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

Warrington College of Business Administration, University of Florida, Gainesville, Florida
jane.feng{at}cba.ufl.edu

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.

Key Words: Slot allocation; optimal mechanism; common ranking; auction
History: Received: February 3, 2006;