Split of an Optimization Variable in Game Theory

Rajae Aboulaich (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 general multiobjective optimization problem is stated as a Nash game. In the nonrestrictive case of two objectives, we address the problem of the splitting of the design variable between the two players. The so-called territory splitting problem is solved by means of an allocative approach. We propose two algorithms in order to find fair allocation tables.

Domaines: Optimisation et contrôle [math.OC]

Rajae Aboulaich, Abderrahmane Habbal, Noureddine Moussaid. Split of an Optimization Variable in Game Theory. Mathematical Modelling of Natural Phenomena, 2010, 5 (7), pp.122-127. ⟨10.1051/mmnp/20105720⟩. ⟨inria-00544355⟩