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 4.3 Multi-phase model and classical Bayesian persuasion Note that the pruned tree will potentially be unbalanced. Lemma 7. Given an N-phase trial M with binary-outcome experiments, if there exists a pruned N-phase trial model P run(M) such that the following two conditions hold, then the sender’s expected utility is given by an equivalent single-phase Bayesian persuasion model. For every non-trivial determined experiment, its sibling is either a trivial or a sender-designed experiment.


There exists a least one sender-designed experiment in each (from root to leaf) experiment sequence of P run(M). References Au, P.H.: Dynamic information disclosure. The RAND Journal of Economics 46(4), 791–823 (2015)


Basu, D.: Statistical information and likelihood [with discussion]. Sankhy¯a: The Indian Journal of Statistics, Series A pp. 1–71 (1975)


Bergemann, D., Morris, S.: Information design: A unified perspective. Journal of Economic Literature 57(1), 44–95 (2019)


Bizzotto, J., R¨udiger, J., Vigier, A.: Dynamic persuasion with outside information. American Economic Journal: Microeconomics 13(1), 179–94 (2021)


Bizzotto, J., Vigier, A.: Can a better informed listener be easier to persuade? Economic Theory 72(3), 705–721 (2021)


Blackwell, D.: Equivalent comparisons of experiments. The annals of mathematical statistics pp. 265–272 (1953)


Dughmi, S., Kempe, D., Qiang, R.: Persuasion with limited communication. In: Proceedings of the 2016 ACM Conference on Economics and Computation. pp. 663–680 (2016)


Dughmi, S., Xu, H.: Algorithmic Bayesian persuasion. SIAM Journal on Computing 50(3), 68–97 (2019)


Ely, J.C.: Beeps. American Economic Review 107(1), 31–53 (2017)


Ely, J.C., Szydlowski, M.: Moving the goalposts. Journal of Political Economy 128(2), 468–506 (2020)


Farhadi, F., Teneketzis, D.: Dynamic information design: A simple problem on optimal sequential information disclosure. Available at SSRN 3554960 (2020)


Forges, F., Koessler, F.: Long persuasion games. Journal of Economic Theory 143(1), 1–35 (2008)


Gradwohl, R., Hahn, N., Hoefer, M., Smorodinsky, R.: Algorithms for persuasion with limited communication. In: Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA). pp. 637–652. SIAM (2021)


Honryo, T.: Dynamic persuasion. Journal of Economic Theory 178, 36–58 (2018)


Kamenica, E.: Bayesian persuasion and information design. Annual Review of Economics 11, 249 272 (2019)


Kamenica, E., Gentzkow, M.: Bayesian persuasion. American Economic Review 101(6), 2590–2615 (2011)


Kolotilin, A., Mylovanov, T., Zapechelnyuk, A., Li, M.: Persuasion of a privately informed receiver. Econometrica 85(6), 1949–1964 (2017)


Le Treust, M., Tomala, T.: Persuasion with limited communication capacity. Journal of Economic Theory 184, 104940 (2019)


Li, F., Norman, P.: On Bayesian persuasion with multiple senders. Economics Letters 170, 66–70 (2018)


Li, J., Zhou, J.: Blackwell’s informativeness ranking with uncertainty-averse preferences. Games and Economic Behavior 96, 18–29 (2016)


Meigs, E., Parise, F., Ozdaglar, A., Acemoglu, D.: Optimal dynamic information provision in traffic routing. arXiv preprint arXiv:2001.03232 (2020)


Nguyen, A., Tan, T.Y.: Bayesian persuasion with costly messages. Available at SSRN 3298275 (2019)


Su, S.T., Subramanian, V., Schoenebeck, G.: Bayesian persuasion in sequential trials. arXiv preprint arXiv:2110.09594 (2021) 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 4.3 Multi-phase model and classical Bayesian persuasion Note that the pruned tree will potentially be unbalanced. Lemma 7. Given an N-phase trial M with binary-outcome experiments, if there exists a pruned N-phase trial model P run(M) such that the following two conditions hold, then the sender’s expected utility is given by an equivalent single-phase Bayesian persuasion model. Lemma 7. Given an N-phase trial M with binary-outcome experiments, if there exists a pruned N-phase trial model P run(M) such that the following two conditions hold, then the sender’s expected utility is given by an equivalent single-phase Bayesian persuasion model. For every non-trivial determined experiment, its sibling is either a trivial or a sender-designed experiment. There exists a least one sender-designed experiment in each (from root to leaf) experiment sequence of P run(M). For every non-trivial determined experiment, its sibling is either a trivial or a sender-designed experiment. For every non-trivial determined experiment, its sibling is either a trivial or a sender-designed experiment. For every non-trivial determined experiment, its sibling is either a trivial or a sender-designed experiment. There exists a least one sender-designed experiment in each (from root to leaf) experiment sequence of P run(M). There exists a least one sender-designed experiment in each (from root to leaf) experiment sequence of P run(M). There exists a least one sender-designed experiment in each (from root to leaf) experiment sequence of P run(M). References Au, P.H.: Dynamic information disclosure. The RAND Journal of Economics 46(4), 791–823 (2015) Basu, D.: Statistical information and likelihood [with discussion]. Sankhy¯a: The Indian Journal of Statistics, Series A pp. 1–71 (1975) Bergemann, D., Morris, S.: Information design: A unified perspective. Journal of Economic Literature 57(1), 44–95 (2019) Bizzotto, J., R¨udiger, J., Vigier, A.: Dynamic persuasion with outside information. American Economic Journal: Microeconomics 13(1), 179–94 (2021) Bizzotto, J., Vigier, A.: Can a better informed listener be easier to persuade? Economic Theory 72(3), 705–721 (2021) Blackwell, D.: Equivalent comparisons of experiments. The annals of mathematical statistics pp. 265–272 (1953) Dughmi, S., Kempe, D., Qiang, R.: Persuasion with limited communication. In: Proceedings of the 2016 ACM Conference on Economics and Computation. pp. 663–680 (2016) Dughmi, S., Xu, H.: Algorithmic Bayesian persuasion. SIAM Journal on Computing 50(3), 68–97 (2019) Ely, J.C.: Beeps. American Economic Review 107(1), 31–53 (2017) Ely, J.C., Szydlowski, M.: Moving the goalposts. Journal of Political Economy 128(2), 468–506 (2020) Farhadi, F., Teneketzis, D.: Dynamic information design: A simple problem on optimal sequential information disclosure. Available at SSRN 3554960 (2020) Forges, F., Koessler, F.: Long persuasion games. Journal of Economic Theory 143(1), 1–35 (2008) Gradwohl, R., Hahn, N., Hoefer, M., Smorodinsky, R.: Algorithms for persuasion with limited communication. In: Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA). pp. 637–652. SIAM (2021) Honryo, T.: Dynamic persuasion. Journal of Economic Theory 178, 36–58 (2018) Kamenica, E.: Bayesian persuasion and information design. Annual Review of Economics 11, 249 272 (2019) Kamenica, E., Gentzkow, M.: Bayesian persuasion. American Economic Review 101(6), 2590–2615 (2011) Kolotilin, A., Mylovanov, T., Zapechelnyuk, A., Li, M.: Persuasion of a privately informed receiver. Econometrica 85(6), 1949–1964 (2017) Le Treust, M., Tomala, T.: Persuasion with limited communication capacity. Journal of Economic Theory 184, 104940 (2019) Li, F., Norman, P.: On Bayesian persuasion with multiple senders. Economics Letters 170, 66–70 (2018) Li, J., Zhou, J.: Blackwell’s informativeness ranking with uncertainty-averse preferences. Games and Economic Behavior 96, 18–29 (2016) Meigs, E., Parise, F., Ozdaglar, A., Acemoglu, D.: Optimal dynamic information provision in traffic routing. arXiv preprint arXiv:2001.03232 (2020) Nguyen, A., Tan, T.Y.: Bayesian persuasion with costly messages. Available at SSRN 3298275 (2019) Su, S.T., Subramanian, V., Schoenebeck, G.: Bayesian persuasion in sequential trials. arXiv preprint arXiv:2110.09594 (2021) Au, P.H.: Dynamic information disclosure. The RAND Journal of Economics 46(4), 791–823 (2015) Au, P.H.: Dynamic information disclosure. The RAND Journal of Economics 46(4), 791–823 (2015) Basu, D.: Statistical information and likelihood [with discussion]. Sankhy¯a: The Indian Journal of Statistics, Series A pp. 1–71 (1975) Basu, D.: Statistical information and likelihood [with discussion]. Sankhy¯a: The Indian Journal of Statistics, Series A pp. 1–71 (1975) Bergemann, D., Morris, S.: Information design: A unified perspective. Journal of Economic Literature 57(1), 44–95 (2019) Bergemann, D., Morris, S.: Information design: A unified perspective. Journal of Economic Literature 57(1), 44–95 (2019) Bizzotto, J., R¨udiger, J., Vigier, A.: Dynamic persuasion with outside information. American Economic Journal: Microeconomics 13(1), 179–94 (2021) Bizzotto, J., R¨udiger, J., Vigier, A.: Dynamic persuasion with outside information. American Economic Journal: Microeconomics 13(1), 179–94 (2021) Bizzotto, J., Vigier, A.: Can a better informed listener be easier to persuade? Economic Theory 72(3), 705–721 (2021) Bizzotto, J., Vigier, A.: Can a better informed listener be easier to persuade? Economic Theory 72(3), 705–721 (2021) Blackwell, D.: Equivalent comparisons of experiments. The annals of mathematical statistics pp. 265–272 (1953) Blackwell, D.: Equivalent comparisons of experiments. The annals of mathematical statistics pp. 265–272 (1953) Dughmi, S., Kempe, D., Qiang, R.: Persuasion with limited communication. In: Proceedings of the 2016 ACM Conference on Economics and Computation. pp. 663–680 (2016) Dughmi, S., Kempe, D., Qiang, R.: Persuasion with limited communication. In: Proceedings of the 2016 ACM Conference on Economics and Computation. pp. 663–680 (2016) Dughmi, S., Xu, H.: Algorithmic Bayesian persuasion. SIAM Journal on Computing 50(3), 68–97 (2019) Dughmi, S., Xu, H.: Algorithmic Bayesian persuasion. SIAM Journal on Computing 50(3), 68–97 (2019) Ely, J.C.: Beeps. American Economic Review 107(1), 31–53 (2017) Ely, J.C.: Beeps. American Economic Review 107(1), 31–53 (2017) Ely, J.C., Szydlowski, M.: Moving the goalposts. Journal of Political Economy 128(2), 468–506 (2020) Ely, J.C., Szydlowski, M.: Moving the goalposts. Journal of Political Economy 128(2), 468–506 (2020) Farhadi, F., Teneketzis, D.: Dynamic information design: A simple problem on optimal sequential information disclosure. Available at SSRN 3554960 (2020) Farhadi, F., Teneketzis, D.: Dynamic information design: A simple problem on optimal sequential information disclosure. Available at SSRN 3554960 (2020) Forges, F., Koessler, F.: Long persuasion games. Journal of Economic Theory 143(1), 1–35 (2008) Forges, F., Koessler, F.: Long persuasion games. Journal of Economic Theory 143(1), 1–35 (2008) Gradwohl, R., Hahn, N., Hoefer, M., Smorodinsky, R.: Algorithms for persuasion with limited communication. In: Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA). pp. 637–652. SIAM (2021) Gradwohl, R., Hahn, N., Hoefer, M., Smorodinsky, R.: Algorithms for persuasion with limited communication. In: Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA). pp. 637–652. SIAM (2021) Honryo, T.: Dynamic persuasion. Journal of Economic Theory 178, 36–58 (2018) Honryo, T.: Dynamic persuasion. Journal of Economic Theory 178, 36–58 (2018) Kamenica, E.: Bayesian persuasion and information design. Annual Review of Economics 11, 249 272 (2019) Kamenica, E.: Bayesian persuasion and information design. Annual Review of Economics 11, 249 272 (2019) Kamenica, E., Gentzkow, M.: Bayesian persuasion. American Economic Review 101(6), 2590–2615 (2011) Kamenica, E., Gentzkow, M.: Bayesian persuasion. American Economic Review 101(6), 2590–2615 (2011) Kolotilin, A., Mylovanov, T., Zapechelnyuk, A., Li, M.: Persuasion of a privately informed receiver. Econometrica 85(6), 1949–1964 (2017) Kolotilin, A., Mylovanov, T., Zapechelnyuk, A., Li, M.: Persuasion of a privately informed receiver. Econometrica 85(6), 1949–1964 (2017) Le Treust, M., Tomala, T.: Persuasion with limited communication capacity. Journal of Economic Theory 184, 104940 (2019) Le Treust, M., Tomala, T.: Persuasion with limited communication capacity. Journal of Economic Theory 184, 104940 (2019) Li, F., Norman, P.: On Bayesian persuasion with multiple senders. Economics Letters 170, 66–70 (2018) Li, F., Norman, P.: On Bayesian persuasion with multiple senders. Economics Letters 170, 66–70 (2018) Li, J., Zhou, J.: Blackwell’s informativeness ranking with uncertainty-averse preferences. Games and Economic Behavior 96, 18–29 (2016) Li, J., Zhou, J.: Blackwell’s informativeness ranking with uncertainty-averse preferences. Games and Economic Behavior 96, 18–29 (2016) Meigs, E., Parise, F., Ozdaglar, A., Acemoglu, D.: Optimal dynamic information provision in traffic routing. arXiv preprint arXiv:2001.03232 (2020) Meigs, E., Parise, F., Ozdaglar, A., Acemoglu, D.: Optimal dynamic information provision in traffic routing. arXiv preprint arXiv:2001.03232 (2020) Nguyen, A., Tan, T.Y.: Bayesian persuasion with costly messages. Available at SSRN 3298275 (2019) Nguyen, A., Tan, T.Y.: Bayesian persuasion with costly messages. Available at SSRN 3298275 (2019) Su, S.T., Subramanian, V., Schoenebeck, G.: Bayesian persuasion in sequential trials. arXiv preprint arXiv:2110.09594 (2021) Su, S.T., Subramanian, V., Schoenebeck, G.: Bayesian persuasion in sequential trials. arXiv preprint arXiv:2110.09594 (2021) 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

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Generalizing Signaling Strategies in Multi-phase Trials

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