AbstractWe investigate the existence of classical solutions to second-order quadratic Mean-Field Games systems with local and strongly decreasing couplings of the form $$-\sigma m^\alpha $$
-
σ
m
α
,$$\alpha \ge 2/N$$
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 $$\sigma $$
σ
is small enough. For large $$\sigma $$
σ
, we show that existence may fail whenever the time horizon T is large.
Lax connection and conserved quantities of quadratic mean field games
