A gossip algorithm for aggregative games on graphs

We consider a class of games, termed as aggregative games, being played over a distributed multi-agent networked system. In an aggregative game, an agent's objective function is coupled through a function of the aggregate of all agents decisions. Every agent maintains an estimate of the aggregate and agents exchange this information over a connected network. We study the gossip-based distributed algorithm for the exchange of information and computation of equilibrium decisions of agents over the network. Our primary emphasis lies in proving the convergence of the algorithm under an assumption of a diminishing (agent-specific) step-size sequence. Under standard conditions, we establish the almost-sure convergence of the generated sequence to the unique equilibrium point.