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We propose a numerical algorithm for computing approximately optimalsolutions of the matching for teams problem. Our algorithm is efficient forproblems involving a large number of agent categories and allows for themeasures describing the agent types to be non-discrete. Specifically, weparametrize the so-called transfer functions and develop a parametric versionof the dual formulation. Our algorithm tackles this parametric formulation andproduces feasible and approximately optimal solutions for the primal and dualformulations of the matching for teams problem. These solutions also yieldupper and lower bounds for the optimal value, and the difference between theupper and lower bounds provides a direct sub-optimality estimate of thecomputed solutions. Moreover, we are able to control a theoretical upper boundon the sub-optimality to be arbitrarily close to 0 under mild conditions. Wesubsequently prove that the approximate primal and dual solutions converge whenthe sub-optimality goes to 0 and their limits constitute a true matchingequilibrium. Thus, the outputs of our algorithm are regarded as an approximatematching equilibrium. We also analyze the theoretical computational complexityof our parametric formulation as well as the sparsity of the resultingapproximate matching equilibrium. Through numerical experiments, we showcasethat the proposed algorithm can produce high-quality approximate matchingequilibria and is applicable to versatile settings, including ahigh-dimensional setting involving 100 agent categories.

Feasible approximation of matching equilibria for large-scale matching for teams problems