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Perfect Bayesian Equilibria in repeated sales

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  • 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
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    2. Yonatan Gur & Gregory Macnamara & Daniela Saban, 2022. "Sequential Procurement with Contractual and Experimental Learning," Management Science, INFORMS, vol. 68(4), pages 2714-2731, April.
    3. 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.
    4. Modibo Camara & Jason Hartline & Aleck Johnsen, 2020. "Mechanisms for a No-Regret Agent: Beyond the Common Prior," Papers 2009.05518, arXiv.org.
    5. 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.
    6. 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.
    7. Breig, Zachary, 2022. "Repeated contracting without commitment," Journal of Economic Theory, Elsevier, vol. 204(C).

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    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

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