Distributed event-triggered Nash equilibrium seeking for non-cooperative games on unbalanced digraphs

This paper addresses a Nash equilibrium (NE) seeking problem for non-cooperative games with double-integrator agents who communicate with each other on an unbalanced directed graph. To deal with the unbalance in the consensus term, an auxiliary variable is introduced in the designed distributed NE seeking algorithm and is the estimation of the left eigenvector of the Laplacian matrix associated with the zero eigenvalue. Moreover, an event-triggered broadcasting scheme is proposed to reduce communication loads in the network. It is shown that the proposed communication scheme is free of the Zeno behavior and the asymptotic convergence of the designed algorithm is obtained. Simulation results are demonstrated to validate the proposed methods.