  This study addresses primal-dual dynamics for a stochastic programming
problem for capacity network design. It is proven that consensus can be
achieved on the \textit{here and now} variables which represent the capacity of
the network. The main contribution is a heuristic approach which involves the
formulation of the problem as a mean-field game. Every agent in the mean-field
game has control over its own primal-dual dynamics and seeks consensus with
neighboring agents according to a communication topology. We obtain theoretical
results concerning the existence of a mean-field equilibrium. Moreover, we
prove that the consensus dynamics converge such that the agents agree on the
capacity of their respective micro-networks. Lastly, we emphasize how penalties
on control and state influence the dynamics of agents in the mean-field game.
