Distributed Nash Equilibrium Seeking for Monotone Generalized Noncooperative Games by a Regularized Penalty Method

TL;DR

This paper introduces a distributed regularized penalty algorithm for finding Nash equilibria in monotone generalized noncooperative games with constraints, ensuring convergence to the least-norm variational equilibrium.

Contribution

It proposes a novel distributed method combining time-varying penalty and regularization to handle inequality constraints and monotonicity in generalized games.

Findings

Algorithm converges asymptotically to the least-norm variational equilibrium.

Numerical examples demonstrate the method's effectiveness and efficiency.

The approach effectively manages inequality constraints in distributed settings.

Abstract

In this work, we study the distributed Nash equilibrium seeking problem for monotone generalized noncooperative games with set constraints and shared affine inequality constraints. A distributed regularized penalty method is proposed. The idea is to use a differentiable penalty function with a time-varying penalty parameter to deal with the inequality constraints. A time-varying regularization term is used to deal with the ill-poseness caused by the monotonicity assumption and the time-varying penalty term. The asymptotic convergence to the least-norm variational equilibrium of the game is proven. Numerical examples show the effectiveness and efficiency of the proposed algorithm.