The Limits of Reciprocity for Social Cooperation

Reciprocity constraints facilitate the achievement of cooperative outcomes in many game-theoretic settings. Yet, in some situations the equilibrium induced by a reciprocity constraint may not be socially optimal. After presenting the case in which reciprocity yields privately and socially optimal levels of cooperation, this paper identifies the conditions under which reciprocity generates inefficient cooperation. Two groups of cases are presented. In one group reciprocity undershoots (i.e., the parties cooperate less than is socially optimal). In the other, more puzzling case, reciprocity constraints overshoot (i.e., the parties 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 reciprocity constraint to induce a reciprocal social optimum, where a social optimum requires equal levels of effort by the two parties, and identifies situations where reciprocity fails to induce such an optimum