Discriminatory Auctions with Resale

We consider multi-unit discriminatory auctions where ex-ante symmetric bidders have single-unit demands and resale is allowed after the bidding stage. When bidders use the optimal auction to sell the items in the resale stage, the equilibrium without resale is not an equilibrium. We find a symmetric and monotone equilibrium when there are two units for sale, and, interestingly, show that there may not be a symmetric and monotone equilibrium if there are more than two units