A Characterization of the Conditions for Optimal Auction with Resale

Zheng has proposed a seller-optimal auction for (asymmetric) independent-privatevalue environments where inter-bidder resale is possible. Zheng’s construction requires novel conditions — Resale Monotonicity, Transitivity, and Invariance — on the bidders’ value distribution profile. The only known examples of distribution profiles satisfying these conditions in environments with three or more bidders are uniform distributions. Our characterization result shows that Zheng’s conditions, while being strong, are satisfied by many non-uniform distribution profiles. A crucial step in our analysis is to show that Invariance implies Resale Monotonicity and Transitivity.