TY - JOUR
T1 - Existence of Weak Solutions to Stationary Mean-Field Games through Variational Inequalities
AU - Ferreira, Rita
AU - Gomes, Diogo A.
N1 - KAUST Repository Item: Exported on 2021-02-23
Acknowledgements: The work of the authors was partially supported by KAUST baseline and start-up funds and by KAUST SRI, Center for Uncertainty Quantification in Computational Science and Engineering.
PY - 2018/12/4
Y1 - 2018/12/4
N2 - Here, we consider stationary monotone mean-field games (MFGs) and study the existence of weak solutions induced by monotonicity. First, we introduce a regularized problem that preserves the monotonicity. Next, using variational inequality techniques, we prove the existence of solutions to the regularized problem. Then, using Minty's method, we establish the existence of weak solutions for the original MFG. Finally, we examine the properties of these weak solutions in several examples. Our methods provide a general framework to construct weak solutions to stationary MFGs with local, nonlocal, or congestion terms.
AB - Here, we consider stationary monotone mean-field games (MFGs) and study the existence of weak solutions induced by monotonicity. First, we introduce a regularized problem that preserves the monotonicity. Next, using variational inequality techniques, we prove the existence of solutions to the regularized problem. Then, using Minty's method, we establish the existence of weak solutions for the original MFG. Finally, we examine the properties of these weak solutions in several examples. Our methods provide a general framework to construct weak solutions to stationary MFGs with local, nonlocal, or congestion terms.
UR - http://hdl.handle.net/10754/631098
UR - https://epubs.siam.org/doi/10.1137/16M1106705
UR - http://www.scopus.com/inward/record.url?scp=85060554030&partnerID=8YFLogxK
U2 - 10.1137/16M1106705
DO - 10.1137/16M1106705
M3 - Article
AN - SCOPUS:85060554030
VL - 50
SP - 5969
EP - 6006
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
SN - 0036-1410
IS - 6
ER -