Distributed Regularization-Based Nash Equilibrium Seeking for Merely Monotone Games Under Directed Graphs: A Prescribed-Time Approach

In this paper, we consider the prescribed-time distributed Nash equilibrium (PTDNE) seeking problem in noncooperative monotone games under directed graphs. For the purpose of compensating for the absence of strong monotoncity condition, a time-varying decay regularization term is implemented in the merely monotone game. By using the regularization scheme, a new prescribed-time distributed algorithm is established for seeking the least-norm Nash equilibrium in monotone games, where the leader-following consensus protocol and gradient play are incorporated. Based on the proposed strategies, some sufficient conditions on time-varying parameters are provided through Lyapunov function analysis, under which the players’ actions are capable of converging to the least-norm one of the Nash equilibria in a prescribed time. Finally, numerical simulations on a network of players demonstrate the benefits of the proposed algorithm in achieving convergence at any arbitrary time.