher realization from their chosen distribution wins. I formalize the connection between maxmin persuasion and similar games used to model political spending, all-pay auctions, and competitive persuasion. In both a standard binary-state setting and a new continuous-state setting, Sender optimally linearizes the prior distribution over states to create a distribution of posterior means that is uniform on a known interval with an atom at the lower bound of its support.
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I thank Drew Fudenberg, Stephen Morris, Frank Schillbach, Dmitry Taubinsky, participants in MIT Theory Lunch, participants in MIT 14.192, and especially Alexander Wolitzky for helpful discussions and comments. I also thank two anonymous referees for their feedback and suggestions. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. 1745302.
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Sapiro-Gheiler, E. Persuasion with ambiguous receiver preferences. Econ Theory 77, 1173–1218 (2024). https://doi.org/10.1007/s00199-023-01522-z
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DOI: https://doi.org/10.1007/s00199-023-01522-z