A Distributed Algorithm for Aggregative Games on Directed Communication Graphs

This study focuses on aggregative games, a type of Nash games that is played over a network. In these games, the cost function of an agent is affected by its own choice and the sum of all decision variables of the players involved. We consider a distributed algorithm over a network, whereby to reach a Nash equilibrium point, each agent maintains a prediction of the aggregate decision variable and share it with its local neighbors over a strongly connected directed network. The existing literature provides such algorithms for undirected graphs which typically require the use doubly stochastic weight matrices. We consider a fixed directed communication network and investigate a synchronous distributed gradient-based method for computing a Nash equilibrium. We provide convergence analysis of the method showing that the algorithm converges to the Nash equilibrium of the game, under some standard conditions.