We investigate the existence of classical solutions to second-order quadratic Mean-Field Games systems with local and strongly decreasing couplings of the form - σmα,α≥ 2 / N, where m is the population density and N is the dimension of the state space. We prove the existence of solutions under the assumption that σ is small enough. For large σ, we show that existence may fail whenever the time horizon T is large.
Existence and non-existence for time-dependent mean field games with strong aggregation
Cirant M.;Ghilli D.
2021
Abstract
We investigate the existence of classical solutions to second-order quadratic Mean-Field Games systems with local and strongly decreasing couplings of the form - σmα,α≥ 2 / N, where m is the population density and N is the dimension of the state space. We prove the existence of solutions under the assumption that σ is small enough. For large σ, we show that existence may fail whenever the time horizon T is large.
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