### Abstract

We consider a class of stochastic games with finite number of resource states, individual states and actions per states. At each stage, a random set of players interact. The states and the actions of all the interacting players determine together the instantaneous payoffs and the transitions to the next states. We study the convergence of the stochastic game with variable set of interacting players when the total number of possible players grow without bound. We provide sufficient conditions for mean field convergence. We characterize the mean field payoff optimality by solutions of a coupled system of backward-forward equations. The limiting games are equivalent to discrete time anonymous sequential population games or to differential population games. Using multidimensional diffusion processes, a general mean field convergence to coupled stochastic differential equation is given. Finally, the computation of mean field equilibria is addressed using Q/H learning.

Original language | English (US) |
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Title of host publication | Proceedings of the 2011 American Control Conference, ACC 2011 |

Pages | 2423-2428 |

Number of pages | 6 |

State | Published - Sep 29 2011 |

Event | 2011 American Control Conference, ACC 2011 - San Francisco, CA, United States Duration: Jun 29 2011 → Jul 1 2011 |

### Other

Other | 2011 American Control Conference, ACC 2011 |
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Country | United States |

City | San Francisco, CA |

Period | 6/29/11 → 7/1/11 |

### Fingerprint

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

*Proceedings of the 2011 American Control Conference, ACC 2011*(pp. 2423-2428). [5991087]

**Mean field stochastic games : Convergence, Q/H-learning and optimality.** / Hamidou, Tembine.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 2011 American Control Conference, ACC 2011.*, 5991087, pp. 2423-2428, 2011 American Control Conference, ACC 2011, San Francisco, CA, United States, 6/29/11.

}

TY - GEN

T1 - Mean field stochastic games

T2 - Convergence, Q/H-learning and optimality

AU - Hamidou, Tembine

PY - 2011/9/29

Y1 - 2011/9/29

N2 - We consider a class of stochastic games with finite number of resource states, individual states and actions per states. At each stage, a random set of players interact. The states and the actions of all the interacting players determine together the instantaneous payoffs and the transitions to the next states. We study the convergence of the stochastic game with variable set of interacting players when the total number of possible players grow without bound. We provide sufficient conditions for mean field convergence. We characterize the mean field payoff optimality by solutions of a coupled system of backward-forward equations. The limiting games are equivalent to discrete time anonymous sequential population games or to differential population games. Using multidimensional diffusion processes, a general mean field convergence to coupled stochastic differential equation is given. Finally, the computation of mean field equilibria is addressed using Q/H learning.

AB - We consider a class of stochastic games with finite number of resource states, individual states and actions per states. At each stage, a random set of players interact. The states and the actions of all the interacting players determine together the instantaneous payoffs and the transitions to the next states. We study the convergence of the stochastic game with variable set of interacting players when the total number of possible players grow without bound. We provide sufficient conditions for mean field convergence. We characterize the mean field payoff optimality by solutions of a coupled system of backward-forward equations. The limiting games are equivalent to discrete time anonymous sequential population games or to differential population games. Using multidimensional diffusion processes, a general mean field convergence to coupled stochastic differential equation is given. Finally, the computation of mean field equilibria is addressed using Q/H learning.

UR - http://www.scopus.com/inward/record.url?scp=80053146604&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80053146604&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9781457700804

SP - 2423

EP - 2428

BT - Proceedings of the 2011 American Control Conference, ACC 2011

ER -