Discrete Time, Finite State Space Mean Field Games

@article{Gomes2010DiscreteTF,
  title={Discrete Time, Finite State Space Mean Field Games},
  author={Diogo A. Gomes and Joana Mohr and Rafael R. Souza},
  journal={Journal de Math{\'e}matiques Pures et Appliqu{\'e}es},
  year={2010},
  volume={93},
  pages={308-328}
}
In this paper we report on some recent results for mean field models in discrete time with a finite number of states. These models arise in situations that involve a very large number of agents moving from state to state according to certain optimality criteria. The mean field approach for optimal control and differential games (continuous state and time) was introduced by Lasry and Lions (C. R. Math. Acad. Sci. Paris, 343(9):619–625, 2006; 343(10):679–684, 2006; Jpn. J. Math., 2(1):229–260… 

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References

SHOWING 1-6 OF 6 REFERENCES

Mean Field Games: Numerical Methods

TLDR
Numerical methods for the approximation of the stationary and evolutive versions of stochastic differential game models are proposed here and existence and uniqueness properties as well as bounds for the solutions of the discrete schemes are investigated.

Mean field games

Abstract.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

Introduction to Optimization

Series Preface*Preface*Introduction*Linear Programming*Nonlinear Programming* Approximation Techniques*Variational Problems and Dynamic Programming*Optimal Control*References*Index