Reciprocity-Induced Cooperation

Many legal systems foster metarules of reciprocity to facilitate cooperative outcomes. This paper considers the role of reciprocity rules in various strategic environments. We start by considering the effect of reciprocity constraints in a classic prisoners' dilemma with two symmetric parties and linear payoffs. We extend the analysis to continuous strategies and then further extend the basic model of reciprocity to (a) asymmetric players and (b) nonlinear payoff functions. Then we examine the welfare properties of the reciprocity-induced equilibrium. In many game-theoretic situations, reciprocity constraints facilitate the achievement of cooperative outcomes. Yet the reciprocity-induced equilibrium is not always socially optimal.