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Selling Two Identical Objects

Author

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  • Sushil Bikhchandani

    (UCLA)

  • Debasis Mishra

    (Indian Statistical Institute, Delhi)

Abstract

It is well-known that optimal (i.e., revenue-maximizing) selling mechanisms in multidimensional type spaces may involve randomization. We study mechanisms for selling two identical, indivisible objects to a single buyer. We analyze two settings: (i) decreasing marginal values (DMV) and (ii) increasing marginal values (IMV). Thus, the two marginal values of the buyer are not independent. We obtain sucient conditions on the distribution of buyer values for the existence of an optimal mechanism that is deterministic. In the DMV model, we show that under a well-known condition, it is optimal to sell the first unit deterministically. Under the same sucient condition, a bundling mechanism (which is deterministic) is optimal in the IMV model. Under a stronger sufficient condition, a deterministic mechanism is optimal in the DMV model. Our results apply to heterogenous objects when there is a specified sequence in which the two objects must be sold.

Suggested Citation

  • Sushil Bikhchandani & Debasis Mishra, 2020. "Selling Two Identical Objects," Discussion Papers 20-07, Indian Statistical Institute, Delhi.
    • Handle: RePEc:alo:isipdp:20-07
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    References listed on IDEAS

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    Cited by:

    1. Debasis Mishra & Kolagani Paramahamsa, 2022. "Selling to a principal and a budget-constrained agent," Discussion Papers 22-02, Indian Statistical Institute, Delhi.
    2. Dirk Bergemann & Alessandro Bonatti & Andreas Haupt & Alex Smolin, 2021. "The Optimality of Upgrade Pricing," Papers 2107.10323, arXiv.org, revised Dec 2021.
    3. Komal Malik & Kolagani Paramahamsa, 2024. "Selling two complementary goods," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(2), pages 423-447, June.
    4. Rochet, Jean-Charles, 2024. "Multidimensional screening after 37 years," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    5. Patrick Lahr & Axel Niemeyer, 2024. "Extreme Points in Multi-Dimensional Screening," Papers 2412.00649, arXiv.org.
    6. Debasis Mishra & Kolagani Paramahamsa, 2022. "Selling to a principal and a budget-constrained agent," Papers 2202.10378, arXiv.org, revised Oct 2024.

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    More about this item

    JEL classification:

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

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