Title: Privacy-Preserving Multi-Period Demand Response: A Game Theoretic Approach,
Abstract: We study a multi-period demand response problem in the smart grid with
multiple companies and their consumers. We model the interactions by a
Stackelberg game, where companies are the leaders and consumers are the
followers. It is shown that this game has a unique equilibrium at which the
companies set prices to maximize their revenues while the consumers respond
accordingly to maximize their utilities subject to their local constraints.
Billing minimization is achieved as an outcome of our method. Closed-form
expressions are provided for the strategies of all players. Based on these
solutions, a power allocation game has been formulated, and which is shown to
admit a unique pure-strategy Nash equilibrium, for which closed-form
expressions are provided. For privacy, we provide a distributed algorithm for
the computation of all strategies. We study the asymptotic behavior of
equilibrium strategies when the numbers of periods and consumers grow. We find
an appropriate company-to-user ratio for the large population regime.
Furthermore, it is shown, both analytically and numerically, that the
multi-period scheme, compared with the single-period one, provides more
incentives for energy consumers to participate in demand response. We have also
carried out case studies on real life data to demonstrate the benefits of our
approach, including billing savings of up to 30\%.