Research Note—Optimal Mechanism for Selling a Set of Commonly Ranked Objects

Abstract

This paper designs an optimal mechanism for selling a set of commonly ranked objects. Although buyers rank these objects in the same order, the rates at which their valuations change for a less-preferred object might be different. Four stylized cases are identified according to this difference: parallel, convergent, divergent, and convergent-then-divergent. In general, the optimal mechanism cannot be interpreted as a conventional second-price auction. A reserve price is imposed for each object. Depending on which of the four stylized cases is considered, a higher-value bidder may be allocated a higher-ranked or lower-ranked object. There is also a positive probability that a higher-ranked object is not allocated while a lower-ranked one is allocated. In a departure from the extant mechanism-design literature, the individual-rationality constraint for a mid-range type of bidder can be binding.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 42 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.