This paper shows in two ways that the degree to which free-riding diminishes the performance of deterministic partnerships may be less than has been generally thought. First, a necessary and sufficient condition is provided for a partnership to sustain full efficiency. It implies that many non-trivial partnerships sustain efficiency, such as generic ones with finite action spaces, and neoclassical ones with Leontief technologies. Second, approximate efficiency is shown to be achievable in a large class of partnerships, including ones with smooth and monotonic production and disutility functions. Approximate efficiency is achieved by mixed-strategy equilibria: one partner takes, with small probability, an inefficient action. The degree to which efficiency is approximated is restricted only by the amount of liability the partners can bear. Nonetheless, their equilibrium payments are not arbitrarily large.

We study frictionless matching in large economies with and without market imperfections, providing sufficient conditions for monotone matching that are weaker than those previously known. Necessary conditions, which depend on a key analytical object we call the surplus function, are also offered. Changes in the surplus yield valuable information about the comparative statics of matching patterns across environments. We apply our framework to some examples adapted from the literature, accounting for and extending several comparative-static and welfare results. We also explore the dependence of the matching pattern on the type distribution.