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Mean Field Games with Ergodic cost for Discrete Time Markov Processes

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arxiv 1510.08968 v1 pith:4VVDNN5Y submitted 2015-10-30 math.PR math.OC

Anup Biswas This is my paper · ORCID
classification math.PRmath.OC
keywords fieldgamemeanprocessescostdiscreteequilibriumergodic
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abstract

We consider mean field games with ergodic cost in the framework of a general discrete time controlled Markov processes. The state space of the processes is given by a general $\sigma$-compact Polish space. Under certain conditions, we show the existence of a mean field game equilibrium. We also study the $N$-person game where the players interacts with each other via their empirical measure. We show that the $N$-person game has Nash equilibrium and as $N$ tends to infinity the equilibria converge to a mean field game solution.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Mean Field Games of Control and Cryptocurrency Mining

    math.OC 2025-04 conditional novelty 7.0 of 10

    For a class of intensity-control mean field games, including cryptocurrency mining, the paper proves equilibrium existence and shows continuous-time equilibria arise as limits of discrete-time ones.

  2. Value Iteration Algorithm for Mean-field Games

    eess.SY 2019-09 conditional novelty 6.0 of 10

    A Q-function value iteration scheme converges to a mean-field equilibrium in discrete-time mean-field games for both discounted and average costs.

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

    math.OC 2019-08 conditional novelty 6.0 of 10

    Discrete-time average-cost mean-field games on Polish spaces admit mean-field equilibria under drift and minorization conditions, and these equilibria yield approximate Nash equilibria for finite-player games.

  4. Robustness and Approximation of Discrete-time Mean-field Games under Discounted Cost Criterion

    eess.SY 2023-10 unverdicted novelty 5.0 of 10

    Stationary mean-field equilibria from value iteration remain robust to dynamics misspecification and finite-state quantizations converge to the nominal equilibrium when the grid is sufficiently fine.

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