Mean Field Games: Convergence of a Finite Difference Method
نویسندگان
چکیده
منابع مشابه
Socio-economic applications of finite state mean field games.
In this paper, we present different applications of finite state mean field games to socio-economic sciences. Examples include paradigm shifts in the scientific community or consumer choice behaviour in the free market. The corresponding finite state mean field game models are hyperbolic systems of partial differential equations, for which we present and validate different numerical methods. We...
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Abstract. Mean field type models describing the limiting behavior of stochastic differential games as the number of players tends to +∞, have been recently introduced by J-M. Lasry and P-L. Lions. Under suitable assumptions, they lead to a system of two coupled partial differential equations, a forward Bellman equation and a backward Fokker-Planck equations. Finite difference schemes for the ap...
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Abstract. Mean field type models describing the limiting behavior of stochastic differential games as the number of players tends to +∞, have been recently introduced by J-M. Lasry and P-L. Lions. Under suitable assumptions, they lead to a system of two coupled partial differential equations, a forward Bellman equation and a backward Fokker-Planck equations. Finite difference schemes for the ap...
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The convergence rates for the non-linear coarse mesh finite difference (CMFD) method and the coarse mesh rebalance (CMR) method are derived analytically for one-group, one-dimensional solutions of the fixed source diffusion problem in a non-multiplying infinite homogeneous medium. The derivation was performed by linearizing the non-linear algorithm and by applying Fourier error analysis to the ...
متن کاملMean Field Games
We survey here some recent studies concerning what we call mean-field models by analogy with Statistical Mechanics and Physics. More precisely, we present three examples of our mean-field approach to modelling in Economics and Finance (or other related subjects. . . ). Roughly speaking, we are concerned with situations that involve a very large number of “rational players” with a limited inform...
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ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 2013
ISSN: 0036-1429,1095-7170
DOI: 10.1137/120882421