  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.
