The degeneracy of the mean field games poses
Research gap analysis derived from 3 mathematics papers in our local library.
The gap
The degeneracy of the mean field games poses a significant technical challenge. The unboundedness of the functional diffusion coefficients also poses a challenge. The need to establish the well-posedness and regularity of the value function
Evidence profile
Sourced from the future-work section and stated research gap and stated challenges of the source papers, classified as general, spanning 3 journals.
Research trend
Established — well-defined area with open sub-problems.
Supporting evidence — 4 representative gaps
- Well-posedness of McKean-Vlasov SDEs with density-dependent drift (2026) · Stochastics and Dynamics · doi
The paper suggests that future research should focus on extending the results to more general cases, such as unbounded drift coefficients or non-distribution-free diffusion coefficients. The paper suggests that future research should explore the applications of the results to mean-field games and other contexts.
generalfuture-work sectionevidence 5/5Keywords: paper suggests future research focus extending results general - Noise through an Additional Variable for Mean Field Games Master Equation on Finite State Space (2026) · SIAM Journal on Mathematical Analysis · doi
The paper identifies a gap in the study of mean field games master equations associated to games in which a common source of randomness is affecting all players through a finite dimensional parameter. It notes that the class of MFG master equation naturally models situations which are not proper MFG, but general economic equilibria of large populations.
generalstated research gapevidence 5/5Keywords: paper identifies gap study mean field games master - A Class of Degenerate Mean Field Games, Associated FBSDEs, and Master Equations (2026) · SIAM Journal on Control and Optimization · doi
The lack of a comprehensive study on degenerate mean field games with state-distribution dependent and unbounded functional diffusion coefficients. The need for a novel approach to solving degenerate MFGs. The gap in prior research on the well-posedness and regularity of the value functional.
generalstated research gapevidence 5/5Keywords: lack comprehensive study degenerate mean field games state-distribution - A Class of Degenerate Mean Field Games, Associated FBSDEs, and Master Equations (2026) · SIAM Journal on Control and Optimization · doi
The degeneracy of the mean field games poses a significant technical challenge. The unboundedness of the functional diffusion coefficients also poses a challenge. The need to establish the well-posedness and regularity of the value functional is a key challenge.
generalstated challengesevidence 5/5Keywords: degeneracy mean field games poses significant technical challenge
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