Marine reserves are promoted as an effective supplement to traditional fishery management techniques of harvest quotas and effort limitation. However, quantitative fishery models have ignored the impact of noncompliance (poaching). Here we link a model of a harvested fish population to a game-theoretic representation of fisherman behavior to quantify the effect of poaching on fishery yield and the enforcement effort required to maintain any desired level of reserve effectiveness. Although higher fish densities inside reserves will typically entice fishermen to poach, we show that the initial investment in enforcement efforts provides the greatest return on maintaining the benefits of the reserve to the fishery. Furthermore, we find that poaching eliminates the positive effect of fish dispersal on yield that is predicted by traditional models that ignore fisherman behavior. Our results broaden a fundamental insight from previous models of marine reserves, the effective equivalence of the harvest quota and reserve fraction, to the more realistic scenario in which fishermen attempt to maximize their economic payoffs.