  We consider a smart-grid connecting several agents, modeled as stochastic
dynamical systems, who may be electricity consumers/producers. At each discrete
time instant, which may represent a 15 minute interval, each agent may
consume/generate some quantity of electrical energy. The Independent System
Operator (ISO) is given the task of assigning consumptions/generations to the
agents so as to maximize the sum of the utilities accrued to the agents,
subject to the constraint that energy generation equals consumption at each
time.
  This task of coordinating generation and demand has to be accomplished by the
ISO without the agents revealing their system states, dynamics, or utility/cost
functions. We show how and when a simple iterative procedure converges to the
optimal solution. The ISO iteratively obtains electricity bids by the agents,
and declares the tentative market clearing prices. In response to these prices,
the agents submit new bids.
  On the demand side, the solution yields an optimal demand response for
dynamic and stochastic loads. On the generation side, it provides the optimal
utilization of stochastically varying renewables such as solar/wind, and
generation with fossil fuel based generation with dynamic constraints such as
ramping rates. Thereby we solve a decentralized stochastic control problem,
without agents sharing any information about their system models, states or
utility functions.
