A note on Zheng’s conditions for implementing an optimal auction with resale

Zheng has recently proposed a seller-optimal auction for (asymmetric) independentprivate- value environments where inter-bidder resale is possible. Zheng's construction requires novel conditions on the bidders' value distribution profile. We clarify the restrictions implied by these conditions. Given distributions for two bidders and the supports of the other bidders' distributions, Zheng's conditions uniquely determine the entire distribution profile. Moreover, if the bidders' distributions have the same support then Zheng's conditions imply that all distributions except one are identical, so that the final allocation is obtained after a single resale transaction, regardless of the number of bidders.