Normalized equilibrium in Tullock rent seeking game

Games with Common Coupled Constraints represent many real life situations. In these games, if one player fails to satisfy its constraints common to other players, then the other players are also penalised. Therefore these games can be viewed as being cooperative in goals related to meeting the common constraints, and non cooperative in terms of the utilities. We study in this paper the Tullock rent seeking game with additional common coupled constraints. We have succeded in showing that the utilities satisfy the property of diagonal strict concavity (DSC), which can be viewed as an extention of concavity to a game setting. It not only guarantees the uniqueness of the Nash equilibrium but also of the normalized equilibrium.