Distributed seeking of time-varying Nash equilibrium for non-cooperative games

In this paper, we consider a time-varying Nash equilibrium seeking problem for non-cooperative games, where each player updates its strategy by employing an extremum seeking algorithm. In contrast to most of the classical Nash seeking algorithms that require model knowledge, we propose a non-model-based seeking scheme. The variation of the Nash equilibrium is considered to be of a general form. The proposed Nash equilibrium seeking algorithm includes the gradient estimation part and the gradient search part. A delay-based gradient estimation law is designed to extract the gradient and a Robust Integral of the Sign of the Error (RISE) control strategy is employed for gradient search. An example and numerical simulations are provided to demonstrate the performance of the designed Nash equilibrium seeking algorithm.