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By utilizing tools from game theory, we develop a novelmulti-period-multi-company demand response framework considering theinteractions between companies (sellers of energy) and their consumers (buyersof energy). We model the interactions in terms of a Stackelberg game, wherecompanies set their prices and consumers respond by choosing their demands. Weshow that the underlying game has a unique equilibrium at which the companiesmaximize their revenues while the consumers maximize their utilities subject totheir local constraints. Closed-form expressions are provided for the optimalstrategies of all players. Based on these solutions, a power allocation gamehas been formulated, which is shown to admit a unique pure-strategy Nashequilibrium, for which closed-form expressions are also provided. Thisequilibrium is found under the assumption that companies can freely allocatetheir power across the time horizon, but we also demonstrate that it ispossible to relax this assumption. We further provide a fast distributedalgorithm for the computation of all optimal strategies using only localinformation. We also study the effect of variations in the number of periods(subdivisions of the time horizon) and the number of consumers. As aconsequence, we are able to find an appropriate company-to-consumer ratio whenthe number of consumers participating in demand response exceeds somethreshold. Furthermore, we show, both analytically and numerically, that themulti-period scheme provides incentives for energy consumers to participate indemand response, compared to the single-period framework studied in theliterature. In our framework, we provide a condition for the minimum budgetsconsumers need, and carry out case studies using real life data to demonstratethe benefits of the approach, which show potential savings of up to $30\%$ andequilibrium prices that have low volatility.

A Game-Theoretic Framework for Multi-Period-Multi-Company Demand Response Management in the Smart Grid