Optimal multi-unit mechanisms with private demands

Nikhil R. Devanur, Nima Haghpanah, Alexandros Psomas

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)482-505
Number of pages24
JournalGames and Economic Behavior
StatePublished - May 2020

All Science Journal Classification (ASJC) codes

  • Finance
  • Economics and Econometrics


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