# Continuous Time Finite State Mean Field Games

Continuous Time Finite State Mean Field Games In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N +1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N →∞ of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

# Continuous Time Finite State Mean Field Games

, Volume 68 (1) – Aug 1, 2013
45 pages

/lp/springer_journal/continuous-time-finite-state-mean-field-games-lAfXx0povU
Publisher
Springer US
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-013-9202-8
Publisher site
See Article on Publisher Site

### Abstract

In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N +1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N →∞ of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games.

### Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Aug 1, 2013

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