Self-Triggered Best-Response Dynamics for Continuous Games

Motivated by the development of novel and practically implementable coordination algorithms for multi-agent systems, here we investigate the adaptation of classical best-response dynamics by means of self-triggered communications. First, we show that, if the best response dynamics is defined for a continuous-action-space potential game, convergence towards the Nash Equilibria set is guaranteed under continuity on utilities and component-wise pseudo-concavity of the potential function. Then, we modify the best-response dynamics to account for more economic self-triggered communication strategies while ensuring convergence to the equilibrium set. The proposed algorithm is then analyzed in the framework of hybrid systems theory.