  This technical note presents a leader-follower scheme for network aggregative
games. The followers and leader are selfish cost minimizing agents. The cost
function of each follower is affected by strategy of leader and aggregated
strategies of its neighbors through a communication graph. The leader
infinitely often wakes up and receives the aggregated strategy of the
followers, updates its decision value and broadcasts it to all the followers.
Then, the followers apply the updated strategy of the leader into their cost
functions. The establishment of information exchange between each neighboring
pair of followers, and the activeness of each follower to update its decision
at each iteration are both considered to be drawn from two arbitrary
distributions. Moreover, a distributed algorithm based on subgradient method is
proposed for updating the strategies of leader and followers. The convergence
of the proposed algorithm to the unique generalized Nash equilibrium point of
the game is proven in both almost sure and mean square senses.
