Mean field game theory

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Mean field game theory is the study of strategic decision making in very large populations of small interacting individuals. This class of problems was considered in the economics literature by Jovanovic and Rosenthal,[1] in the engineering literature by Peter E. Caines and his co-workers[2][3] and independently and around the same time by Jean-Michel Lasry and Pierre-Louis Lions.[4][5][6][7]

Use of the term 'mean field' is inspired by mean field theory in physics which considers the behaviour of systems of large numbers of particles where individual particles have negligible impact upon the system.

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  1. ^ Jovanovic, Boyan and Rosenthal, Robert W., 1988. "Anonymous sequential games," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 77–87, February
  2. ^ M.Y. Huang, R.P. Malhame and P.E. Caines, "Large Population Stochastic Dynamic Games: Closed-Loop McKean–Vlasov Systems and the Nash Certainty Equivalence Principle," Special issue in honor of the 65th birthday of Tyrone Duncan,Communications in Information and Systems. Vol 6, Number 3, 2006, pp 221–252.
  3. ^ M. Nourian and P. E. Caines, "ε–Nash mean field game theory for nonlinear stochastic dynamical systems with major and minor agents," SIAM Journal on Control and Optimization, Vol. 51, No. 4, 2013, pp. 3302–3331.
  4. ^ Lions, P. L.; Lasry, J. M. (2007). "Large investor trading impacts on volatility". Annales de l'Institut Henri Poincaré C. 24 (2): 311. doi:10.1016/j.anihpc.2005.12.006. 
  5. ^ Lasry, J. M.; Lions, P. L. (2007). "Mean field games". Japanese Journal of Mathematics. 2: 229. doi:10.1007/s11537-007-0657-8. 
  6. ^ Lasry, J. M.; Lions, P. L. (2006). "Jeux à champ moyen. II – Horizon fini et contrôle optimal". Comptes Rendus Mathematique. 343 (10): 679. doi:10.1016/j.crma.2006.09.018. 
  7. ^ Lasry, J. M.; Lions, P. L. (2006). "Jeux à champ moyen. I – Le cas stationnaire". Comptes Rendus Mathematique. 343 (9): 619. doi:10.1016/j.crma.2006.09.019. 

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