Mean-field games with logistic population dynamics

Diogo A. Gomes, Ricardo de Lima Ribeiro

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations

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.
Original languageEnglish (US)
Title of host publication52nd IEEE Conference on Decision and Control
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Pages2513-2518
Number of pages6
ISBN (Print)9781467357173
DOIs
StatePublished - Dec 2013

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