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Theoretical analysis establishes well-posedness of master equations with common noise in finite state spaces, demonstrating existence of Lipschitz continuous solutions on arbitrary time intervals.
This paper provides a mathematical study of the well-posedness of a master equation with terms modeling common noise on finite state space. In this setting, the solution of the master equation depends on an additional variable modeling the value of a stochastic process impacting all players. Using techniques from viscosity solutions, we give sufficient conditions for the existence of a Lipschitz continuous solution on any time interval. Under some structural assumptions, we are even able to treat cases in which the dynamics of this stochastic process depend on the state of the game.
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Bertucci et al. (2026) studied this question.
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