Position Auctions with Multidimensional Types: Revenue Maximization and Efficiency (by Ryuji Sano)
This study considers revenue-optimal auction design for two ordered substitutes, such as positions or priorities. Bidders have a two-dimensional type about a valuation for the top position and a discount rate of the second position for the top. An auction mechanism is dominant-strategy incentive compatible if and only if it satisfies the “Law of One Price,” which requires that bidders’ payments are independent of their own discount rate. The simple “virtually efficient mechanism,” which maximizes the unconstrained virtual surplus, is not incentive compatible for any type distribution if the discount-rate-type space includes at least two interior values. If the discount-rate-type space includes at most a single interior value, there exist distributions under which the virtually efficient mechanism is incentive compatible, and therefore optimal.