Abstract
In 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.
Original language | English (US) |
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Pages (from-to) | 1030-1055 |
Number of pages | 26 |
Journal | SIAM Journal on Control and Optimization |
Volume | 54 |
Issue number | 2 |
DOIs | |
State | Published - Apr 21 2016 |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledgements: Both authors were
supported by KAUST baseline and start-up funds and KAUST SRI, Center for Uncertainty Quantification in Computational Science and Engineering.