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A simple proof of strong duality in the linear persuasion problem

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  • Dizdar, Deniz
  • Kováč, Eugen

Abstract

We provide a simple proof of strong duality for the linear persuasion problem. The duality is established in Dworczak and Martini (2019), under slightly stronger assumptions, using techniques from the literature on optimization with stochastic dominance constraints and several approximation arguments. We provide a short, alternative proof that is based on a direct argument to show the existence of optimal price functions, and on switching the roles of the primal and the dual to show that there is no duality gap.

Suggested Citation

  • Dizdar, Deniz & Kováč, Eugen, 2020. "A simple proof of strong duality in the linear persuasion problem," Games and Economic Behavior, Elsevier, vol. 122(C), pages 407-412.
    • Handle: RePEc:eee:gamebe:v:122:y:2020:i:c:p:407-412
    DOI: 10.1016/j.geb.2020.04.017
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    References listed on IDEAS

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    1. Constantinos Daskalakis & Alan Deckelbaum & Christos Tzamos, 2017. "Strong Duality for a Multiple‐Good Monopolist," Econometrica, Econometric Society, vol. 85, pages 735-767, May.
    2. Emir Kamenica & Matthew Gentzkow, 2011. "Bayesian Persuasion," American Economic Review, American Economic Association, vol. 101(6), pages 2590-2615, October.
    3. Kolotilin, Anton, 2018. "Optimal information disclosure: a linear programming approach," Theoretical Economics, Econometric Society, vol. 13(2), May.
    4. 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.
    5. Piotr Dworczak & Giorgio Martini, 2019. "The Simple Economics of Optimal Persuasion," Journal of Political Economy, University of Chicago Press, vol. 127(5), pages 1993-2048.
    6. Andreas Kleiner & Alejandro Manelli, 2019. "Strong Duality in Monopoly Pricing," Econometrica, Econometric Society, vol. 87(4), pages 1391-1396, July.
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    Cited by:

    1. Andreas Kleiner & Benny Moldovanu & Philipp Strack, 2021. "Extreme Points and Majorization: Economic Applications," Econometrica, Econometric Society, vol. 89(4), pages 1557-1593, July.
    2. Itai Arieli & Yakov Babichenko & Fedor Sandomirskiy, 2023. "Feasible Conditional Belief Distributions," Papers 2307.07672, arXiv.org, revised Nov 2024.
    3. Kun Zhang, 2022. "Withholding Verifiable Information," Papers 2206.09918, arXiv.org, revised Sep 2022.
    4. Emiliano Catonini & Sergey Stepanov, 2022. "On the optimality of full disclosure," Papers 2202.07944, arXiv.org, revised Feb 2023.
    5. Alexander V. Kolesnikov & Fedor Sandomirskiy & Aleh Tsyvinski & Alexander P. Zimin, 2022. "Beckmann's approach to multi-item multi-bidder auctions," Papers 2203.06837, arXiv.org, revised Sep 2022.
    6. Kim, Kyungmin & Koh, Youngwoo, 2022. "Auctions with flexible information acquisition," Games and Economic Behavior, Elsevier, vol. 133(C), pages 256-281.
    7. Gregorio Curello & Ludvig Sinander, 2022. "The comparative statics of persuasion," Papers 2204.07474, arXiv.org, revised Oct 2024.
    8. Dworczak, Piotr & Kolotilin, Anton, 2024. "The persuasion duality," Theoretical Economics, Econometric Society, vol. 19(4), November.

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