Continuous-time distributed Nash equilibrium seeking algorithms for non-cooperative constrained games

This paper studies the Nash equilibrium seeking problem for non-cooperative games subject to set and nonlinear inequality constraints. The cost function for each player and the constrained function are determined by all the players' decision variables. Each player is assigned a constrained set while all the players are subject to a coupling nonlinear inequality constraint. A continuous-time distributed seeking algorithm using local information interaction is proposed, where the players deliver/receive information unidirectionally over a directed network. In particular, a distributed observer is first introduced for each player to estimate all the others' decision variables. Then, by using these estimates, a seeking algorithm is synthesized with a projection operator. Based on the time-scale separation approach, it is shown that the proposed continuous-time distributed seeking algorithm guarantees the convergence of the strategy profile to an arbitrarily small neighborhood of the generalized Nash equilibrium satisfying a KKT condition. An illustrative example is finally presented to validate the theoretical results. (C) 2021 Elsevier Ltd. All rights reserved.