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Selling Two Identical Objects

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  • Sushil Bikhchandani
  • Debasis Mishra

Abstract

It is well-known that optimal (i.e., revenue-maximizing) selling mechanisms in multidimensional type spaces may involve randomization. We obtain conditions under which deterministic mechanisms are optimal 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 values of the buyer for the two units are not independent. We show that under a well-known condition on distributions~(due to McAfee and McMillan (1988)), (a) it is optimal to sell the first unit deterministically in the DMV model and (b) it is optimal to bundle (which is a deterministic mechanism) in the IMV model. Under a stronger sufficient condition on distributions, a deterministic mechanism is optimal in the DMV model. Our results apply to heterogeneous 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," Papers 2009.11545, arXiv.org, revised Aug 2021.
    • Handle: RePEc:arx:papers:2009.11545
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    References listed on IDEAS

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    Cited by:

    1. Dirk Bergemann & Alessandro Bonatti & Andreas Haupt & Alex Smolin, 2021. "The Optimality of Upgrade Pricing," Papers 2107.10323, arXiv.org, revised Dec 2021.
    2. Debasis Mishra & Kolagani Paramahamsa, 2022. "Selling to a principal and a budget-constrained agent," Discussion Papers 22-02, Indian Statistical Institute, Delhi.
    3. Debasis Mishra & Kolagani Paramahamsa, 2022. "Selling to a principal and a budget-constrained agent," Papers 2202.10378, arXiv.org, revised Jul 2022.

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    JEL classification:

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

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