Variational inequality for n-player strategic chance-constrained games

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

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 distributions. We prove the equivalence between a Nash equilibrium problem and a variational inequality problem. We reformulate the latter as a nonlinear complementarity problem (NCP) through the Karush-Kuhn-Tucker (KKT) conditions. Then, we prove the existence of the Nash equilibrium via 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.

Domaines: Informatique et théorie des jeux [cs.GT]

Shangyuan Zhang, Makhlouf Hadji, Abdel Lisser, Yacine Mezali. Variational inequality for n-player strategic chance-constrained games. SN Computer Science, 2023, 4 (82), ⟨10.1007/s42979-022-01488-0⟩. ⟨hal-03845071⟩