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 asymmetric players 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 non-cooperation. The paper also addresses the possibility of enhancing cooperation through more flexible fishing strategies. The results indicate that partial cooperation is stable under a specific sharing scheme. It is also shown that substantial economic benefits could have been realised by reallocating the fishing effort.