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Implementation in generalized matching problems. (English) Zbl 0876.90012
Summary: We search for (Nash) implementable solutions on a class of one-to-one matching problems which includes both the housing market and marriage problems. 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 correspondence. That is, the core correspondence is the minimal solution that is Pareto efficient, individually rational, and implementable. A corollary of independent interest in the context of the housing market is that the core correspondence is the only single-valued solution that is Pareto efficient, individually rational, and implementable.

MSC:
91B14 Social choice
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