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AbstractIn this paper, we consider mean-field games where the interaction of each player with the mean field takes into account not only the states of the players but also their collective behavior. To do so, we develop a random variable framework that is particularly convenient for these problems. We prove an existence result for extended mean-field games and establish uniqueness conditions. In the last section, we consider the Master Equation and discuss properties of its solutions.
CitationExtended Deterministic Mean-Field Games 2016, 54 (2):1030 SIAM Journal on Control and Optimization
SponsorsBoth authors were supported by KAUST baseline and start-up funds and KAUST SRI, Center for Uncertainty Quantification in Computational Science and Engineering.