Formulating Optimal Signaling Strategies in Constrained Bayesian Persuasion Trials

Authors: (1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu); (2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu); (3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Table of Links Abstract and 1. Introduction 2. Problem Formulation 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3.2 Assumptions and induced strategies 3.3 Constraints given by phase-II experiments 3.4 Persuasion ratio and the optimal signaling structure 3.5 Comparison with classical Bayesian persuasion strategies 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4.2 Determined versus sender-designed experiments 4.3 Multi-phase model and classical Bayesian persuasion and References 2 Problem Formulation Before the receiver takes his action, a trial consisting of multiple phases will be run, and the outcome in each phase will be revealed to him. In each phase, one experiment will be conducted, which is chosen according to the outcomes in earlier phases. Hence, the experiment outcomes in earlier phases not only affect the interim belief but also influence the possible (sequence of) experiments that will be conducted afterward. In the most sender-friendly setup where the sender can choose any experiment in each phase without any constraints, the problem is equivalent to the classical Bayesian persuasion problem with an enlarged signal space. However, when some experiments are pre-determined conditional on a set of outcomes, the sender must take these constraints into account to design her optimal signaling structure. To present our results on the influence of multiple phases on the sender’s signaling strategy, we start with a model of two-phase trials with binary-outcome experiments in the rest of this section. We then analyze the optimal signaling strategy of this model in Section 3. After that, we will introduce the general model of multiple-phase trials with binary-outcome experiments and propose a systematic approach to analyze the optimal signaling structure in Section 4. This paper is available on arxiv under CC 4.0 license. Authors: (1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu); (2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu); (3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Authors: Authors: (1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu); (2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu); (3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2. Problem Formulation 2. Problem Formulation 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3.2 Assumptions and induced strategies 3.2 Assumptions and induced strategies 3.3 Constraints given by phase-II experiments 3.3 Constraints given by phase-II experiments 3.4 Persuasion ratio and the optimal signaling structure 3.4 Persuasion ratio and the optimal signaling structure 3.5 Comparison with classical Bayesian persuasion strategies 3.5 Comparison with classical Bayesian persuasion strategies 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4.2 Determined versus sender-designed experiments 4.2 Determined versus sender-designed experiments 4.3 Multi-phase model and classical Bayesian persuasion and References 4.3 Multi-phase model and classical Bayesian persuasion and References 2 Problem Formulation Before the receiver takes his action, a trial consisting of multiple phases will be run, and the outcome in each phase will be revealed to him. In each phase, one experiment will be conducted, which is chosen according to the outcomes in earlier phases. Hence, the experiment outcomes in earlier phases not only affect the interim belief but also influence the possible (sequence of) experiments that will be conducted afterward. In the most sender-friendly setup where the sender can choose any experiment in each phase without any constraints, the problem is equivalent to the classical Bayesian persuasion problem with an enlarged signal space. However, when some experiments are pre-determined conditional on a set of outcomes, the sender must take these constraints into account to design her optimal signaling structure. To present our results on the influence of multiple phases on the sender’s signaling strategy, we start with a model of two-phase trials with binary-outcome experiments in the rest of this section. We then analyze the optimal signaling strategy of this model in Section 3. After that, we will introduce the general model of multiple-phase trials with binary-outcome experiments and propose a systematic approach to analyze the optimal signaling structure in Section 4. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv