An invariance principle in large population stochastic dynamic games

Journal of Systems Science and Complexity

Volumn 20, Issue 2, 2007, Pages 162-172

  Huang, Minyi ^a   Caines, Peter E ^b,d   Malhamé, Roland P ^c,d  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b MCGILL UNIVERSITY   (Canada)

^c ÉCOLE POLYTECHNIQUE DE MONTRÉAL   (Canada)

^d GERAD   (Canada)

Author keywords

Large population; Martingale representation; Nash equilibrium; Optimal control; Stochastic dynamic games

Indexed keywords

LARGE POPULATION; MARTINGALE REPRESENTATION; NASH EQUILIBRIUM; STOCHASTIC DYNAMIC GAMES;

DYNAMICAL SYSTEMS; INVARIANCE; OPTIMAL CONTROL SYSTEMS; PROBLEM SOLVING; STOCHASTIC CONTROL SYSTEMS;

GAME THEORY;

EID: 34249075491     PISSN: 10096124     EISSN: 15597067     Source Type: Journal    
DOI: 10.1007/s11424-007-9015-4     Document Type: Conference Paper

References (16)

1. R. P. Isaacs, Differential Games, John Wiley, 1965.
2. T. Başar and G. J. Olsder, Dynamic Noncooperative Game Theory (2nd Ed.), Academic Press, London, UK, 1995.
3. G. M. Erickson, Differential game models of advertsing competition, Europ. J. Oper. Res., 1995, 83: 431-438.
4. E. J. Green, Continuum and finite-player noncooperative models of competition, Econometrica, 1984, 52(4): 975-993.
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.
6. V. E. Lambson, Self-enforcing collusion in large dynamic markets, J. Econ. Theory, 1984, 34: 282-291.
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.
8. M. Huang, R. P. Malhamé, and P. E. Caines, Nash equilibria for large-population linear stochastic systems of weakly coupled agents, in Analysis, Control and Optimization of Complex Dynamic Systems (ed. by E. K. Boukas and R. P. Malhamé), Springer, New York, 2005, 215-252.
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.
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.
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 ε-Nash equilibria, IEEE Transactions on Automatic Control, 2007, 52, to appear.
12. R. Boel and P. Varaiya, Optimal control of jump processes, SIAM J. Control Optim., 1977, 15(1): 92-119.
13. M. H. A. Davis and P. Varaiya, Dynamic programming conditions for partially observable stochastic systems, SIAM J. Control Optim., 1973, 11: 226-261.
14. D. A. Dawson and J. Gärtner, Large deviations from the McKean-Vlasov limit for weakly interacting diffusions, Stochastics, 1987, 20: 247-308.
15. A. S. Sznitman, Topics in propagation of chaos, in Ecole d'Eté de Probabilities de Saint-Flour XIX-1989, Lect. Notes Math. 1464, Springer-Verlag, Berlin, 1991, 165-252.
16. A. Bensoussan, Stochastic Control of Partially Observable Systems, Cambridge Univ. Press, 1992.