Distributed averaging integral Nash equilibrium seeking on networks

Continuous-time gradient-based Nash equilibrium seeking algorithms enjoy a passivity property under a suitable monotonicity assumption. This feature has been exploited to design distributed algorithms that converge to Nash equilibria and use local information only. We further exploit the passivity property to interconnect the algorithms with distributed averaging integral controllers that tune on-line the weights of the communication graph. The main advantage is to guarantee convergence to a Nash equilibrium without requiring a strong coupling condition on the algebraic connectivity of the communication graph over which the players exchange information, nor a global high-gain.