Distributed Nash equilibrium seeking for non-cooperative convex games with local constraints

This paper considers the problem of Nash equilibrium seeking in non-cooperative convex games subjected to local constraints including both equality and inequality constraints. Each player in the game is individually associated with a local objective function, which is coupled with the actions of the other players. The players cannot observe the actions of the players that are not their neighbors. Instead, the players are capable of exchanging information of actions via an undirected and connected communication graph. Thus, a leader-following consensus-based estimation of actions of the players is conducted. Furthermore, a Nash equilibrium seeking algorithm is proposed. Stability analysis by means of continuous time Lyapunov approach is presented and it is shown that the algorithm is capable of achieving global convergence to the Nash equilibrium. A numerical example is given to verify the effectiveness of the results of the paper.