The recent fisheries management approach by Mauritania recommends that Total Allowable Catch (TAC) quotas, identified as essential for maintaining fish stocks, be shared (allocated) among fishing fleets operating in Mauritanian waters. However, the efficiency of such management regulations is debated. This issue can be identified as the typical dilemma between distant-fishing countries and coastal countries. We developed a theoretical model to determine how to allocate TAC quotas between the fishing fleets of Mauritania (RIM) and the European Union (EU). We discuss the various procedures and conditions for optimizing the allocation of fishing quotas (by country) in context of the Nash equilibrium. We found that both equilibria are characterized by strategic interactions of the exploitation that influence both the supply of TAC quotas available on the market and the cost of externalities due to RIM's dependence on financial compensation by the EU and available TAC quotas.