TY - JOUR
T1 - One-Dimensional Stationary Mean-Field Games with Local Coupling
AU - Gomes, Diogo A.
AU - Nurbekyan, Levon
AU - Prazeres, Mariana
N1 - KAUST Repository Item: Exported on 2020-10-01
PY - 2017/5/25
Y1 - 2017/5/25
N2 - A standard assumption in mean-field game (MFG) theory is that the coupling between the Hamilton–Jacobi equation and the transport equation is monotonically non-decreasing in the density of the population. In many cases, this assumption implies the existence and uniqueness of solutions. Here, we drop that assumption and construct explicit solutions for one-dimensional MFGs. These solutions exhibit phenomena not present in monotonically increasing MFGs: low-regularity, non-uniqueness, and the formation of regions with no agents.
AB - A standard assumption in mean-field game (MFG) theory is that the coupling between the Hamilton–Jacobi equation and the transport equation is monotonically non-decreasing in the density of the population. In many cases, this assumption implies the existence and uniqueness of solutions. Here, we drop that assumption and construct explicit solutions for one-dimensional MFGs. These solutions exhibit phenomena not present in monotonically increasing MFGs: low-regularity, non-uniqueness, and the formation of regions with no agents.
UR - http://hdl.handle.net/10754/625594
UR - https://link.springer.com/article/10.1007%2Fs13235-017-0223-9
UR - http://www.scopus.com/inward/record.url?scp=85045415487&partnerID=8YFLogxK
U2 - 10.1007/s13235-017-0223-9
DO - 10.1007/s13235-017-0223-9
M3 - Article
SN - 2153-0785
VL - 8
SP - 315
EP - 351
JO - Dynamic Games and Applications
JF - Dynamic Games and Applications
IS - 2
ER -