This paper studies Mean Field Games (MFGs) in which agent dynamics are given
by jump processes of controlled intensity, with mean-field interaction via the
controls and affecting the jump intensities. We establish the existence of MFG
equilibria in a general discrete-time setting, and prove a limit theorem as the
time discretization goes to zero, establishing equilibria in the
continuous-time setting for a class of MFGs of intensity control. This
motivates numerical schemes that involve directly solving discrete-time games
as opposed to coupled Hamilton-Jacobi-Bellman and Kolmogorov equations. As an
example of the general theory, we consider cryptocurrency mining competition,
modeled as an MFG both in continuous and discrete time, and illustrate the
effectiveness of the discrete-time algorithm to solve it.

Dieser Artikel untersucht Zeitreisen und deren Auswirkungen.

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