Nonlinear complementarity problems for n-player strategic chance-constrained games

Shangyuan Zhang (1, 2) , Makhlouf Hadji (1) , Abdel Lisser (2) , Yacine Mezali (1, 2)

1 IRT SystemX
2 L2S - Laboratoire des signaux et systèmes

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.

Mots clés: Chance-constrained optimization; Game theory; Nonlinear complementarity problem; Normal/Cauchy distribution

Domaines: Informatique et théorie des jeux [cs.GT]; Optimisation et contrôle [math.OC]

Shangyuan Zhang, Makhlouf Hadji, Abdel Lisser, Yacine Mezali. Nonlinear complementarity problems for n-player strategic chance-constrained games. International Conference on Operations Research and Enterprise Systems (ICORES), Feb 2022, Online Streaming, France. ⟨10.5220/0011005600003117⟩. ⟨hal-03519138⟩