Authors:
Shangyuan Zhang
1
;
2
;
Makhlouf Hadji
2
;
Abdel Lisser
1
and
Yacine Mezali
2
Affiliations:
1
CentraleSupelec, L2S, Université Paris Saclay, 3 Rue Curie Joliot, 91190, Gif-sur-Yvette, France
;
2
Institut de Recherche Technologique SystemX, 8 Avenue de la Vauve, 91120 Palaiseau, France
Keyword(s):
Chance-constrained Optimization, Game Theory, Nonlinear Complementarity Problem, Normal/Cauchy Distribution.
Abstract:
In this paper, we focus on n-player strategic chance-constrained games where the payoff of each player follows either Cauchy or normal distribution. We transform the Nash equilibrium problem into its equivalent nonlinear complementarity problem (NCP) through the Karush-Kuhn-Tucker (KKT) conditions. Then, we prove the existence of the Nash equilibrium by the mean of Brouwer’s fixed-point theorem. In order to show the efficiency of our approach, we perform numerical experiments on a set of randomly generated instances.
