| Summary: | This paper proves the existence and uniqueness results (in the sense of
maximally defined regularity) as well as the stability analysis for the
solutions to a class of nonlocal fully-nonlinear parabolic systems, where the
nonlocality stems from the flow feature (controlled by an external temporal
parameter) of the systems. The derived mathematical results generalize the
theory of stochastic differential games to incorporate with behavioral factors
such as time-inconsistent preferences, which facilitate developments of many
studies in financial economics including robust stochastic controls and games
under relative performance concerns. Moreover, with the well-posedness results,
we establish a general multidimensional Feynman--Kac formula in the presence of
nonlocality (time inconsistency).
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