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- W4300172015 abstract "We show the convergence of finite state symmetric N-player differential games, where players control their transition rates from state to state, to a limiting dynamics given by a finite state Mean Field Game system made of two coupled forward-backward ODEs. We exploit the so-called Master Equation, which in this finite-dimensional framework is a first order PDE in the simplex of probability measures, obtaining the convergence of the feedback Nash equilibria, the value functions and the optimal trajectories. The convergence argument requires only the regularity of a solution to the Master equation. Moreover, we employ the convergence method to prove a Central Limit Theorem and a Large Deviation Principle for the evolution of the N-player empirical measures. The well-posedness and regularity of solution to the Master Equation are also studied." @default.
- W4300172015 created "2022-10-03" @default.
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- W4300172015 creator A5066278454 @default.
- W4300172015 date "2017-07-06" @default.
- W4300172015 modified "2023-09-24" @default.
- W4300172015 title "Convergence, Fluctuations and Large Deviations for finite state Mean Field Games via the Master Equation" @default.
- W4300172015 doi "https://doi.org/10.48550/arxiv.1707.01819" @default.
- W4300172015 hasPublicationYear "2017" @default.
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