Exponentially convergent distributed Nash equilibrium seeking for constrained aggregative games

Distributed Nash equilibrium seeking of aggregative games is investigated and a continuous-time algorithm is proposed. The algorithm is designed by virtue of projected gradient play dynamics and aggregation tracking dynamics, and is applicable to games with constrained strategy sets and weight-balanced communication graphs. The key feature of our method is that the proposed projected dynamics achieves exponential convergence, whereas such convergence results are only obtained for non-projected dynamics in existing works on distributed optimization and equilibrium seeking. Numerical examples illustrate the effectiveness of our methods.