A new algorithm for approaching Nash equilibrium and Kalai Smoridinsky solution

Rajae Aboulaich (1) , Rachid Ellaia (1) , Samira El Moumen (1) , Abderrahmane Habbal (2, 3) , Noureddine Moussaid (1)

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

In the present paper, a new formulation of Nash games is proposed for solving general multi-objective optimization problems. The main idea of this approach is to split the optimization variables which allow us to determine numerically the strategies between two players. The first player minimizes his cost function using the variables of the first table P, the second player, using the second table Q. The original contribution of this work concerns the construction of the two tables of allocations that lead to a Nash equilibrium on the Pareto front. On the other hand, we search P and Q that lead to a solution which is both a Nash equilibrium and a Kalai Smorodinsky solution. For this, we proposed and tried out successfully two algorithms which calculate P, Q and their associated Nash equilibrium, by using some extension of Normal Boundary Intersection approach (NBI).

Domaines: Optimisation et contrôle [math.OC]

Rajae Aboulaich, Rachid Ellaia, Samira El Moumen, Abderrahmane Habbal, Noureddine Moussaid. A new algorithm for approaching Nash equilibrium and Kalai Smoridinsky solution. 2011. ⟨hal-00648693⟩