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Finite State Mean Field Games with Common Shocks (2404.08316v1)
Published 12 Apr 2024 in math.OC and math.PR
Abstract: We present a novel framework for mean field games with finite state space and common noise, where the common noise is given through shocks that occur at random times. We first analyze the game for up to $n$ shocks, in which case we are able to characterize mean field equilibria through a system of parameterized and coupled forward-backward equations. We establish existence and uniqueness of solutions to this system for small time horizons. In addition, we show that mean field equilibria for the $n$-shock setting constitute approximate equilibria for the corresponding mean field game with infinitely many common shocks. Our results are illustrated in a corruption detection model with random audits.
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