The Current Method for Stationary Mean-Field Games on Networks

Diego Marcon Farias1, Diogo Gomes2, Al Saleh Fatimah2

  • 1Universidade Federal do Rio Grande do Sul
  • 2King Abdullah University of Science and Technology

Details

11:00 - 11:20 | Wed 11 Dec | Méditerranée B12 | WeA09.4

Session: Mean-Field Games I

Abstract

We discuss first-order stationary mean-field games (MFG) on networks. These models arise in traffic and pedestrian flows. First, we address the mathematical formulation of first-order MFG on networks, including junction conditions for the Hamilton-Jacobi (HJ) equation and transmission conditions for the transport equation. Then, using the current method, we convert the MFG into a system of algebraic equations and inequalities. For critical congestion models, we show how to solve this system by linear programming.