First-order, stationary mean-field games with congestion
 
 
Description:  Mean-field games (MFGs) are models for large populations of competing, rational agents that seek to optimize a suitable functional. In the case of congestion, this functional takes into account the difficulty of moving in high-density areas.

In this talk, I will present a recent contribution on MFGs with congestion with power-like Hamiltonians. First, using explicit examples, I will illustrate two main difficulties: the lack of classical solutions and the existence of areas with vanishing density. Next, I will present our main contribution - a new variational formulation for MFGs with congestion. This formulation was not previously known, and, thanks to it, we prove the existence and uniqueness of solutions. Consequently, we show that the MFG congestion model under consideration is well-posed for a far larger set of parameters than it was previously known.

Furthermore, I will discuss various new transformations for MFGs with congestion that, in some cases, significantly simplify the problem. Finally, I will present some numerical applications.

 

Date:  2017-10-27
Start Time:   14:30
Speaker:  Levon Nurbekyan (KAUST, Saudi Arabia)
Institution:  KAUST, Saudi Arabia
Place:  Room 5.5
Research Groups: -Analysis
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