Optimal persuasion via bi-pooling

• 成果类型: Article
• 署名作者: Arieli, Itai; Babichenko, Yakov; Smorodinsky, Rann; Yamashita, Takuro
• 署名单位: Technion Israel Institute of Technology; Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics
• 刊物名称: THEORETICAL ECONOMICS
• ISSN/ISSBN: 1933-6837
• DOI: 10.3982/TE4663
• 发表日期: 2023-01-01
• 页码: 15-36
• 关键词: Bayesian persuasion; mean preserving contraction; bi-pooling; information disclosure; price function; signaling; extreme points; C72; D82; D83

摘要

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.