arxiv:2603.05624

Mean-field games with unbounded controls: a weak formulation approach to global solutions

Published on Mar 5

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Abstract

Existence of equilibrium is established for non-Markovian mean-field games with unbounded control space through new results for quadratic-growth generalized McKean-Vlasov BSDEs without requiring boundedness assumptions on model parameters or time horizons.

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We establish an existence of equilibrium result for a class of non-Markovian mean-field games with unbounded control space in weak formulation. Our result is based on new existence and stability results for quadratic-growth generalized McKean-Vlasov BSDEs. Unlike earlier approaches, our approach does not require boundedness assumptions on the model parameters or time horizons and allows for running costs that are quadratic in the control variable.

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