This paper studies a multi-period demand response management problem in thesmart grid where multiple utility companies compete among themselves. Theuser-utility interactions are modeled by a noncooperative game of a Stackelbergtype where the interactions among the utility companies are captured through aNash equilibrium. It is shown that this game has a unique Stackelbergequilibrium at which the utility companies set prices to maximize theirrevenues (within a Nash game) while the users respond accordingly to maximizetheir utilities subject to their budget constraints. Closed-form expressionsare provided for the corresponding strategies of the users and the utilitycompanies. It is shown that the multi- period scheme, compared with thesingle-period case, provides more incentives for the users to participate inthe game. A necessary and sufficient condition on the minimum budget needed fora user to participate is provided.
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