Existence and non-existence for time-dependent mean field games with strong aggregation
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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.
2019 ◽
Vol 45
(2)
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pp. 146-190
2015 ◽
Vol 92
(3)
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pp. 778-799
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2016 ◽
Vol 8
(1)
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pp. 199-210
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2017 ◽
Vol 27
(01)
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pp. 75-113
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2017 ◽
Vol 30
(4)
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pp. 1365-1388
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