Finding Nash equilibrium for a class of multi-person noncooperative games via solving tensor complementarity problem

摘要

Recently, Huang and Qi formulated a class of multi-person noncooperative games as a tensor complementarity problem in Huang and Qi (2017) [15]. In this paper, we rewrite the resulted tensor in the formulation and propose a semismooth Newton method to find a Nash equilibrium for the multi-person noncooperative game via solving the corresponding tensor complementarity problem. The convergence of the proposed method is established. Finally, some preliminary numerical results for solving the multi-person noncooperative games are reported. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.