text: 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.
  @cite_2: Abstract : The lecture is designed to survey modern development of the theory of general equilibrium in a competitive economy and its role in the allocation of resources. A survey is given of the state of the theory as developed by J.R. Hicks, P.A. Samuelson, and their predecessors as of about 1945, followed by an evaluation of the needs for further development. The differing general equilibrium tradition in the German-language literature is summarized.
summary: We show below that the ISO Problem is an example of a decentralized control system with non-classical observation patterns in which signaling can successfully result in globally optimum performance. The agents need not reveal their observations, state values, their individual system dynamics or their individual cost-functions. We construct concrete signaling schemes which encode-decode the information required in order to recover the same performance as that of centralized control. From the economics side, this work is an extension of general equilibrium theory @cite_2 . To the authors' knowledge there does not appear to be any similar result for coordinating multiple LQG systems or the efficiency of the simplified signaling.