We examine markets in which agents make investments and then match into pairs, creating surpluses that depend on their investments and that can be split between the matched agents. In general, each of the matched agents would ”own" part of the surplus in the absence of interagent transfers. Most of the work in the large bargaining-and matching literature ignores this initial ownership of the surplus. We show that when investments are not observable to potential partners, initial ownership affects the efficiency of equilibrium investments and affects the agents' payoffs. In particular, it is possible that reallocating initial ownership could increase welfare on both sides of the match.