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Optimal multi-unit mechanisms with private demands

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  • Devanur, Nikhil R.
  • Haghpanah, Nima
  • Psomas, Alexandros

Abstract

A seller can produce multiple units of a single good. The buyer has constant marginal value for each unit she receives up to a demand, and zero marginal value for units beyond the demand. The marginal value and the demand are drawn from a distribution and are privately known to the buyer. We show that under natural regularity conditions on the distribution, the optimal (revenue-maximizing) selling mechanism is deterministic. It is a price schedule that specifies the payment based on the number of units purchased. Further, under the same conditions, the revenue as a function of the price schedule is concave, which in turn implies that the optimal price schedule can be found in polynomial time. We give a more detailed characterization of the optimal prices when there are only two possible demands.

Suggested Citation

  • Devanur, Nikhil R. & Haghpanah, Nima & Psomas, Alexandros, 2020. "Optimal multi-unit mechanisms with private demands," Games and Economic Behavior, Elsevier, vol. 121(C), pages 482-505.
    • Handle: RePEc:eee:gamebe:v:121:y:2020:i:c:p:482-505
    DOI: 10.1016/j.geb.2020.03.007
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    References listed on IDEAS

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    4. Komal Malik & Kolagani Paramahamsa, 2021. "Selling two complementary goods," Discussion Papers 21-01, Indian Statistical Institute, Delhi.

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