Two numerical approaches to stationary mean-field games
Provides numerical tools for solving stationary mean-field games, which are important in economics and game theory, but the contribution is incremental as it applies known techniques to a specific class of problems.
The paper develops two numerical methods for stationary mean-field games: a gradient-flow method based on variational characterization and a method exploiting monotonicity properties. The methods are demonstrated on 1D periodic, congestion, and higher-dimensional examples.
Here, we consider numerical methods for stationary mean-field games (MFG) and investigate two classes of algorithms. The first one is a gradient-flow method based on the variational characterization of certain MFG. The second one uses monotonicity properties of MFG. We illustrate our methods with various examples, including one-dimensional periodic MFG, congestion problems, and higher-dimensional models.