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Title: 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{yields}{infinity} 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.
Authors:
 [1] ; ;  [2]
  1. Instituto Superior Tecnico, Center for Mathematical Analysis, Geometry, and Dynamical Systems, Departamento de Matematica (Portugal)
  2. UFRGS, Instituto de Matematica (Brazil)
Publication Date:
OSTI Identifier:
22122868
Resource Type:
Journal Article
Resource Relation:
Journal Name: Applied Mathematics and Optimization; Journal Volume: 68; Journal Issue: 1; Other Information: Copyright (c) 2013 Springer Science+Business Media New York; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; APPROXIMATIONS; CONVERGENCE; D STATES; DIFFERENTIAL EQUATIONS; GAME THEORY; MATHEMATICAL SOLUTIONS; MEAN-FIELD THEORY; SYMMETRY