Persuasion Without Priors

Alexei Parakhonyak and Anton Sobolev (anton.sobolev@uni-mannheim.de)

CRC TR 224 Discussion Paper Series from University of Bonn and University of Mannheim, Germany

Abstract: We consider an information design problem when the sender faces ambiguity regarding the probability distribution over the states of the world, the utility function and the prior of the receiver. The solution concept is minimax loss (regret), that is, the sender minimizes the distance from the full information benchmark in the worst-case scenario. We show that in the binary states and binary actions setting the optimal strategy involves a mechanism with a continuum of messages, which admits a representation as a randomization over mechanisms consisting of two messages. A small level of uncertainty regarding the re- ceiver’s prior makes the sender more truthful than in the full information benchmark, but as uncertainty increases at some point the sender starts to lie more. If the sender either knows the probability distribution over the states of the world, or knows that the receiver knows it, then the maximal loss is bounded from above by 1/e. This result generalizes to an infinite state model, provided that the set of admissible mechanisms is limited to cut-off strategies.

Keywords: Persuasion; Robustness; Multiple priors; Minimax regret (search for similar items in EconPapers)
JEL-codes: D81 D82 D83 (search for similar items in EconPapers)
Pages: 87
Date: 2022-07
New Economics Papers: this item is included in nep-des, nep-gth, nep-mic and nep-upt
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