One-dimensional, forward-forward mean-field games with congestion
| Autor: | Marc Sedjro, Diogo A. Gomes |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
0209 industrial biotechnology
Conservation law Applied Mathematics 010102 general mathematics 02 engineering and technology 01 natural sciences Upper and lower bounds Binary entropy function Riemann hypothesis symbols.namesake 020901 industrial engineering & automation Mean field theory symbols Discrete Mathematics and Combinatorics Applied mathematics Convergence problem 0101 mathematics Invariant (mathematics) Analysis Mathematics |
| Zdroj: | Discrete & Continuous Dynamical Systems - S. 11:901-914 |
| ISSN: | 1937-1179 |
| DOI: | 10.3934/dcdss.2018054 |
| Popis: | Here, we consider one-dimensional forward-forward mean-field games (MFGs) with congestion, which were introduced to approximate stationary MFGs. We use methods from the theory of conservation laws to examine the qualitative properties of these games. First, by computing Riemann invariants and corresponding invariant regions, we develop a method to prove lower bounds for the density. Next, by combining the lower bound with an entropy function, we prove the existence of global solutions for parabolic forward-forward MFGs. Finally, we construct traveling-wave solutions, which settles in a negative way the convergence problem for forward-forward MFGs. A similar technique gives the existence of time-periodic solutions for non-monotonic MFGs. |
| Databáze: | OpenAIRE |
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