Generalizing Signaling Strategies in Multi-phase Trials

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.

1. For every non-trivial determined experiment, its sibling is either a trivial or a sender-designed experiment.

   
   

2. There exists a least one sender-designed experiment in each (from root to leaf) experiment sequence of P run(M).

References

1. Au, P.H.: Dynamic information disclosure. The RAND Journal of Economics 46(4), 791–823 (2015)

   
   

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

   
   

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

   
   

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

   
   

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

   
   

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

   
   

7. 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)

   
   

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

   
   

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

   
   

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

    
    

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

    
    

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

13. 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)

    
    

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

    
    

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

    
    

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

    
    

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

    
    

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

    
    

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

    
    

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

    
    

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

    
    

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

    
    

23. Su, S.T., Subramanian, V., Schoenebeck, G.: Bayesian persuasion in sequential trials. arXiv preprint arXiv:2110.09594 (2021)