Fourier approximation methods for first-order nonlocal mean-field games
نویسندگان
چکیده
منابع مشابه
Mean Field Games: Numerical Methods
Mean field type models describing the limiting behavior of stochastic differential game problems, as the number of players tends to +∞, have recently been introduced by J-M. Lasry and P-L. Lions. Numerical methods for the approximation of stationary and nonstationary such models are proposed. In particular, existence and uniqueness are investigated, as well as bounds on the solutions. Numerical...
متن کاملWeak solutions for first order mean field games with local coupling
Existence and uniqueness of a weak solution for first order mean field game systems with local coupling are obtained by variational methods. This solution can be used to devise ǫ−Nash equilibria for deterministic differential games with a finite (but large) number of players. For smooth data, the first component of the weak solution of the MFG system is proved to satisfy (in a viscosity sense) ...
متن کاملMean-field approximation for a limit order driven market model.
A mean-field variant of the model of limit order driven market introduced recently by Maslov is formulated and solved. The agents do not have any strategies and the memory of the system is kept within the order book. We show that the evolution of the order book is governed by a matrix multiplicative process. The resulting stationary distribution of step-to-step price changes is calculated. It e...
متن کاملMean Field Games: Numerical Methods for the Planning Problem
Mean fields games describe the asymptotic behavior of differential games in which the number of players tends to +∞. Here we consider a numerical method for the optimal planning problem, i.e. the problem in which the positions of a very large number of identical rational agents, with common value function, evolve from a given initial spatial density to a desired target density at the final hori...
متن کاملMean-Field Games for Marriage
This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Portugaliae Mathematica
سال: 2019
ISSN: 0032-5155
DOI: 10.4171/pm/2023