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
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.
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