Optimal Auction With Resale—A Characterization Of The Conditions

Zheng has proposed a seller-optimal auction for (asymmetric) independent-private-value environments where inter-bidder resale is possible. Zheng’s construction requires novel assumptions—Resale Monotonicity, Transitivity, and Invariance—on the bidders’ value distribution profile. The only known examples of distribution profiles satisfying these assumptions in environments with three or more bidders are uniform distributions. Using inverse virtual valuation functions as a novel tool, we characterize the set of distribution profiles satisfying Zheng’s assumptions. Our characterization result shows that the assumptions, while being strong, are satisfied by many non-uniform distribution profiles. Hence, Zheng’s result applies more generally than one may have thought before. A crucial step in our analysis is to show that Invariance implies Resale Monotonicity and Transitivity.