{
  "id": "1710.00145",
  "version": "v1",
  "published": "2017-09-30T03:51:13.000Z",
  "updated": "2017-09-30T03:51:13.000Z",
  "title": "A Game-Theoretic Method for Multi-Period Demand Response: Revenue Maximization, Power Allocation, and Asymptotic Behavior",
  "authors": [
    "Khaled Alshehri",
    "Ji Liu",
    "Xudong Chen",
    "Tamer Başar"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "We study a multi-period demand response management problem in the smart grid with multiple utility companies and consumers. The user-utility interactions are modeled by a Stackelberg game where the interactions among the utility companies are captured through a Nash price selection game. It is shown that this game has a unique Stackelberg equilibrium at which the utility companies set prices to maximize their revenues (within a Nash game) while the users respond accordingly to maximize their utilities subject to their budget constraints. Closed-form expressions are provided for the corresponding strategies of the users and the utility companies. 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 programs. Based on closed-form solutions, a power allocation game for utility companies has been formulated, and it is shown to admit a unique pure-strategy Nash equilibrium, for which a full expression is obtained. We study the asymptotic behavior of the equilibrium strategies when the number of periods and users are large. We find an appropriate company-to-user ratio for the large population regime. For privacy, we provide a distributed algorithm for the computation of all optimal strategies.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-30T03:51:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "utility companies",
      "power allocation",
      "asymptotic behavior",
      "game-theoretic method",
      "revenue maximization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}