Reciprocity-Induced Cooperation

The concept of reciprocity gains importance where there is no external authority to enforce agreements. Many legal systems foster meta-rules 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 prisoner's 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) non-linear payoff functions. Then we examine the welfare properties of the reciprocity-induced equilibrium. In many game-theoretic situations, reciprocity facilitates the achievement of cooperative outcomes. Yet the reciprocity-induced equilibrium is not always socially optimal.