IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v118y2019icp570-588.html
   My bibliography  Save this article

Perfect Bayesian Equilibria in repeated sales

Author

Listed:
  • Devanur, Nikhil R.
  • Peres, Yuval
  • Sivan, Balasubramanian

Abstract

A special case of Myerson's classic result describes the revenue-optimal equilibrium when a seller offers a single item to a buyer. We study a repeated sales extension of this model: a seller offers to sell a single fresh copy of an item to the same buyer every day via a posted price. The buyer's private value for the item is drawn initially from a publicly known distribution F and remains the same throughout. A key aspect of this game is that the seller might try to learn the buyer's private value to extract more revenue, while the buyer is motivated to hide it. We study the Perfect Bayesian Equilibria (PBE) in this setting with varying levels of commitment power to the seller. We find that the seller having the commitment power to not raise prices subsequent to a purchase significantly improves revenue in a PBE.

Suggested Citation

  • Devanur, Nikhil R. & Peres, Yuval & Sivan, Balasubramanian, 2019. "Perfect Bayesian Equilibria in repeated sales," Games and Economic Behavior, Elsevier, vol. 118(C), pages 570-588.
    • Handle: RePEc:eee:gamebe:v:118:y:2019:i:c:p:570-588
    DOI: 10.1016/j.geb.2019.01.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825619300016
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2019.01.001?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. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Skreta, Vasiliki, 2015. "Optimal auction design under non-commitment," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 854-890.
    3. Larry M. Ausubel & Raymond J. Deneckere, 1989. "Reputation in Bargaining and Durable Goods Monopoly," Levine's Working Paper Archive 201, David K. Levine.
    4. Ausubel, Lawrence M. & Cramton, Peter & Deneckere, Raymond J., 2002. "Bargaining with incomplete information," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 50, pages 1897-1945, Elsevier.
    5. Schmidt Klaus M., 1993. "Commitment through Incomplete Information in a Simple Repeated Bargaining Game," Journal of Economic Theory, Elsevier, vol. 60(1), pages 114-139, June.
    6. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    7. Xavier Freixas & Roger Guesnerie & Jean Tirole, 1985. "Planning under Incomplete Information and the Ratchet Effect," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(2), pages 173-191.
    8. Anna, Petrenko, 2016. "Мaркування готової продукції як складова частина інформаційного забезпечення маркетингової діяльності підприємств овочепродуктового підкомплексу," Agricultural and Resource Economics: International Scientific E-Journal, Agricultural and Resource Economics: International Scientific E-Journal, vol. 2(1), March.
    9. Sham M. Kakade & Ilan Lobel & Hamid Nazerzadeh, 2013. "Optimal Dynamic Mechanism Design and the Virtual-Pivot Mechanism," Operations Research, INFORMS, vol. 61(4), pages 837-854, August.
    10. Ausubel, Lawrence M & Deneckere, Raymond J, 1989. "Reputation in Bargaining and Durable Goods Monopoly," Econometrica, Econometric Society, vol. 57(3), pages 511-531, May.
    11. Bulow, Jeremy I, 1982. "Durable-Goods Monopolists," Journal of Political Economy, University of Chicago Press, vol. 90(2), pages 314-332, April.
    12. Baron, David P. & Besanko, David, 1984. "Regulation and information in a continuing relationship," Information Economics and Policy, Elsevier, vol. 1(3), pages 267-302.
    13. Nancy L. Stokey, 1981. "Rational Expectations and Durable Goods Pricing," Bell Journal of Economics, The RAND Corporation, vol. 12(1), pages 112-128, Spring.
    14. Gul, Faruk & Sonnenschein, Hugo & Wilson, Robert, 1986. "Foundations of dynamic monopoly and the coase conjecture," Journal of Economic Theory, Elsevier, vol. 39(1), pages 155-190, June.
    15. Oliver D. Hart & Jean Tirole, 1988. "Contract Renegotiation and Coasian Dynamics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 55(4), pages 509-540.
    16. Coase, Ronald H, 1972. "Durability and Monopoly," Journal of Law and Economics, University of Chicago Press, vol. 15(1), pages 143-149, April.
    17. Laffont, Jean-Jacques & Tirole, Jean, 1988. "The Dynamics of Incentive Contracts," Econometrica, Econometric Society, vol. 56(5), pages 1153-1175, September.
    18. Drew Fudenberg & Jean Tirole, 1983. "Sequential Bargaining with Incomplete Information," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(2), pages 221-247.
    19. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    20. Vasiliki Skreta, 2006. "Sequentially Optimal Mechanisms -super-1," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(4), pages 1085-1111.
    21. Vincent Conitzer & Curtis R. Taylor & Liad Wagman, 2012. "Hide and Seek: Costly Consumer Privacy in a Market with Repeat Purchases," Marketing Science, INFORMS, vol. 31(2), pages 277-292, March.
    22. Joel Sobel & Ichiro Takahashi, 1983. "A Multistage Model of Bargaining," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(3), pages 411-426.
    23. Drew Fudenberg & David K. Levine & Jean Tirole, 1985. "Infinite-Horizon Models of Bargaining with One-Sided Incomplete Information," Levine's Working Paper Archive 1098, David K. Levine.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Vahab Mirrokni & Renato Paes Leme & Pingzhong Tang & Song Zuo, 2020. "Non‐Clairvoyant Dynamic Mechanism Design," Econometrica, Econometric Society, vol. 88(5), pages 1939-1963, September.
    2. Xiaotie Deng & Ron Lavi & Tao Lin & Qi Qi & Wenwei Wang & Xiang Yan, 2020. "A Game-Theoretic Analysis of the Empirical Revenue Maximization Algorithm with Endogenous Sampling," Papers 2010.05519, arXiv.org.
    3. Breig, Zachary, 2022. "Repeated contracting without commitment," Journal of Economic Theory, Elsevier, vol. 204(C).
    4. Modibo Camara & Jason Hartline & Aleck Johnsen, 2020. "Mechanisms for a No-Regret Agent: Beyond the Common Prior," Papers 2009.05518, arXiv.org.
    5. Nicol`o Cesa-Bianchi & Tommaso Cesari & Roberto Colomboni & Federico Fusco & Stefano Leonardi, 2021. "A Regret Analysis of Bilateral Trade," Papers 2102.08754, arXiv.org.
    6. Yonatan Gur & Gregory Macnamara & Daniela Saban, 2022. "Sequential Procurement with Contractual and Experimental Learning," Management Science, INFORMS, vol. 68(4), pages 2714-2731, April.
    7. Maxime C. Cohen & Antoine Désir & Nitish Korula & Balasubramanian Sivan, 2023. "Best of Both Worlds Ad Contracts: Guaranteed Allocation and Price with Programmatic Efficiency," Management Science, INFORMS, vol. 69(7), pages 4027-4050, July.

    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. Beccuti, Juan & Möller, Marc, 2021. "Screening by mode of trade," Games and Economic Behavior, Elsevier, vol. 129(C), pages 400-420.
    2. Arieh Gavious & Ella Segev, 2017. "Price Discrimination Based on Buyers’ Purchase History," Dynamic Games and Applications, Springer, vol. 7(2), pages 229-265, June.
    3. Hannu Vartiainen, 2003. "Auction Design without Commitment," Working Papers 2003.24, Fondazione Eni Enrico Mattei.
    4. Doval, Laura & Skreta, Vasiliki, 0. "Optimal mechanism for the sale of a durable good," Theoretical Economics, Econometric Society.
    5. Bergemann, Dirk & Pavan, Alessandro, 2015. "Introduction to Symposium on Dynamic Contracts and Mechanism Design," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 679-701.
    6. Lawrence M. Ausubel & Raymond J. Deneckere, 1989. "Bargaining and the Right to Remain Silent," Discussion Papers 856, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    7. Cheng, Harrison, 2011. "Auctions with resale and bargaining power," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 300-308.
    8. Patrick Hummel, 2018. "Reserve prices in repeated auctions," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(1), pages 273-299, March.
    9. Laura Doval & Vasiliki Skreta, 2022. "Mechanism Design With Limited Commitment," Econometrica, Econometric Society, vol. 90(4), pages 1463-1500, July.
    10. Vasiliki Skreta, 2000. "Sequentially Optimal Mechanisms," Econometric Society World Congress 2000 Contributed Papers 1521, Econometric Society.
    11. Abreu, Dilip & Pearce, David G. & Stacchetti, Ennio, 2015. "One-sided uncertainty and delay in reputational bargaining," Theoretical Economics, Econometric Society, vol. 10(3), September.
    12. Skreta, Vasiliki, 2015. "Optimal auction design under non-commitment," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 854-890.
    13. Kjell Hausken, 1997. "Game-theoretic and Behavioral Negotiation Theory," Group Decision and Negotiation, Springer, vol. 6(6), pages 511-528, December.
    14. Francesc Dilmé, 2021. "The Role of Discounting in Bargaining with One-Sided Offers," ECONtribute Discussion Papers Series 063, University of Bonn and University of Cologne, Germany.
    15. Bradley J Larsen, 2021. "The Efficiency of Real-World Bargaining: Evidence from Wholesale Used-Auto Auctions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 88(2), pages 851-882.
    16. Stefan Buehler & Nicolas Eschenbaum, 2021. "Dynamic Monopoly Pricing With Multiple Varieties: Trading Up," Papers 2108.07146, arXiv.org, revised Dec 2021.
    17. Peter C. Cramton, 1992. "Strategic Delay in Bargaining with Two-Sided Uncertainty," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(1), pages 205-225.
    18. James J. Anton & Gary Biglaiser, 2010. "Quality, Upgrades, and Equilibrium in a Dynamic Monopoly Model," Working Papers 10-36, Duke University, Department of Economics.
    19. James J. Anton & Gary Biglaiser, 2007. "Quality Upgrades and the (loss) of Market Power in a Dynamic Monopoly Model," Working Papers 18, Portuguese Competition Authority.
    20. Walter Beckert, 2004. "Dynamic Monopolies with Stochastic Demand," Birkbeck Working Papers in Economics and Finance 0404, Birkbeck, Department of Economics, Mathematics & Statistics.

    More about this item

    Keywords

    Repeated sales; Perfect Bayesian Equilibria; Price commitment;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

    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:gamebe:v:118:y:2019:i:c:p:570-588. 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/622836 .

    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.