A mean field route choice game model

We study a route choice game model, where a large number of drivers are circulating on a road network. Given an origin-destination pair, each driver tries to pick the shortest least congested route to minimize his/her travel time. We develop a mean field game based algorithm that generates the drivers' optimal choices and anticipates the evolution of their probability distribution on the network. The optimal choices, which constitute a Nash equilibrium in the limit of an infinite number of drivers, guide a generic driver to his/her destination with the most efficient road. Moreover, they define a maximum likelihood function that can be used to estimate the model's parameters. Our algorithm takes only the drivers' initial distribution as an input, which is typically provided to the drivers by navigation applications. Finally, we illustrate via a numerical scheme how the model can also be used to evaluate the performance of different network configurations. An example shows how adding a road link to an existing network might not improve the expected travel time of the drivers.