Game Theory for Networks. Third International ICST Conference, GameNets 2012, Vancouver, BC, Canada, May 24-26, 2012, Revised Selected Papers

Research Article

Mean Field Stochastic Games with Discrete States and Mixed Players

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  • @INPROCEEDINGS{10.1007/978-3-642-35582-0_11,
        author={Minyi Huang},
        title={Mean Field Stochastic Games with Discrete States and Mixed Players},
        proceedings={Game Theory for Networks. Third International ICST Conference, GameNets 2012, Vancouver, BC, Canada, May 24-26, 2012, Revised Selected Papers},
        proceedings_a={GAMENETS},
        year={2012},
        month={12},
        keywords={mean field game finite states major player minor player},
        doi={10.1007/978-3-642-35582-0_11}
    }
    
  • Minyi Huang
    Year: 2012
    Mean Field Stochastic Games with Discrete States and Mixed Players
    GAMENETS
    Springer
    DOI: 10.1007/978-3-642-35582-0_11
Minyi Huang1,*
  • 1: Carleton University
*Contact email: mhuang@math.carleton.ca

Abstract

We consider mean field Markov decision processes with a major player and a large number of minor players which have their individual objectives. The players have decoupled state transition laws and are coupled by the costs via the state distribution of the minor players. We introduce a stochastic difference equation to model the update of the limiting state distribution process and solve limiting Markov decision problems for the major player and minor players using local information. Under a solvability assumption of the consistent mean field approximation, the obtained decentralized strategies are stationary and have an -Nash equilibrium property.