Games with Common Coupled Constraints represent manyreal life situations. In these games, if one player fails tosatisfy its constraints common to other players, then theother players are also penalised. Therefore these games canbe viewed as being cooperative in goals related to meetingthe common constraints, and non cooperative in terms ofthe utilities. We study in this paper the Tullock rent seekinggame with additional common coupled constraints. We havesucceded in showing that the utilities satisfy the property ofdiagonal strict concavity (DSC), which can be viewed asan extention of concavity to a game setting. It not onlyguarantees the uniqueness of the Nash equilibrium but also of the normalized equilibrium.