Bayesian Persuasion in Sequential Trials: Assumptions and induced strategies

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 3.2 Assumptions and induced strategies Next we detail the optimal signaling strategy in our two-phase trial setting with general binary-outcome experiments. To aid in the presentation and to avoid repetition, we make two assumptions without loss of generality and introduce several explanatory concepts before the analysis. Lemma 2. We can make the following two assumptions WLOG. The sender’s strategy consists of the following: choice of phase-I experiment parameters (p1, p2) and the persuasion strategies in phase-II for each outcome of the phase-I experiment. To understand better the choices available to the sender and her reasoning in determining her best strategy, we will study the possible persuasion strategies in phase-II; these will be called induced strategies to distinguish them from the entire strategy. Given the assumptions above on phase-II experiments, it’ll turn out we can directly rule out one class of induced strategies from the sender’s consideration. The other set of induced strategies will need careful assessment that we present next. This paper is available on arxiv under CC 4.0 license. [3] In terms of the Blackwell informativeness from [6]. 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 3.2 Assumptions and induced strategies Next we detail the optimal signaling strategy in our two-phase trial setting with general binary-outcome experiments. To aid in the presentation and to avoid repetition, we make two assumptions without loss of generality and introduce several explanatory concepts before the analysis. Lemma 2. We can make the following two assumptions WLOG. Lemma 2. We can make the following two assumptions WLOG. The sender’s strategy consists of the following: choice of phase-I experiment parameters (p1, p2) and the persuasion strategies in phase-II for each outcome of the phase-I experiment. To understand better the choices available to the sender and her reasoning in determining her best strategy, we will study the possible persuasion strategies in phase-II; these will be called induced strategies to distinguish them from the entire strategy. Given the assumptions above on phase-II experiments, it’ll turn out we can directly rule out one class of induced strategies from the sender’s consideration. The other set of induced strategies will need careful assessment that we present next. 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 [3] In terms of the Blackwell informativeness from [6].