IMPLEMENTATION IN GENERALIZED MATCHING PROBLEMS

We search for (Nash) implementable solutions on a class of one-to-one matching problems which includes both the housing market (Shapley and Scarf, Journal of Mathematical Economics, 1974, 1, 23-28) and marriage problems (Gale and Shapley, American Mathematical Monthly, 1962, 69, 9-15). We show that the core correspondence is implementable. We show, furthermore, that any solution that is Pareto efficient, individually rational, and implementable is a supersolution of the core correspond ence. That is, the core correspondence is the minimal solution that is Pareto efficient, individually rational, and implementable. A corolla ry of independent interest in the context of the housing market is tha t the core correspondence is the only single-valued solution that is P areto efficient, individually rational, and implementable.