Mean-field games with logistic population dynamics

Abstract
In its standard form, a mean-field game can be defined by coupled system of equations, a Hamilton-Jacobi equation for the value function of agents and a Fokker-Planck equation for the density of agents. Traditionally, the latter equation is adjoint to the linearization of the former. Since the Fokker-Planck equation models a population dynamic, we introduce natural features such as seeding and birth, and nonlinear death rates. In this paper we analyze a stationary meanfield game in one dimension, illustrating various techniques to obtain regularity of solutions in this class of systems. In particular we consider a logistic-type model for birth and death of the agents which is natural in problems where crowding affects the death rate of the agents. The introduction of these new terms requires a number of new ideas to obtain wellposedness. In a forthcoming publication we will address higher dimensional models. ©2013 IEEE.

Citation
Aguiar Gomes, D., & de Lima Ribeiro, R. (2013). Mean-field games with logistic population dynamics. 52nd IEEE Conference on Decision and Control. doi:10.1109/cdc.2013.6760258

Publisher
Institute of Electrical and Electronics Engineers (IEEE)

Journal
52nd IEEE Conference on Decision and Control

Conference/Event Name
52nd IEEE Conference on Decision and Control, CDC 2013

DOI
10.1109/CDC.2013.6760258

Permanent link to this record