# Nonlinear Complementarity Problems for n-Player Strategic Chance-constrained Games

### Shangyuan Zhang, Shangyuan Zhang, Makhlouf Hadji, Abdel Lisser, Yacine Mezali

#### 2022

#### 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.

Download#### Paper Citation

#### in Harvard Style

Zhang S., Hadji M., Lisser A. and Mezali Y. (2022). **Nonlinear Complementarity Problems for n-Player Strategic Chance-constrained Games**. In *Proceedings of the 11th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,* ISBN 978-989-758-548-7, pages 94-104. DOI: 10.5220/0011005600003117

#### in Bibtex Style

@conference{icores22,

author={Shangyuan Zhang and Makhlouf Hadji and Abdel Lisser and Yacine Mezali},

title={Nonlinear Complementarity Problems for n-Player Strategic Chance-constrained Games},

booktitle={Proceedings of the 11th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},

year={2022},

pages={94-104},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0011005600003117},

isbn={978-989-758-548-7},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 11th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,

TI - Nonlinear Complementarity Problems for n-Player Strategic Chance-constrained Games

SN - 978-989-758-548-7

AU - Zhang S.

AU - Hadji M.

AU - Lisser A.

AU - Mezali Y.

PY - 2022

SP - 94

EP - 104

DO - 10.5220/0011005600003117