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Finite State Graphon Games with Applications to Epidemics

Author

Listed:
  • Alexander Aurell

    (Princeton University)

  • René Carmona

    (Princeton University)

  • Gökçe Dayanıklı

    (Princeton University)

  • Mathieu Laurière

    (Princeton University)

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.

Suggested Citation

  • Alexander Aurell & René Carmona & Gökçe Dayanıklı & Mathieu Laurière, 2022. "Finite State Graphon Games with Applications to Epidemics," Dynamic Games and Applications, Springer, vol. 12(1), pages 49-81, March.
    • Handle: RePEc:spr:dyngam:v:12:y:2022:i:1:d:10.1007_s13235-021-00410-2
    DOI: 10.1007/s13235-021-00410-2
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    References listed on IDEAS

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