Mean field difference games: McKean-Vlasov dynamics

Tembine Hamidou, M. Huang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We study a class of mean field stochastic games in discrete time and continuous state space. Each player has its own individual state evolution described by a stochastic difference equation which depends not only on the control of the corresponding player but also on the states of the other players. Considering the specific structure of aggregate drift and diffusion terms, we use classical asymptotic indistinguishability properties to prove a mean field convergence in distribution. The methodology is extended to multiple classes of players, each class satisfying the asymptotic indistinguishability property, and a propagation of chaos result is obtained over the hull trajectory. Finally, we derive combined backward-forward equations that characterize the mean field equilibria for finite horizon problems.

Original languageEnglish (US)
Title of host publication2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Pages1006-1011
Number of pages6
DOIs
StatePublished - Dec 1 2011
Event2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 - Orlando, FL, United States
Duration: Dec 12 2011Dec 15 2011

Other

Other2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
CountryUnited States
CityOrlando, FL
Period12/12/1112/15/11

Fingerprint

Difference equations
Chaos theory
Mean Field
Trajectories
Game
Asymptotic Properties
Propagation of Chaos
Stochastic Difference Equation
Convergence in Distribution
Stochastic Games
Finite Horizon
State Space
Discrete-time
Trajectory
Methodology
Term
Class

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

Hamidou, T., & Huang, M. (2011). Mean field difference games: McKean-Vlasov dynamics. In 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 (pp. 1006-1011). [6160875] https://doi.org/10.1109/CDC.2011.6160875

Mean field difference games : McKean-Vlasov dynamics. / Hamidou, Tembine; Huang, M.

2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. 2011. p. 1006-1011 6160875.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Hamidou, T & Huang, M 2011, Mean field difference games: McKean-Vlasov dynamics. in 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011., 6160875, pp. 1006-1011, 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011, Orlando, FL, United States, 12/12/11. https://doi.org/10.1109/CDC.2011.6160875
Hamidou T, Huang M. Mean field difference games: McKean-Vlasov dynamics. In 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. 2011. p. 1006-1011. 6160875 https://doi.org/10.1109/CDC.2011.6160875
Hamidou, Tembine ; Huang, M. / Mean field difference games : McKean-Vlasov dynamics. 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. 2011. pp. 1006-1011
@inproceedings{e7eddb465f4b492b97b232f99894546c,
title = "Mean field difference games: McKean-Vlasov dynamics",
abstract = "We study a class of mean field stochastic games in discrete time and continuous state space. Each player has its own individual state evolution described by a stochastic difference equation which depends not only on the control of the corresponding player but also on the states of the other players. Considering the specific structure of aggregate drift and diffusion terms, we use classical asymptotic indistinguishability properties to prove a mean field convergence in distribution. The methodology is extended to multiple classes of players, each class satisfying the asymptotic indistinguishability property, and a propagation of chaos result is obtained over the hull trajectory. Finally, we derive combined backward-forward equations that characterize the mean field equilibria for finite horizon problems.",
author = "Tembine Hamidou and M. Huang",
year = "2011",
month = "12",
day = "1",
doi = "10.1109/CDC.2011.6160875",
language = "English (US)",
isbn = "9781612848006",
pages = "1006--1011",
booktitle = "2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011",

}

TY - GEN

T1 - Mean field difference games

T2 - McKean-Vlasov dynamics

AU - Hamidou, Tembine

AU - Huang, M.

PY - 2011/12/1

Y1 - 2011/12/1

N2 - We study a class of mean field stochastic games in discrete time and continuous state space. Each player has its own individual state evolution described by a stochastic difference equation which depends not only on the control of the corresponding player but also on the states of the other players. Considering the specific structure of aggregate drift and diffusion terms, we use classical asymptotic indistinguishability properties to prove a mean field convergence in distribution. The methodology is extended to multiple classes of players, each class satisfying the asymptotic indistinguishability property, and a propagation of chaos result is obtained over the hull trajectory. Finally, we derive combined backward-forward equations that characterize the mean field equilibria for finite horizon problems.

AB - We study a class of mean field stochastic games in discrete time and continuous state space. Each player has its own individual state evolution described by a stochastic difference equation which depends not only on the control of the corresponding player but also on the states of the other players. Considering the specific structure of aggregate drift and diffusion terms, we use classical asymptotic indistinguishability properties to prove a mean field convergence in distribution. The methodology is extended to multiple classes of players, each class satisfying the asymptotic indistinguishability property, and a propagation of chaos result is obtained over the hull trajectory. Finally, we derive combined backward-forward equations that characterize the mean field equilibria for finite horizon problems.

UR - http://www.scopus.com/inward/record.url?scp=84860701580&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84860701580&partnerID=8YFLogxK

U2 - 10.1109/CDC.2011.6160875

DO - 10.1109/CDC.2011.6160875

M3 - Conference contribution

AN - SCOPUS:84860701580

SN - 9781612848006

SP - 1006

EP - 1011

BT - 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011

ER -