IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v212y2023ics0022053123000868.html
   My bibliography  Save this article

Derandomization of persuasion mechanisms

Author

Listed:
  • Zeng, Yishu

Abstract

We consider a setting where one sender can communicate with several privately informed receivers through a persuasion mechanism before the receivers play a game. We show that for any potentially randomized persuasion mechanism, under certain conditions, there is an effectively equivalent deterministic persuasion mechanism, and these two mechanisms have the same set of equilibria. We exhibit the usefulness of our result in an information disclosure application, where our technique helps to derive the optimal persuasion mechanism. Overall, this paper provides a rationale for the fact that persuasion mechanisms are often deterministic in practice.

Suggested Citation

  • Zeng, Yishu, 2023. "Derandomization of persuasion mechanisms," Journal of Economic Theory, Elsevier, vol. 212(C).
    • Handle: RePEc:eee:jetheo:v:212:y:2023:i:c:s0022053123000868
    DOI: 10.1016/j.jet.2023.105690
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022053123000868
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jet.2023.105690?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Gentzkow, Matthew & Kamenica, Emir, 2017. "Bayesian persuasion with multiple senders and rich signal spaces," Games and Economic Behavior, Elsevier, vol. 104(C), pages 411-429.
    2. Bergemann, Dirk & Morris, Stephen, 2016. "Bayes correlated equilibrium and the comparison of information structures in games," Theoretical Economics, Econometric Society, vol. 11(2), May.
    3. Dirk Bergemann & Stephen Morris, 2019. "Information Design: A Unified Perspective," Journal of Economic Literature, American Economic Association, vol. 57(1), pages 44-95, March.
    4. He, Wei & Sun, Yeneng, 2019. "Pure-strategy equilibria in Bayesian games," Journal of Economic Theory, Elsevier, vol. 180(C), pages 11-49.
    5. Emir Kamenica & Matthew Gentzkow, 2011. "Bayesian Persuasion," American Economic Review, American Economic Association, vol. 101(6), pages 2590-2615, October.
    6. Khan, M. Ali & Zhang, Yongchao, 2014. "On the existence of pure-strategy equilibria in games with private information: A complete characterization," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 197-202.
    7. Anton Kolotilin & Tymofiy Mylovanov & Andriy Zapechelnyuk & Ming Li, 2017. "Persuasion of a Privately Informed Receiver," Econometrica, Econometric Society, vol. 85(6), pages 1949-1964, November.
    8. Kolotilin, Anton, 2018. "Optimal information disclosure: a linear programming approach," Theoretical Economics, Econometric Society, vol. 13(2), May.
    9. Arieli, Itai & Babichenko, Yakov & Smorodinsky, Rann & Yamashita, Takuro, 2023. "Optimal persuasion via bi-pooling," Theoretical Economics, Econometric Society, vol. 18(1), January.
    10. Dworczak, Piotr & Kolotilin, Anton, 2024. "The persuasion duality," Theoretical Economics, Econometric Society, vol. 19(4), November.
    11. Khan, M. Ali & Yeneng, Sun, 1995. "Pure strategies in games with private information," Journal of Mathematical Economics, Elsevier, vol. 24(7), pages 633-653.
    12. Andreas Kleiner & Benny Moldovanu & Philipp Strack, 2021. "Extreme Points and Majorization: Economic Applications," Econometrica, Econometric Society, vol. 89(4), pages 1557-1593, July.
    13. Liu, Heng, 2018. "Efficient dynamic mechanisms in environments with interdependent valuations: the role of contingent transfers," Theoretical Economics, Econometric Society, vol. 13(2), May.
    14. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    15. Luis Rayo & Ilya Segal, 2010. "Optimal Information Disclosure," Journal of Political Economy, University of Chicago Press, vol. 118(5), pages 949-987.
    16. M. Khan & Kali Rath & Yeneng Sun, 2006. "The Dvoretzky-Wald-Wolfowitz theorem and purification in atomless finite-action games," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(1), pages 91-104, April.
    17. Roy Radner & Robert W. Rosenthal, 1982. "Private Information and Pure-Strategy Equilibria," Mathematics of Operations Research, INFORMS, vol. 7(3), pages 401-409, August.
    18. Khan, M. Ali & Rath, Kali P., 2009. "On games with incomplete information and the Dvoretsky-Wald-Wolfowitz theorem with countable partitions," Journal of Mathematical Economics, Elsevier, vol. 45(12), pages 830-837, December.
    19. Myerson, Roger B., 1982. "Optimal coordination mechanisms in generalized principal-agent problems," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 67-81, June.
    20. Konrad Podczeck, 2009. "On purification of measure-valued maps," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 399-418, February.
    21. Myerson, Roger B, 1986. "Multistage Games with Communication," Econometrica, Econometric Society, vol. 54(2), pages 323-358, March.
    22. Yingni Guo & Eran Shmaya, 2019. "The Interval Structure of Optimal Disclosure," Econometrica, Econometric Society, vol. 87(2), pages 653-675, March.
    23. Paul R. Milgrom & Robert J. Weber, 1985. "Distributional Strategies for Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 619-632, November.
    24. Matthew Gentzkow & Emir Kamenica, 2016. "A Rothschild-Stiglitz Approach to Bayesian Persuasion," American Economic Review, American Economic Association, vol. 106(5), pages 597-601, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ozan Candogan & Philipp Strack, 2021. "Optimal Disclosure of Information to a Privately Informed Receiver," Papers 2101.10431, arXiv.org, revised Jan 2022.
    2. Eduardo Perez‐Richet & Vasiliki Skreta, 2022. "Test Design Under Falsification," Econometrica, Econometric Society, vol. 90(3), pages 1109-1142, May.
    3. Chan, Jimmy & Gupta, Seher & Li, Fei & Wang, Yun, 2019. "Pivotal persuasion," Journal of Economic Theory, Elsevier, vol. 180(C), pages 178-202.
      • Jimmy Chan & Seher Gupta & Fei Li & Yun Wang, 2018. "Pivotal Persuasion," Working Papers 2018-11-03, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    4. Lily Ling Yang, 2024. "Information Design with Costly State Verifi cation," CRC TR 224 Discussion Paper Series crctr224_2024_502, University of Bonn and University of Mannheim, Germany.
    5. Dirk Bergemann & Stephen Morris, 2019. "Information Design: A Unified Perspective," Journal of Economic Literature, American Economic Association, vol. 57(1), pages 44-95, March.
    6. Anton Kolotilin & Andriy Zapechelnyuk, 2018. "Persuasion Meets Delegation," Discussion Papers 2018-06, School of Economics, The University of New South Wales.
    7. Anton Kolotilin & Alexander Wolitzky, 2020. "Assortative Information Disclosure," Discussion Papers 2020-08, School of Economics, The University of New South Wales.
    8. Whitmeyer, Joseph & Whitmeyer, Mark, 2021. "Mixtures of mean-preserving contractions," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    9. Kolotilin, Anton & Li, Hongyi, 2021. "Relational communication," Theoretical Economics, Econometric Society, vol. 16(4), November.
    10. Grant, Simon & Meneghel, Idione & Tourky, Rabee, 2016. "Savage games," Theoretical Economics, Econometric Society, vol. 11(2), May.
    11. Wei He & Xiang Sun & Yeneng Sun & Yishu Zeng, 2021. "Characterization of equilibrium existence and purification in general Bayesian games," Papers 2106.08563, arXiv.org.
    12. Khan, M. Ali & Zhang, Yongchao, 2014. "On the existence of pure-strategy equilibria in games with private information: A complete characterization," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 197-202.
    13. Grant, Simon & Meneghel, Idione & Tourky, Rabee, 2013. "Savage Games: A Theory of Strategic Interaction with Purely Subjective Uncertainty," Risk and Sustainable Management Group Working Papers 151501, University of Queensland, School of Economics.
    14. Beißner, Patrick & Khan, M. Ali, 2019. "On Hurwicz–Nash equilibria of non-Bayesian games under incomplete information," Games and Economic Behavior, Elsevier, vol. 115(C), pages 470-490.
    15. Maryam Saeedi & Ali Shourideh, 2020. "Optimal Rating Design under Moral Hazard," Papers 2008.09529, arXiv.org, revised Jul 2023.
    16. Carroll, Gabriel, 2016. "Informationally robust trade and limits to contagion," Journal of Economic Theory, Elsevier, vol. 166(C), pages 334-361.
    17. Lyu, Chen, 2023. "Information design for selling search goods and the effect of competition," Journal of Economic Theory, Elsevier, vol. 213(C).
    18. Tsakas, Elias & Tsakas, Nikolas, 2021. "Noisy persuasion," Games and Economic Behavior, Elsevier, vol. 130(C), pages 44-61.
    19. Khan, M. Ali & Rath, Kali P. & Sun, Yeneng & Yu, Haomiao, 2013. "Large games with a bio-social typology," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1122-1149.
    20. He, Wei & Sun, Xiang, 2014. "On the diffuseness of incomplete information game," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 131-137.

    More about this item

    Keywords

    Derandomization; Persuasion mechanism; Bayesian persuasion; Information design;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jetheo:v:212:y:2023:i:c:s0022053123000868. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.