The Effect of Punishment and Reward on Cooperation in a Prisoners' Dilemma Game

Abstract: This work studies the effect of incentives (in the form of punishment and reward) on the equilibrium fraction of cooperators and defectors in an iterated n-person prisoners' dilemma game. With a finite population of players employing a strategy of nice tit-for-tat or universal defect, an equilibrium fraction of each player-type can be identified from linearized payoff functions. Incentives take the form of targeted and general punishment, and targeted and general reward. The primary contribution of this work is in clearly articulating the design and marginal effect of these incentives on cooperation. Generalizable results indicate that while targeted incentives have the potential to substantially reduce but never entirely eliminate defection, they exhibit diminishing marginal effectiveness. General incentives on the other hand have the potential to eliminate all defection from the population of players. Applications to policy are briefly considered.