Distributed Nash Equilibrium Computation Under Round-Robin Scheduling Protocol

This article is concerned with distributed Nash equilibrium (NE) problem for multiplayer games under the Round-Robin (RR) protocol. For the purpose of effectively mitigating data congestion and saving communication resources, the RR protocol is adopted for each player, under which the player is permitted to transmit data to only one of its neighbors at each time instant. The resulting protocol-induced communication graph become time-varying and even disconnected, even though the original graph is assumed to be strongly connected. The aim of the addressed problem is to develop a distributed algorithm in the partial-decision information setting such the convergence of NE can be guaranteed under the
$B$
-strong connectivity of graphs and the row-stochasticity of weighted adjacency matrix. The sufficient condition on the convergence of the NE is derived for the algorithm with diminishing step-sizes. Some discussions are provided on convergence rate of the proposed algorithm. Finally, one numerical example is provided to verify the developed algorithm.