Learning Manipulation Through Information Dissemination

• 成果类型: Article
• 署名作者: Keppo, Jussi; Kim, Michael Jong; Zhang, Xinyuan
• 署名单位: National University of Singapore; National University of Singapore; University of British Columbia
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2021.2209
• 发表日期: 2022
• 页码: 3490-3510
• 关键词: Bayesian dynamic programming; information design; dynamic learning; information disclosure; deceptive advertising; exponential tilting; social learning; relative entropy

摘要

We study optimal manipulation of a Bayesian learner through adaptive provisioning of information. The problem is motivated by settings in which a firm can disseminate possibly biased information at a cost, to influence the public's belief about a hidden parameter related to the firm's payoffs. For example, firms advertise to sell products. We study a sequential optimizationmodel in which the firmdynamically decides on the quantity and content of information sent to the public, aiming to maximize its expected total discounted profits over an infinite horizon. We solve the associated Bayesian dynamic programming equation and explicitly characterize the optimal manipulation policy in closed form. The explicit solution allows us to further characterize the evolution of the public's posterior belief under suchmanipulation over time. We also extend our analysis to consider the public as partially Bayesian social learners who rely on public reviews to resist manipulation. We show that the public asymptotically learns the truth in this extended setting.