IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2606.22720.html

Screening Under Competition

Author

Listed:
  • Yu-Ting Ho

Abstract

We study competition among multiple firms that offer differentiated varieties of the same good to a unit-demand agent. The agent has heterogeneous valuations for goods from different firms. Firms do not observe the agent's exact valuations, but they know their distribution. Firms simultaneously post menus of contracts, after which the agent chooses a firm and one of its contracts to maximize her utility. This defines a game in which firms aim to maximize expected revenue. We introduce a sufficient condition, density-regularity, under which each firm's best response to any arbitrary menu profile posted by its opponents is equivalent to posting a menu that contains only a posted-price contract. Our result is not a direct extension of the canonical Myersonian model with a single seller. The standard argument in the literature breaks down once heterogeneous preferences and competition are introduced. We therefore adopt an optimal-control approach, in which the density-regularity condition is essential for establishing the optimality of posted prices. When this condition fails, posted prices may fail to be a best response.

Suggested Citation

  • Yu-Ting Ho, 2026. "Screening Under Competition," Papers 2606.22720, arXiv.org.
    • Handle: RePEc:arx:papers:2606.22720
    as

    Download full text from publisher

    File URL: https://arxiv.org/pdf/2606.22720
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, vol. 64(1), pages 51-75, January.
    2. Champsaur, Paul & Rochet, Jean-Charles, 1989. "Multiproduct Duopolists," Econometrica, Econometric Society, vol. 57(3), pages 533-557, May.
    3. McAfee, R Preston, 1993. "Mechanism Design by Competing Sellers," Econometrica, Econometric Society, vol. 61(6), pages 1281-1312, November.
    4. Stole, Lars A, 1995. "Nonlinear Pricing and Oligopoly," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 4(4), pages 529-562, Winter.
    5. David Martimort, 1992. "Multi-principaux avec anti-sélection," Annals of Economics and Statistics, GENES, issue 28, pages 1-37.
    6. Jean-Charles Rochet & Lars A. Stole, 2002. "Nonlinear Pricing with Random Participation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(1), pages 277-311.
    7. Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, vol. 18(2), pages 301-317, August.
    8. Manelli, Alejandro M. & Vincent, Daniel R., 2012. "Multidimensional mechanism design: Revenue maximization and the multiple-good monopoly. A corrigendum," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2492-2493.
    9. Jullien, Bruno, 2000. "Participation Constraints in Adverse Selection Models," Journal of Economic Theory, Elsevier, vol. 93(1), pages 1-47, July.
    10. Severin Borenstein, 1985. "Price Discrimination in Free-Entry Markets," RAND Journal of Economics, The RAND Corporation, vol. 16(3), pages 380-397, Autumn.
    11. Armstrong, Mark & Vickers, John, 2001. "Competitive Price Discrimination," RAND Journal of Economics, The RAND Corporation, vol. 32(4), pages 579-605, Winter.
    12. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    13. Eric Maskin & John Riley, 1984. "Monopoly with Incomplete Information," RAND Journal of Economics, The RAND Corporation, vol. 15(2), pages 171-196, Summer.
    14. Spulber, Daniel F., 1989. "Product variety and competitive discounts," Journal of Economic Theory, Elsevier, vol. 48(2), pages 510-525, August.
    15. repec:adr:anecst:y:1992:i:28:p:01 is not listed on IDEAS
    16. Epstein, Larry G. & Peters, Michael, 1999. "A Revelation Principle for Competing Mechanisms," Journal of Economic Theory, Elsevier, vol. 88(1), pages 119-160, September.
    17. Claudio Mezzetti, 1997. "Common Agency with Horizontally Differentiated Principals," RAND Journal of Economics, The RAND Corporation, vol. 28(2), pages 323-345, Summer.
    18. Stole, Lars A., 2007. "Price Discrimination and Competition," Handbook of Industrial Organization, in: Mark Armstrong & Robert Porter (ed.), Handbook of Industrial Organization, edition 1, volume 3, chapter 34, pages 2221-2299, Elsevier.
    19. Peters, Michael, 2001. "Common Agency and the Revelation Principle," Econometrica, Econometric Society, vol. 69(5), pages 1349-1372, September.
    20. David Martimort & Lars Stole, 2002. "The Revelation and Delegation Principles in Common Agency Games," Econometrica, Econometric Society, vol. 70(4), pages 1659-1673, July.
    21. Biglaiser Gary & Mezzetti Claudio, 1993. "Principals Competing for an Agent in the Presence of Adverse Selection and Moral Hazard," Journal of Economic Theory, Elsevier, vol. 61(2), pages 302-330, December.
    22. Katz, Michael L, 1984. "Price Discrimination and Monopolistic Competition," Econometrica, Econometric Society, vol. 52(6), pages 1453-1471, November.
    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. Stole, Lars A., 2007. "Price Discrimination and Competition," Handbook of Industrial Organization, in: Mark Armstrong & Robert Porter (ed.), Handbook of Industrial Organization, edition 1, volume 3, chapter 34, pages 2221-2299, Elsevier.
    2. Hector Chade & Jeroen Swinkels, 2021. "Screening in Vertical Oligopolies," Econometrica, Econometric Society, vol. 89(3), pages 1265-1311, May.
    3. Bonatti, Alessandro, 2011. "Brand-specific tastes for quality," International Journal of Industrial Organization, Elsevier, vol. 29(5), pages 562-575, September.
    4. Martimort, David & Stole, Lars A., 2022. "Participation constraints in discontinuous adverse selection models," Theoretical Economics, Econometric Society, vol. 17(3), July.
    5. Khaled Diaw & Jérôme Pouyet, 2005. "Information, competition and (In) complete discrimination," Working Papers hal-00243025, HAL.
    6. Udo Schmidt-Mohr & J. Villas-Boas, 2008. "Competitive product lines with quality constraints," Quantitative Marketing and Economics (QME), Springer, vol. 6(1), pages 1-16, March.
    7. Mark Armstrong, 2016. "Nonlinear Pricing," Annual Review of Economics, Annual Reviews, vol. 8(1), pages 583-614, October.
    8. Fabian Herweg, 2012. "Relaxing competition through quality differentiation and price discrimination," Journal of Economics, Springer, vol. 106(1), pages 1-26, May.
    9. Jian Shen & Huanxing Yang & Lixin Ye, 2016. "Competitive Nonlinear Pricing and Contract Variety," Journal of Industrial Economics, Wiley Blackwell, vol. 64(1), pages 64-108, March.
    10. Jensen, S., 2000. "Price Discrimination and Three Part Tariffs in a Duopoly," Papers 3/2000, Norwegian School of Economics and Business Administration-.
    11. Burani, Nadia & Mantovani, Andrea, 2020. "Non-linear pricing and conscious consumption," International Journal of Industrial Organization, Elsevier, vol. 68(C).
    12. repec:aen:journl:ej35-1-04 is not listed on IDEAS
    13. David Martimort & Lars Stole, 2009. "Market participation in delegated and intrinsic common‐agency games," RAND Journal of Economics, RAND Corporation, vol. 40(1), pages 78-102, March.
    14. Aryal, Gaurab & Gabrielli, Maria F., 2020. "An empirical analysis of competitive nonlinear pricing," International Journal of Industrial Organization, Elsevier, vol. 68(C).
    15. Martimort, David & Stole, Lars, 2011. "Public Contracting in Delegated Agency Games," MPRA Paper 32874, University Library of Munich, Germany.
    16. Ye, Lixin & Zhang, Chenglin, 2017. "Monopolistic nonlinear pricing with consumer entry," Theoretical Economics, Econometric Society, vol. 12(1), January.
    17. Hernández-Murillo, Rubén, 2019. "Interjurisdictional competition with adverse selection," Journal of Public Economics, Elsevier, vol. 173(C), pages 85-95.
    18. Daniel F Garrett & Renato Gomes & Lucas Maestri, 2019. "Competitive Screening Under Heterogeneous Information," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(4), pages 1590-1630.
    19. Sissel Jensen, 2006. "Implementation of competitive nonlinear pricing: tariffs with inclusive consumption," Review of Economic Design, Springer;Society for Economic Design, vol. 10(1), pages 9-29, April.
    20. Giaume, Stephanie & Guillou, Sarah, 2004. "Price discrimination and concentration in European airline markets," Journal of Air Transport Management, Elsevier, vol. 10(5), pages 305-310.
    21. Jensen, Sissel, 2008. "Two-part tariffs with quality degradation," International Journal of Industrial Organization, Elsevier, vol. 26(2), pages 473-489, March.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:2606.22720. 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: arXiv administrators (email available below). General contact details of provider: https://arxiv.org/ .

    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.