||In a sequence of studies, Budescu, Rapoport, and Suleiman investigated a class of common pool resource (CPR) dilemmas characterized by the presence of both strategic uncertainty and environmental uncertainty about the size of the CPR. We extend this research--both theoretically and experimentally--in two different ways. In the bonus CPR dilemma, a bonus is given to the agent(s) who request the least; and in the penalty CPR dilemma, a penalty is imposed on the agent(s) who request the most. Under equilibrium play, we show that the bonus treatment decreases total group request, whereas the penalty treatment increases it. Our experimental results do not support this prediction. Rather, both treatments increase the rate of provision, and the penalty treatment is more effective in reducing individual requests than the bonus treatment.