  We consider a class of Nash games, termed as aggregative games, being played
over a networked system. In an aggregative game, a player's objective is a
function of the aggregate of all the players' decisions. Every player maintains
an estimate of this aggregate, and the players exchange this information with
their local neighbors over a connected network. We study distributed
synchronous and asynchronous algorithms for information exchange and
equilibrium computation over such a network. Under standard conditions, we
establish the almost-sure convergence of the obtained sequences to the
equilibrium point. We also consider extensions of our schemes to aggregative
games where the players' objectives are coupled through a more general form of
aggregate function. Finally, we present numerical results that demonstrate the
performance of the proposed schemes.
