In this thesis, we consider stationary one-dimensional mean-field games (MFGs) with or without congestion. Our aim is to understand the qualitative features of these games through the analysis of explicit solutions. We are particularly interested in MFGs with a nonmonotonic behavior, which corresponds to situations where agents tend to aggregate.
First, we derive the MFG equations from control theory. Then, we compute
explicit solutions using the current formulation and examine their behavior. Finally, we represent the solutions and analyze the results.
This thesis main contributions are the following: First, we develop the current
method to solve MFG explicitly. Second, we analyze in detail non-monotonic MFGs and discover new phenomena: non-uniqueness, discontinuous solutions, empty regions and unhappiness traps. Finally, we address several regularization procedures and examine the stability of MFGs.
|Date of Award||Apr 5 2017|
|Original language||English (US)|
- Computer, Electrical and Mathematical Science and Engineering
|Supervisor||Diogo Gomes (Supervisor)|
- explicit solutions
- Mean-field games