Privacy-Preserving Multi-Period Demand Response: A Game Theoretic Approach

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\%.