Finite State Graphon Games with Applications to Epidemics

• Published in: Dynamic games and applications Vol. 12; no. 1; pp. 49 - 81
• Main Authors: Aurell, Alexander, Carmona, René, Dayanıklı, Gökçe, Laurière, Mathieu
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.03.2022; Springer Nature B.V
• Subjects: Communications Engineering; Computer Systems Organization and Communication Networks; Differential equations; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Epidemiology; Game Theory; Graphical representations; Machine learning; Management Science; Mathematics; Mathematics and Statistics; Modeling and Control of Epidemics; Networks; Operations Research; Ordinary differential equations; Players; Social and Behav. Sciences; Epidemiological models; Graphon games; Machine learning
• ISSN: 2153-0785; 2153-0793
• DOI: 10.1007/s13235-021-00410-2

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.