Document Open Access Logo

Algorithmic Persuasion with Evidence

Authors Martin Hoefer , Pasin Manurangsi , Alexandros Psomas

PDF
Thumbnail PDF

File

LIPIcs.ITCS.2021.3.pdf
  • Filesize: 0.59 MB
  • 20 pages

Document Identifiers

Author Details

Martin Hoefer
  • Goethe Universitä Frankfurt, Germany
Pasin Manurangsi
  • Google Research, Mountain View, CA, USA
Alexandros Psomas
  • Purdue University, West Lafayette, IN, USA

Funding

  • Hoefer, Martin: GIF grant I-1419-118.4/2017 and DFG grants Ho 3831/5-1, 6-1, and 7-1.

Acknowledgements

This work was done in part while Martin Hoefer and Alexandros Psomas were visiting the Simons Institute for the Theory of Computing. The authors acknowledge financial support and the invitation by the organizers to join the stimulating work environment. This work was done in part while Alexandros Psomas was visiting Google Research, Mountain View, USA.

Cite AsGet BibTex

Martin Hoefer, Pasin Manurangsi, and Alexandros Psomas. Algorithmic Persuasion with Evidence. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 3:1-3:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.ITCS.2021.3

Abstract

We consider a game of persuasion with evidence between a sender and a receiver. The sender has private information. By presenting evidence on the information, the sender wishes to persuade the receiver to take a single action (e.g., hire a job candidate, or convict a defendant). The sender’s utility depends solely on whether or not the receiver takes the action. The receiver’s utility depends on both the action as well as the sender’s private information. We study three natural variations. First, we consider sequential equilibria of the game without commitment power. Second, we consider a persuasion variant, where the sender commits to a signaling scheme and then the receiver, after seeing the evidence, takes the action or not. Third, we study a delegation variant, where the receiver first commits to taking the action if being presented certain evidence, and then the sender presents evidence to maximize the probability the action is taken. We study these variants through the computational lens, and give hardness results, optimal approximation algorithms, as well as polynomial-time algorithms for special cases. Among our results is an approximation algorithm that rounds a semidefinite program that might be of independent interest, since, to the best of our knowledge, it is the first such approximation algorithm for a natural problem in algorithmic economics.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic game theory and mechanism design
  • Theory of computation → Approximation algorithms analysis
Keywords
  • Bayesian Persuasion
  • Semidefinite Programming
  • Approximation Algorithms

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Related Versions

References

  1. Farid Alizadeh. Interior point methods in semidefinite programming with applications to combinatorial optimization. SIAM J. Opt., 5(1):13-51, 1995. Google Scholar
  2. Per Austrin. Balanced MAX 2-SAT might not be the hardest. In Proc. 39th Symp. Theor. Comput. (STOC), pages 189-197, 2007. Google Scholar
  3. Per Austrin. Towards sharp inapproximability for any 2-CSP. SIAM J. Comput., 39(6):2430-2463, 2010. Google Scholar
  4. Jesse Bull and Joel Watson. Hard evidence and mechanism design. Games Econom. Behav., 58:75-–93, 2007. Google Scholar
  5. Gabriel Carroll and Georgy Egorov. Strategic communication with minimal verification. Econometrica, 87(6):1867-1892, 2019. Google Scholar
  6. Shaddin Dughmi. On the hardness of designing public signals. Games Econom. Behav., 118:609-625, 2019. Google Scholar
  7. Shaddin Dughmi, David Kempe, and Ruixin Qiang. Persuasion with limited communication. In Proc. 17th Conf. Economics and Computation (EC), pages 663-680, 2016. Google Scholar
  8. Shaddin Dughmi, Rad Niazadeh, Alexandros Psomas, and Matthew Weinberg. Persuasion and incentives through the lens of duality. In Proc. 15th Int. Conf. Web & Internet Econom. (WINE), pages 142-155, 2019. Google Scholar
  9. Shaddin Dughmi and Haifeng Xu. Algorithmic Bayesian persuasion. In Proc. 48th Symp. Theor. Comput. (STOC), pages 412-425, 2016. Google Scholar
  10. Shaddin Dughmi and Haifeng Xu. Algorithmic persuasion with no externalities. In Proc. 18th Conf. Economics and Computation (EC), pages 351-368, 2017. Google Scholar
  11. Yuval Emek, Michal Feldman, Iftah Gamzu, Renato PaesLeme, and Moshe Tennenholtz. Signaling schemes for revenue maximization. ACM Trans. Econom. Comput., 2(2):1-19, 2014. Google Scholar
  12. Uriel Feige and Michel Goemans. Approximating the value of two power proof systems, with applications to MAX 2-SAT and MAX DI-CUT. In Proc. 3rd Israel Symp. Theor. Comput. Syst., pages 182-189, 1995. Google Scholar
  13. Jacob Glazer and Ariel Rubinstein. On optimal rules of persuasion. Econometrica, 72(6):1715-1736, 2004. Google Scholar
  14. Jacob Glazer and Ariel Rubinstein. A study in the pragmatics of persuasion: a game theoretical approach. Theor. Econom., 1(4):395-410, 2006. Google Scholar
  15. Michel Goemans and David Williamson. .879-approximation algorithms for MAX CUT and MAX 2SAT. In Proc. 26th Symp. Theor. Comput. (STOC), pages 422-431, 1994. Google Scholar
  16. Ronen Gradwohl, Niklas Hahn, Martin Hoefer, and Rann Smorodinsky. Algorithms for persuasion with limited communication, 2020. CoRR abs/2007.12489. URL: http://arxiv.org/abs/2007.12489.
  17. Niklas Hahn, Martin Hoefer, and Rann Smorodinsky. Prophet inequalities for bayesian persuasion. In Proc. 29th Int. Joint Conf. Artificial Intelligence (IJCAI), pages 175-181, 2020. Google Scholar
  18. Niklas Hahn, Martin Hoefer, and Rann Smorodinsky. The secretary recommendation problem. In Proc. 21st Conf. Economics and Computation (EC), page 189, 2020. Google Scholar
  19. Emir Kamenica and Matthew Gentzkow. Bayesian persuasion. Amer. Econom. Rev., 101(6):2590-2615, 2011. Google Scholar
  20. Subhash Khot and Rishi Saket. Hardness of bipartite expansion. In Proc. 24th European Symp. Algorithms (ESA), pages 55:1-55:17, 2016. Google Scholar
  21. Michael Lewin, Dror Livnat, and Uri Zwick. Improved rounding techniques for the MAX 2-SAT and MAX DI-CUT problems. In Int. Conf. Integer Prog. Combinat. Opt. (IPCO), pages 67-82, 2002. Google Scholar
  22. Prasad Raghavendra. Optimal algorithms and inapproximability results for every CSP? In Proc. 40th Symp. Theor. Comput. (STOC), pages 245-254, 2008. Google Scholar
  23. Prasad Raghavendra and David Steurer. How to round any CSP. In Proc. 50th Symp. Foundations of Computer Science (FOCS), pages 586-594, 2009. Google Scholar
  24. Itai Sher. Credibility and determinism in a game of persuasion. Games Econom. Behav., 71(2):409-419, 2011. Google Scholar
  25. Itai Sher. Persuasion and dynamic communication. Theor. Econom., 9(1):99-136, 2014. Google Scholar
  26. Henrik Sjögren. Rigorous analysis of approximation algorithms for MAX 2-CSP. Skolan för datavetenskap och kommunikation, Kungliga Tekniska högskolan, 2009. Google Scholar
  27. Joel Sobel. Giving and receiving advice. Adv. Econom. Econometrics, 1:305-341, 2013. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact