Matching Rules

Institutions often utilize matching rules to facilitate the achievement of cooperative outcomes. Yet, in some situations the equilibrium induced by a matching rule may not be socially optimal. After presenting the case in which matching rules yield privately and socially optimal levels of cooperation, this paper identifies the conditions under which they would instead generate inefficient cooperation. Two groups of cases are presented. In one group matching rules undershoot (i.e., the parties cooperate less than is socially optimal). In the other, more puzzling case, matching rules overshoot (i.e., the parties that interact under a matching constraint are induced to cooperate more than is socially optimal). This paper identifies the conditions for such occurrences. The paper then examines the ability of a matching rule to induce a socially optimal level of cooperation, where a social optimum requires equal levels of effort by the two parties, and identifies situations where matching rules fail to induce such an optimum