An Invariance Principle in Large Population Stochastic Dynamic Games
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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.
KeywordsLarge population martingale representation Nash equilibrium optimal control stochastic dynamic games
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- 1.R. P. Isaacs, Differential Games, John Wiley, 1965.Google Scholar
- 2.Başar, T., Olsder, G.J. 1995Dynamic Noncooperative Game Theory2Academic PressLondon, UKGoogle Scholar
- 5.M. Huang, P. E. Caines, and R. P. Malhamé, Individual and mass behaviour in large population stochastic wireless power control problems: Centralized and Nash equilibrium solutions, in Proc. the 42nd IEEE Conf. Decision Contr., Maui, Hawaii, December 2003, 98–103.Google Scholar
- 7.M. Ali Khan and Y. Sun, Non-cooperative games with many players, in Handbook of Game Theory with Economic Applications (ed. by R. J. Aumann and S. Hart), North-Holland, 2002, 3.Google Scholar
- 9.M. Huang, R. P. Malhamé, and P. E. Caines, Nash certainty equivalence in large population stochastic dynamic games: Connections with the physics of interacting particle systems, in Proc. the 45th IEEE Conference on Decision and Control, San Diego, CA, December 2006, 4921–4926.Google Scholar
- 10.M. Huang, R. P. Malhamé, and P. E. Caines, Large population stochastic dynamic games: Closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle, Communications in Information and Control, 2007, to appear.Google Scholar
- 11.M. Huang, P. E. Caines, and R. P. Malhamé, Large-population cost-coupled LQG problems with non-uniform agents: Individual-mass behavior and decentralized ɛ-Nash equilibria, IEEE Transactions on Automatic Control, 2007, 52, to appear.Google Scholar
- 14.Dawson, D.A., Gärtner, J. 1987Large deviations from the McKean-Vlasov limit for weakly interacting diffusionsStochastics20247308Google Scholar
- 15.A. S. Sznitman, Topics in propagation of chaos, in Ecole d’Eté de Probabilitiés de Saint-Flour XIX−1989, Lect. Notes Math. 1464, Springer-Verlag, Berlin, 1991, 165–252.Google Scholar
- 16.A. Bensoussan, Stochastic Control of Partially Observable Systems, Cambridge Univ. Press, 1992.Google Scholar