A numerical scheme for a mean field game in some queueing systems based on Markov chain approximation method

Erhan Bayraktar; Amarjit Budhiraja; Asaf Cohen

doi:10.1137/17M1154357

A numerical scheme for a mean field game in some queueing systems based on Markov chain approximation method

Erhan Bayraktar, Amarjit Budhiraja, Asaf Cohen

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

We use the Markov chain approximation method to construct approximations for the solution of the mean field game (MFG) with reflecting barriers studied in [E. Bayraktar, A. Budhiraja, and A. Cohen, Ann. Appl. Probab., to appear]. The MFG is formulated in terms of a controlled reflected diffusion with a cost function that depends on the reflection terms in addition to the standard variables: state, control, and the mean field term. This MFG arises from the asymptotic analysis of an N-player game for single server queues with strategic servers. By showing that our scheme is an almost contraction, we establish the convergence of this numerical scheme over a small time interval.

Original language	English
Pages (from-to)	4017-4044
Number of pages	28
Journal	SIAM Journal on Control and Optimization
Volume	56
Issue number	6
DOIs	https://doi.org/10.1137/17M1154357
State	Published - 1 Jan 2018
Externally published	Yes

Keywords

Heavy traffic limits
Markov chain approximation method
Mean field games
Nash equilibrium
Numerical scheme
Queuing systems
Rate control
Reflected diffusions

ASJC Scopus subject areas

Control and Optimization
Applied Mathematics

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10.1137/17M1154357

Cite this

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title = "A numerical scheme for a mean field game in some queueing systems based on Markov chain approximation method",

abstract = "We use the Markov chain approximation method to construct approximations for the solution of the mean field game (MFG) with reflecting barriers studied in [E. Bayraktar, A. Budhiraja, and A. Cohen, Ann. Appl. Probab., to appear]. The MFG is formulated in terms of a controlled reflected diffusion with a cost function that depends on the reflection terms in addition to the standard variables: state, control, and the mean field term. This MFG arises from the asymptotic analysis of an N-player game for single server queues with strategic servers. By showing that our scheme is an almost contraction, we establish the convergence of this numerical scheme over a small time interval.",

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N2 - We use the Markov chain approximation method to construct approximations for the solution of the mean field game (MFG) with reflecting barriers studied in [E. Bayraktar, A. Budhiraja, and A. Cohen, Ann. Appl. Probab., to appear]. The MFG is formulated in terms of a controlled reflected diffusion with a cost function that depends on the reflection terms in addition to the standard variables: state, control, and the mean field term. This MFG arises from the asymptotic analysis of an N-player game for single server queues with strategic servers. By showing that our scheme is an almost contraction, we establish the convergence of this numerical scheme over a small time interval.

AB - We use the Markov chain approximation method to construct approximations for the solution of the mean field game (MFG) with reflecting barriers studied in [E. Bayraktar, A. Budhiraja, and A. Cohen, Ann. Appl. Probab., to appear]. The MFG is formulated in terms of a controlled reflected diffusion with a cost function that depends on the reflection terms in addition to the standard variables: state, control, and the mean field term. This MFG arises from the asymptotic analysis of an N-player game for single server queues with strategic servers. By showing that our scheme is an almost contraction, we establish the convergence of this numerical scheme over a small time interval.

KW - Heavy traffic limits

KW - Markov chain approximation method

KW - Mean field games

KW - Nash equilibrium

KW - Numerical scheme

KW - Queuing systems

KW - Rate control

KW - Reflected diffusions

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A numerical scheme for a mean field game in some queueing systems based on Markov chain approximation method

Abstract

Keywords

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