Abstract
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.
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Dedicated to Professor Han-Fu Chen on the occasion of his 70th birthday.
This work was partially supported by the Australian Research Council (ARC) and National Sciences and Engineering Research Council of Canada (NSERC).
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Huang, M., Caines, P.E. & Malhamé, R.P. An Invariance Principle in Large Population Stochastic Dynamic Games. Jrl Syst Sci & Complex 20, 162–172 (2007). https://doi.org/10.1007/s11424-007-9015-4
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DOI: https://doi.org/10.1007/s11424-007-9015-4