Multi-Resolution Large Population Stochastic Differential Games and Their Application to Demand Response Management in the Smart Grid

Quanyan Zhu, Tamer Başar

Research output: Contribution to journalArticle


Dynamic demand response (DR) management is becoming an integral part of power system and market operational practice. Motivated by the smart grid DR management problem, we propose a multi-resolution stochastic differential game-theoretic framework to model the players' intra-group and inter-group interactions in a large population regime. We study the game in both risk-neutral and risk-sensitive settings, and provide closed-form solutions for symmetric mean-field responses in the case of homogeneous group populations, and characterize the symmetric mean-field Nash equilibrium using the Hamilton-Jacobi-Bellman (HJB) equation together with the Fokker-Planck-Kolmogorov (FPK) equation. Finally, we apply the framework to the smart grid DR management problem and illustrate with a numerical example.

Original languageEnglish (US)
Pages (from-to)68-88
Number of pages21
JournalDynamic Games and Applications
Issue number1
StatePublished - Feb 28 2013



  • Demand response
  • Large-population games
  • Mean-field Nash equilibrium
  • Multi-resolution games
  • Power grid
  • Smart grid
  • Stochastic differential games

ASJC Scopus subject areas

  • Statistics and Probability
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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