Discrete Time, Finite State Space Mean Field Games

  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},
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… 

Mean field limit of a continuous time finite state game

This paper considers the mean field limit of two-state Markov decision problem as the number of players and derives a mean field model, which is a system of coupled ordinary differential equations with initial-terminal data and an estimate of the rate of convergence.

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

Finite Difference Methods for Mean Field Games

Mean field type models describing the limiting behavior of stochastic differential game problems as the number of players tends to + ∞, have been recently introduced by J-M. Lasry and P-L. Lions.

Discrete potential mean field games∗

We propose and investigate a general class of discrete time and finite state space mean field game (MFG) problems with potential structure. Our model incorporates interactions through a congestion

Mean Field Games Models—A Brief Survey

A brief survey of mean-field models as well as recent results and techniques is presented, and a definition of relaxed solution for mean- field games that allows to establish uniqueness under minimal regularity hypothesis is proposed.

Discrete mean field games: Existence of equilibria and convergence

We consider mean field games with discrete state spaces (called discrete mean field games in the following) and we analyze these games in continuous and discrete time, over finite as well as infinite

Stationary Equilibria of Mean Field Games with Finite State and Action Space

A model with finite state and action space, where the dynamics are given by a time-inhomogeneous Markov chain that might depend on the current population distribution and the results allow—given that the generators are irreducible—to characterize the set of stationary mean field equilibria as theset of all fixed points of a map completely characterized by the transition rates and rewards for deterministic strategies.

Discrete-time average-cost mean-field games on Polish spaces

  • Naci Saldi
  • Economics, Mathematics
  • 2020
It is shown that the equilibrium policy in the mean-field game, when adopted by each agent, is an approximate Nash equilibrium for the corresponding finite-agent game with sufficiently many agents.

Finite State N-player and Mean Field Games

Mean field games represent limit models for symmetric non-zero sum dynamic games when the number N of players tends to infinity. In this thesis, we study mean field games and corresponding N- player

Continuous-Time Mean Field Games with Finite State Space and Common Noise

We formulate and analyze a mathematical framework for continuous-time mean field games with finitely many states and common noise, including a rigorous probabilistic construction of the state process



Mean Field Games: Numerical Methods

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