Matching through position auctions

Using a mechanism design framework, we characterize how a profit-maximizing intermediary can design matching markets when each agent is privately informed about his quality as a partner. Sufficient conditions are provided that ensure a version of positive assortative matching (what we call truncated positive assortative matching) maximizes profits. Under these conditions, all-pay position auctions always implement the profit-maximizing allocation. Winners-pay position auctions, however, only do so in sufficiently large markets.