How Optimal Signaling Outperforms Classical Bayesian Strategies in Multi-Phase 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 3.5 Comparison with classical Bayesian persuasion strategies Given the optimal signaling strategy derived in Lemma 5, one natural followup question is the quantification of the sender’s utility improvement obtained by adopting the optimal signaling strategy in comparison to using strategies structurally similar to the optimal strategies in classical Bayesian persuasion for a binary state of the world. Owing the page limit, we directly define a class of strategies structurally similar to the classical Bayesian persuasion strategy below and provide the justification in our online version [23]. Definition 4. With binary states of the world, a (binary-state) Bayesian persuasion (BBP) strategy is a strategy that “mixes two possible states in one signal and reveals the true state on the other signal”. 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 3.5 Comparison with classical Bayesian persuasion strategies Given the optimal signaling strategy derived in Lemma 5, one natural followup question is the quantification of the sender’s utility improvement obtained by adopting the optimal signaling strategy in comparison to using strategies structurally similar to the optimal strategies in classical Bayesian persuasion for a binary state of the world. Owing the page limit, we directly define a class of strategies structurally similar to the classical Bayesian persuasion strategy below and provide the justification in our online version [23]. Definition 4. With binary states of the world, a (binary-state) Bayesian persuasion (BBP) strategy is a strategy that “mixes two possible states in one signal and reveals the true state on the other signal”. Definition 4. With binary states of the world, a (binary-state) Bayesian persuasion (BBP) strategy is a strategy that “mixes two possible states in one signal and reveals the true state on the other signal”. 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