Does Competition Solve the Hold-up Problem?

In an environment in which both workers and firms undertake match specific investments, the presence of market competition for matches may solve the hold-up problems generated by the absence of complete contingent contracts. In particular, this paper shows that when matching is assortative and workers' investments precede market competition for matches investments are constrained efficient. Inefficiencies can arise in this framework as multiple equilibria of the competition game. Only one of these equilibria is efficient in the sense that the worker with the higher innate ability matches with the better firm. A different type of inefficiencies arise when firms undertake their match specific investment before market competition. These inefficiency leads to firms under-investments. However, we show that in this case the aggregate inefficiency is small in a well defined sense independent of the market size.