Ambiguous Persuasion ∗

We study a persuasion game à la Kamenica and Gentzkow (2011) where players are ambiguity averse with maxmin expected utility (Gilboa and Schmeidler, 1989). With no prior ambiguity, Sender might choose to use ambiguous communication devices. The main result characterizes the value of optimal ambiguous persuasion, which is often higher than what is feasible under Bayesian persuasion. We characterize posterior beliefs that are potentially plausible with being generated by some ambiguous devices. One way to construct an optimal ambiguous communication device is by using synonyms, messages that lead to the same posteriors, in which Sender can hedge himself against ambiguity while inducing actions from Receiver that would not be possible under Bayesian communication. Two applications, including the well-known uniform-quadratic example, are considered. Our analysis provides a justification for how ambiguity may emerge endogenously in persuasion. ∗We are grateful to Pierre Fleckinger, Françoise Forges, Sidartha Gordon, Yingni Guo, Sean Horan, Maxim Ivanov, Frédéric Koessler, Marie Laclau, Elliot Lipnowski, Sujoy Mukerji, Peter Norman, Eduardo Perez-Richet, Ludovic Renou, Joel Sobel, Jean-Marc Tallon, Marciano Siniscalchi, and Vassili Vergopoulos for their very helpful comments. We are also grateful to audiences at Stony Brook Game Theory Conference 2016, Midwest Theory conference 2016, 2017, Midwest Political Science Association Conference 2017, Canadian Economic Theory Conference 2017, Asian Summer Meeting of Econometric Society 2017, McMaster University, McGill University, University of Montreal, and Laval University for valuable inputs. This research has benefitted from the research programs "Investissements d’avenir" ANR-10-LABX-93 and "Jeux et ambiguïté" ANR-12-FRAL-0008-01 granted by the Agence Nationale de la Recherche (Beauchêne), "Scientific research, conflicts of interest, and disclosure policy" (SSHRC Insight Development 430-2016-00444, Ming Li), and “Communication avec un public averse à l’ambiguïté” (FRQSC 2018-NP-206978, Jian Li). Part of the research was conducted while Beauchêne, Dorian was writing his Ph.D. dissertation at Paris School of Economics, and while Li, Ming was visiting ISER at Osaka University, who is grateful for the hospitality. †MAPP Economics. E-mail: [email protected] ‡McGill University and CIREQ. Email: [email protected]. §Concordia University and CIREQ. Email: [email protected].