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Constrained Information Design

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  • Laura Doval
  • Vasiliki Skreta

Abstract

We provide tools to analyze information design problems subject to constraints. We do so by extending the insight in Le Treust and Tomala (2019) to the case of multiple inequality and equality constraints. Namely, that an information design problem subject to constraints can be represented as an unconstrained information design problem with a additional states, one for each constraint. Thus, without loss of generality, optimal solutions induce as many posteriors as the number of states and constraints. We provide results that refine this upper bound. Furthermore, we provide conditions under which there is no duality gap in constrained information design, thus validating a Lagrangian approach. We illustrate our results with applications to mechanism design with limited commitment (Doval and Skreta, 2022a) and persuasion of a privately informed receiver (Kolotilin et al., 2017).

Suggested Citation

  • Laura Doval & Vasiliki Skreta, 2018. "Constrained Information Design," Papers 1811.03588, arXiv.org, revised Aug 2022.
    • Handle: RePEc:arx:papers:1811.03588
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    References listed on IDEAS

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    1. Le Treust, Maël & Tomala, Tristan, 2019. "Persuasion with limited communication capacity," Journal of Economic Theory, Elsevier, vol. 184(C).
    2. Laura Doval & Vasiliki Skreta, 2022. "Mechanism Design With Limited Commitment," Econometrica, Econometric Society, vol. 90(4), pages 1463-1500, July.
    3. Piotr Dworczak & Scott Duke Kominers & Mohammad Akbarpour, 2021. "Redistribution Through Markets," Econometrica, Econometric Society, vol. 89(4), pages 1665-1698, July.
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    Cited by:

    1. Laura Doval & Vasiliki Skreta, 2022. "Mechanism Design With Limited Commitment," Econometrica, Econometric Society, vol. 90(4), pages 1463-1500, July.
    2. Dworczak, Piotr & Kolotilin, Anton, 2024. "The persuasion duality," Theoretical Economics, Econometric Society, vol. 19(4), November.
    3. Gregorio Curello & Ludvig Sinander, 2022. "The comparative statics of persuasion," Papers 2204.07474, arXiv.org, revised Oct 2024.
    4. Le Treust, Maël & Tomala, Tristan, 2019. "Persuasion with limited communication capacity," Journal of Economic Theory, Elsevier, vol. 184(C).
    5. Onuchic, Paula & Ray, Debraj, 2023. "Conveying value via categories," Theoretical Economics, Econometric Society, vol. 18(4), November.
    6. George Georgiadis & Balazs Szentes, 2020. "Optimal Monitoring Design," Econometrica, Econometric Society, vol. 88(5), pages 2075-2107, September.
    7. Shih-Tang Su & Vijay G. Subramanian & Grant Schoenebeck, 2021. "Bayesian Persuasion in Sequential Trials," Papers 2110.09594, arXiv.org, revised Nov 2021.
    8. Roberto Corrao & Yifan Dai, 2023. "The Bounds of Mediated Communication," Papers 2303.06244, arXiv.org, revised Nov 2023.
    9. Mark Whitmeyer, 2019. "Bayesian Elicitation," Papers 1902.00976, arXiv.org, revised Feb 2024.
    10. Yaron Azrieli, 2021. "Constrained versus Unconstrained Rational Inattention," Games, MDPI, vol. 12(1), pages 1-22, January.
    11. Emir Kamenica & Kyungmin Kim & Andriy Zapechelnyuk, 2021. "Bayesian persuasion and information design: perspectives and open issues," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(3), pages 701-704, October.

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