Control and nash games with mean field effect
Mean field theory has raised a lot of interest in the recent years (see in particular the results of Lasry-Lions in 2006 and 2007, of Gueant-Lasry-Lions in 2011, of Huang-Caines-Malham in 2007 and many others). There are a lot of applications. In general, the applications concern approximating an infinite number of players with common behavior by a representative agent. This agent has to solve a control problem perturbed by a field equation, representing in some way the behavior of the average infinite number of agents. This approach does not lead easily to the problems of Nash equilibrium for a finite number of players, perturbed by field equations, unless one considers averaging within different groups, which has not been done in the literature, and seems quite challenging. In this paper, the authors approach similar problems with a different motivation which makes sense for control and also for differential games. Thus the systems of nonlinear partial differential equations with mean field terms, which have not been addressed in the literature so far, are considered here.
KeywordsMean field Dynamic programming Nash games Equilibrium Calculus of variations
2000 MR Subject Classification49L20
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- Bensoussan, A. and Frehse, J., Regularity results for nonlinear elliptic systems and applications, Appl. Math. Sci., 151, Springer-Verlag, Berlin, 2002.Google Scholar
- Bensoussan, A. and Frehse, J., Ergodic Bellman systems for stochastic games, Markus Feestricht Volume Differential Equations, Dynamical Systems and Control Sciences, Lecture Notes in Pure and Appl. Math., K. D. Elworty, W., Norrie Everitt, E. Bruce Lee, M. Dekker (eds.), Vol. 152, 1993, 411–421.Google Scholar