Cooperation, punishment and immigration

We study the incentive to cooperate in a society comprised of citizens and immigrants. The level of cooperation is governed by a steady state under population dynamics, along with the behavior of individual citizens and immigrants. We provide an equilibrium characterization, exhibiting a uniquely determined positive level of cooperation in society. We then use this framework to study the impact of government programs aimed at punishing immigrants who defect. When agents produce offspring, we show that a consequence of such punishment is that, while the incentive for immigrants to defect decreases, there is an equilibrium substitution effect whereby citizens realize an increased incentive to defect.