| Abstract: |
| We consider a strongly degenerate and fully nonlinear MFG system. Our MFG involves a controlled pure jump (nonlocal) Levy diffusion of order less than one, and monotone, smoothing couplings. We study the existence and uniqueness results of such problems. We discuss the key difficulty in obtaining uniqueness for the corresponding Fokker--Planck equation which has degenerate and low regularity diffusion coefficients: since the regularity of the coefficient and the order of the diffusion are interdependent, it holds when the order is sufficiently low. |
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