Assortative Matching with Externalities and Farsighted Agents

We consider a one-to-one assortative matching problem in which matched pairs compete for a prize. With externalities, the standard solution concept—pairwise stable matching—may not exist. In this paper, we consider farsighted agents and analyze the largest consistent set (LCS) of Chwe (J Econ Theory 63:299-325, 1994). Despite the assortative structure of the problem, LCS tend to be large with the standard effectiveness functions: LCS can be the set of all matchings, including an empty matching with no matched pair. By modifying the effectiveness function motivated by Knuth (Marriages stables. Les Presses de l’Universite de Montreal, Montreal, 1976), LCS becomes a singleton of the positive assortative matching. Our results suggest that the choice of the effectiveness function can significantly impact the solution for a matching problem with externalities.