This paper analyses the management of the Atlantic salmon stocks in the Baltic Sea through a coalition game in the partition function form. The signs of economic and biological over-exploitation of these salmon stocks over the last two decades indicate that cooperation among the harvesting countries, under the European Union's Common Fisheries Policy, has been superficial. Combining a two-stage game of four countries with a comprehensive bioeconomic model, we conclude that cooperation under the Relative Stability Principle is not a stable outcome. In contrast, the equilibrium of the game is full non-cooperation. The paper also addresses the possibility of enhancing cooperation through more flexible fishing strategies and sharing schemes. The results show that partial cooperation can be sustained and that there are substantial economic benefits to reallocating fishing effort among harvesting countries.