Generalized Nash Equilibrium Seeking Strategy for Nonsmooth Noncooperative Game with Equality Constraints

Abstract

This article discusses the problem of Nash equilibrium seeking for noncooperative game with equality constraints. In the problem, each player desires to maximize its nonsmooth payoff function which depends on both its own strategy and the strategy of other players. Besides, the game-player is subjected to private local equality constraints. We use a l <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> penalty function to deal with the equality constraints and a Nash equilibrium seeking strategy is designed on the basis of differential inclusions and subgradient methods. And we show that the strategy of player is exponentially convergent to the Nash equilibrium with Lyapunov methods. Finally, a numerical example is presented to illustrate the validity of our theoretical results.