Bayesian Persuasion in Sequential Trials
Abstract
We consider a Bayesian persuasion or information design problem where the sender tries to persuade the receiver to take a particular action via a sequence of signals. This we model by considering multiphase trials with different experiments conducted based on the outcomes of prior experiments. In contrast to most of the literature, we consider the problem with constraints on signals imposed on the sender. This we achieve by fixing some of the experiments in an exogenous manner; these are called determined experiments. This modeling helps us understand realworld situations where this occurs: e.g., multiphase drug trials where the FDA determines some of the experiments, funding of a startup by a venture capital firm, startup acquisition by big firms where latestage assessments are determined by the potential acquirer, multiround job interviews where the candidates signal initially by presenting their qualifications but the rest of the screening procedures are determined by the interviewer. The nondetermined experiments (signals) in the multiphase trial are to be chosen by the sender in order to persuade the receiver best. With a binary state of the world, we start by deriving the optimal signaling policy in the only nontrivial configuration of a twophase trial with binaryoutcome experiments. We then generalize to multiphase trials with binaryoutcome experiments where the determined experiments can be placed at any chosen node in the trial tree. Here we present a dynamic programming algorithm to derive the optimal signaling policy that uses the twophase trial solution's structural insights. We also contrast the optimal signaling policy structure with classical Bayesian persuasion strategies to highlight the impact of the signaling constraints on the sender.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.09594
 Bibcode:
 2021arXiv211009594S
 Keywords:

 Economics  Theoretical Economics;
 Computer Science  Computer Science and Game Theory
 EPrint:
 This is a cameraready version of the 17th conference on web and internet economics (WINE 2021)