This paper examines a market in which a continuum of principals and agents interact in a game. Principals offer contracts while agents decide on sets of acceptable contracts. A mechanism from a class satisfying “efficiency,” “unbiasedness,” and “continuity” properties then matches principals and agents. With risk neutral agents, when the contribution of principals and agents to the total “gains from trade” in a pairing are additively separable, the equilibria of the game coincide with the competitive equilibria for the market. In particular, all contracts used in Nash equilibrium induce first-best effort levels. Both principals and agents have exogenous opportunities outside this market. In equilibrium, agents have endogenously determined outside opportunities available from employment by another principal, and this may be the binding participation constraint in a principal-agent pairing. The results are extended to special non-separable cases and to the case of identical risk averse agents.