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Robust price discrimination

Author

Listed:
  • Arieli, Itai
  • Babichenko, Yakov
  • Madmon, Omer
  • Tennenholtz, Moshe

Abstract

We consider a model of third-degree price discrimination where the seller's product valuation is unknown to the market designer, who aims to maximize buyer surplus by revealing buyer valuation information. Our main result shows that the regret is bounded by a 1e-fraction of the optimal buyer surplus when the seller has zero valuation for the product. This bound is attained by randomly drawing a seller valuation and applying the segmentation of Bergemann et al. (2015) with respect to the drawn valuation. We show that this bound is tight in the case of binary buyer valuation.

Suggested Citation

  • Arieli, Itai & Babichenko, Yakov & Madmon, Omer & Tennenholtz, Moshe, 2025. "Robust price discrimination," Games and Economic Behavior, Elsevier, vol. 154(C), pages 377-395.
    • Handle: RePEc:eee:gamebe:v:154:y:2025:i:c:p:377-395
    DOI: 10.1016/j.geb.2025.09.006
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    References listed on IDEAS

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    1. Babichenko, Yakov & Talgam-Cohen, Inbal & Xu, Haifeng & Zabarnyi, Konstantin, 2022. "Regret-minimizing Bayesian persuasion," Games and Economic Behavior, Elsevier, vol. 136(C), pages 226-248.
    2. Yingni Guo & Eran Shmaya, 2023. "Regret-Minimizing Project Choice," Papers 2309.00214, arXiv.org.
    3. Maxime C. Cohen & Adam N. Elmachtoub & Xiao Lei, 2022. "Price Discrimination with Fairness Constraints," Management Science, INFORMS, vol. 68(12), pages 8536-8552, December.
    4. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, December.
    5. Yingni Guo & Eran Shmaya, 2023. "Regret‐Minimizing Project Choice," Econometrica, Econometric Society, vol. 91(5), pages 1567-1593, September.
    6. Ichihashi, Shota & Smolin, Alex, 2025. "Data provision to an informed seller," Games and Economic Behavior, Elsevier, vol. 153(C), pages 131-144.
    7. Kit Pong Wong, 2020. "Optimal nonlinear pricing by a regret‐averse monopoly," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 41(7), pages 1156-1161, October.
    8. Arieli, Itai & Madmon, Omer & Tennenholtz, Moshe, 2024. "Reputation-based persuasion platforms," Games and Economic Behavior, Elsevier, vol. 147(C), pages 128-147.
    9. Gabriel Carroll, 2015. "Robustness and Linear Contracts," American Economic Review, American Economic Association, vol. 105(2), pages 536-563, February.
    10. Alex Coad, 2009. "On the distribution of product price and quality," Journal of Evolutionary Economics, Springer, vol. 19(4), pages 589-604, August.
    11. Shota Ichihashi & Alex Smolin, 2023. "Buyer-Optimal Algorithmic Recommendations," Papers 2309.12122, arXiv.org, revised Jun 2025.
    12. Yingni Guo & Eran Shmaya, 2025. "Robust Monopoly Regulation," American Economic Review, American Economic Association, vol. 115(2), pages 599-634, February.
    13. , & , & ,, 2006. "Optimal auctions with ambiguity," Theoretical Economics, Econometric Society, vol. 1(4), pages 411-438, December.
    14. Emir Kamenica & Matthew Gentzkow, 2011. "Bayesian Persuasion," American Economic Review, American Economic Association, vol. 101(6), pages 2590-2615, October.
    15. Itai Arieli & Yakov Babichenko & Inbal Talgam-Cohen & Konstantin Zabarnyi, 2025. "A Random Dictator Is All You Need," American Economic Journal: Microeconomics, American Economic Association, vol. 17(1), pages 66-96, February.
    16. Myerson, Roger B. & Satterthwaite, Mark A., 1983. "Efficient mechanisms for bilateral trading," Journal of Economic Theory, Elsevier, vol. 29(2), pages 265-281, April.
    17. Daniel Walton & Gabriel Carroll, 2022. "A General Framework for Robust Contracting Models," Econometrica, Econometric Society, vol. 90(5), pages 2129-2159, September.
    18. Dirk Bergemann & Karl Schlag, 2012. "Robust Monopoly Pricing," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 13, pages 417-441, World Scientific Publishing Co. Pte. Ltd..
    19. Dirk Bergemann & Karl H. Schlag, 2012. "Pricing Without Priors," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 12, pages 405-415, World Scientific Publishing Co. Pte. Ltd..
    20. Bergemann, Dirk & Heumann, Tibor & Wang, Michael, 2024. "A Unified Approach to Second and Third Degree Price Discrimination," CEPR Discussion Papers 18793, C.E.P.R. Discussion Papers.
    21. Piotr Dworczak & Alessandro Pavan, 2022. "Preparing for the Worst but Hoping for the Best: Robust (Bayesian) Persuasion," Econometrica, Econometric Society, vol. 90(5), pages 2017-2051, September.
    22. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2015. "The Limits of Price Discrimination," American Economic Review, American Economic Association, vol. 105(3), pages 921-957, March.
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