Abstract
In [14], Gueant, Lasry and Lions considered the model problem ``What time does meeting start?'' as a prototype for a general class of optimization problems with a continuum of players, called Mean Field Games problems. In this paper we consider a similar model, but with the dynamics of the agents defined on a network. We discuss appropriate transition conditions at the vertices which give a well posed problem and we present some numerical results.
Highlights
The mean field is given by the collective behavior of the population
The model: A meeting is scheduled at the unique boundary vertex (i.e., ∂Γ = {v0}) at a certain time t0
The player spends zero time a.s. at the vertex and it enters with the same probability in one of the incident edges
Summary
A brief introduction to Mean Field Games Definition of networks A MFG problem on networks. The Mean Field Games model (MFG) was proposed by Lasry-Lions, and independently by Huang-Malhamé-Caines, in 2006. Distinctive features of the model: The MFG theory is a model to describe interactions among a very large number of agents. The MFG model has some analogies with Statistical Mechanics, where an external field (usually a statistics of some given physical quantity) influences the behavior of the particles. The single agent by itself cannot influence the collective behavior, it can only optimize its own strategy. The mean field is given by the collective behavior of the population. Basic References for MFG theory: Lasry, J.-M., Lions, P.-L. Lions’ lectures at College de France), www.ceremade.dauphine.fr/ cardalia/
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