Optimal persuasion via bi‐pooling

Abstract

Mean‐preserving contractions are critical for studying Bayesian models of information design. We introduce the class of bi‐pooling policies, and the class of bi‐pooling distributions as their induced distributions over posteriors. We show that every extreme point in the set of all mean‐preserving contractions of any given prior over an interval takes the form of a bi‐pooling distribution. By implication, every Bayesian persuasion problem with an interval state space admits an optimal bi‐pooling distribution as a solution, and conversely, for every bi‐pooling distribution, there is a Bayesian persuasion problem for which that distribution is the unique solution.

Optimal disclosure of information to privately informed agents

“…The next result establishes conditions that need to be satisfied by any solution of problem (14). Our results extend the insights of Candogan (2019b), Arieli et al (2020) and Kleiner, Moldovanu, and Strack (2020), who analyzed the problem of maximizing over mean‐preserving contractions without side‐constraints. We allow for side‐constraints as they naturally appear as incentive constraints and in settings with multiple agents.…”

“…The aforementioned “sandwiching” constraint is equivalent to a majorization constraint restricting the set of feasible posterior distributions. Arieli, Babichenko, Smorodinsky, and Yamashita (2020) and Kleiner, Moldovanu, and Strack (2020) characterize the extreme points of this set. As also observed in Candogan (2019a, 2019b), this characterization implies that in the single‐agent case without private information, one can restrict attention to signals where each state lies in an interval such that for all states in that interval at most two messages are sent.…”

Constructive versus Toxic Argumentation in Debates

“…Linearity refers to the property that the payoffs depend on the posterior belief about the state only through the posterior mean. This approach received a lot of attention on the literature (Emir Kamenica and Matthew Gentzkow, 2011;Matthew Gentzkow and Emir Kamenica, 2016;Anton Kolotilin, Tymofiy Mylovanov, Andriy Zapechelnyuk and Ming Li, 2017;Anton Kolotilin, 2018;Anton Kolotilin and Andriy Zapechelnyuk, 2019;Piotr Dworczak and Giorgio Martini, 2019;Itai Arieli, Yakov Babichenko, Rann Smorodinsky and Takuro Yamashita, 2023;Andreas Kleiner, Benny Moldovanu and Philipp Strack, 2021). It has been used in many applications of information design, including media control (Scott Gehlbach and Konstantin Sonin, 2014;Boris Ginzburg, 2019;Arda Gitmez and Pooya Molavi, 2022;Anton Kolotilin, Tymofiy Mylovanov and Andriy Zapechelnyuk, 2022), clinical trials (Anton Kolotilin, 2015), voter persuasion (Ricardo Alonso and Odilon Câmara, 2016), transparency benchmarks (Darrell Duffie, Piotr Dworczak and Haoxiang Zhu, 2017), stress tests (Itay Goldstein and Yaron Leitner, 2018;Dmitry Orlov, Pavel Zryumov and Andrzej Skrzypach, 2022), online markets (Gleb Romanyuk and Alex Smolin, 2019), attention management (Elliot Lipnowski, Laurent Mathevet and Dong Wei, 2020;Alexander W Bloedel and Ilya Segal, 2020), quality certification (Andriy Zapechelnyuk, 2020;Benjamin Vatter, 2022), and healthcare congestion in epidemics (Ju Hu and Zhen Zhou, 2022).…”