Journal of Systems Science and Complexity

, Volume 20, Issue 2, pp 162–172 | Cite as

An Invariance Principle in Large Population Stochastic Dynamic Games

  • Minyi HuangEmail author
  • Peter E. Caines
  • Roland P. Malhamé


We study large population stochastic dynamic games where the so-called Nash certainty equivalence based control laws are implemented by the individual players. We first show a martingale property for the limiting control problem of a single agent and then perform averaging across the population; this procedure leads to a constant value for the martingale which shows an invariance property of the population behavior induced by the Nash strategies.


Large population martingale representation Nash equilibrium optimal control stochastic dynamic games 


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Copyright information

© Springer Science + Business Media, LLC 2007

Authors and Affiliations

  • Minyi Huang
    • 1
    Email author
  • Peter E. Caines
    • 2
    • 4
  • Roland P. Malhamé
    • 3
    • 4
  1. 1.Department of Information Engineering, Research School of Information Sciences and EngineeringThe Australian National UniversityCanberraAustralia
  2. 2.Department of Electrical and Computer EngineeringMcGill UniversityMontrealCanada
  3. 3.Department of Electrical EngineeringÉcole Polytechnique de MontréalMontrealCanada
  4. 4.GERADMontrealCanada

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