Finite State Graphon Games with Applications to Epidemics

Alexander Aurell, René Carmona, Gökçe Dayanıklı, Mathieu Laurière

Research output: Contribution to journalArticlepeer-review

Abstract

We consider a game for a continuum of non-identical players evolving on a finite state space. Their heterogeneous interactions are represented with a graphon, which can be viewed as the limit of a dense random graph. A player’s transition rates between the states depend on their control and the strength of interaction with the other players. We develop a rigorous mathematical framework for the game and analyze Nash equilibria. We provide a sufficient condition for a Nash equilibrium and prove existence of solutions to a continuum of fully coupled forward-backward ordinary differential equations characterizing Nash equilibria. Moreover, we propose a numerical approach based on machine learning methods and we present experimental results on different applications to compartmental models in epidemiology.

Original languageEnglish (US)
Pages (from-to)49-81
Number of pages33
JournalDynamic Games and Applications
Volume12
Issue number1
DOIs
StatePublished - Mar 2022

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Economics and Econometrics
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

Keywords

  • Epidemiological models
  • Graphon games
  • Machine learning

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