• 1 Laboratoire d'Etudes et Recherche en Mathématiques Appliquées
• 2 Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE
• 3 Laboratoire Jean Alexandre Dieudonné

We are interested here, in multi-criteria optimization problem using game theory. This problem will be treated by using a new algorithm for the splitting of territory in case of concurrent optimization, which presents a new formulation of Nash games between two players using two tables of allocations. Each player minimizes his cost function using the variables allocated by his own table. The two tables are given by an iterative algorithm. An image processing problem is addressed by using the proposed algorithms.