Endogenous Increase in Social Efficiency through the Interaction between Open Relation and Closed Relation

Abstract

This paper examines complementarity between "open relation" and "closed relation" in a repeated prisoners' dilemma game in which payoffs are stochastically determined. In the ``open relation'', each player is randomly matched with another one, and there is an opportunity for them to receive higher payoffs than in the ``closed relation''. However, because their relation is one-shot, their rational behaviors prevent them from the realization of cooperation. In the ``closed relation'', in contrast, we assume that paired players' relation is fixed and that both of them are committed to cooperative behaviors. But, their payoffs are fixed by definition so that there is no opportunity to get higher payoff staying in the relation. Hence, players in the ``closed relation'' incur higher opportunity cost. If only one of the two relations exists in society, the social efficient outcome is not attained. However, if both of them coexist in society and there is mobility between them, then the social outcome improves. This is because the "open relation" has a role as decreasing opportunity costs, the "closed relation" has a role as keeping cooperation, and the dynamics between them functions as endogenous pressures to improve payoffs. But in order to keep the endogenous pressures, it needs that the rate of random breaking of ``closed relation'' is sufficiently low.