Well-defined and enforceable property rights are usually seen as a prerequisite for optimal resource management. However, the interaction effects between different renewable resource pools with different ownership structures are often not well recognized. In this paper we introduce these interaction effects in optimal fishery management theory. Various property rights regimes and market structures for fisheries are analyzed. Furthermore, we perform a sensitivity analysis with respect to the carrying capacity of a fish lake for the different agents. We describe various approach paths towards the new equilibrium after opening up to a common market. We show that a decline in market power leads to a lower stock and a higher supply. Furthermore we identify conditions under which market power might reduce profits.