Finite State Graphon Games with Applications to Epidemics

Alexander Aurell (), René Carmona (), Gökçe Dayanıklı () and Mathieu Laurière ()
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Alexander Aurell: Princeton University
René Carmona: Princeton University
Gökçe Dayanıklı: Princeton University
Mathieu Laurière: Princeton University

Dynamic Games and Applications, 2022, vol. 12, issue 1, No 3, 49-81

Abstract: 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.

Keywords: Graphon games; Epidemiological models; Machine learning (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s13235-021-00410-2

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