Profit-Maximizing Matchmaker

Hideo Konishi () and Chiu Yu Ko
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Chiu Yu Ko: Boston College

No 721, Boston College Working Papers in Economics from Boston College Department of Economics

Abstract: This paper considers a matchmaker game in the Shapley-Shubik (1971) (one-to-one) assignment problem. Each firm proposes how much it is willing to pay each worker if they are matched. Each worker also proposes which salary she is willing to accept from each firm if they are matched. The matchmaker chooses a matching to maximize profit (the sum of the difference between the offering and asking salaries from each matched firm-worker). First, we show that Nash equilibrium may generate inefficient outcomes, but the matchmaker's profit is always zero in every Nash equilibrium. Second, we show that the sets of stable assignments and strong Nash equilibria are equivalent. These results extend to the Kelso-Crawford (1982) many-to-one assignment problem. Interestingly, in the one-to-one matching case, our results are closely related to the common agency game by Bernheim and Whinston (1986), while in the many-to-one assignment problem, such relationships break down completely.

Keywords: two-sided matching problem; stable assignment; strong Nash equilibrium; coalition-proof Nash equilibrium; no-rent property; implementation theory (search for similar items in EconPapers)
JEL-codes: C71 C72 C78 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-bec and nep-gth
Date: 2009-10-28

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