Double Auctions with Complementary Objects

Consider a situation where two objects that are complements are misallocated to different bidders. As a result, bidders try to trade via a double auction. The trade may be inefficient if the identities of buyer and seller are determined before they bid. To overcome inefficiency, we consider that the identities are determined by their bids. Under symmetric beliefs, we show that the bidders’ expected buy and sell prices are equivalent for a rich family of bargaining rules. Consequently, bidders’ expected utilities are equivalent under all bargaining rules. We also capture the impact of endogenous selection on the expected prices and utilities.