We develop a simple game-theoretic model to explain the production decisions of firms when the production of a marketed good is complementary with the output of an associated good for which no market is available and the output of both goods is regulated by exogenously determined common pool output quotas. This scenario matches that of many fisheries in which regulators attempt to simultaneously manage harvests of targeted species and bycatch of other species through common pool quotas and seasonal closures. Under a competitive equilibrium, individual fishermen fail to fully account for the external effects of their harvest decisions on the season length, leading to excessive discards, drastically shortened seasons, and large shares of un-harvested quota for all but the smallest of fishery sizes. These results are robust for even very efficient (low-bycatch) fishing gears. We examine the sensitivity of our predictions to changes in output prices, discard costs, quota allocations and differing degrees of spatial correlation of target and bycatch species. Finally, we derive the optimal bycatch penalty function and describe its significance in light of various policy alternatives available to regulators.