Finite state graphon games with applications to epidemics. (English) Zbl 1489.91052
Summary: 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.
MSC:
| 91A43 | Games involving graphs |
| 91A16 | Mean field games (aspects of game theory) |
| 92D30 | Epidemiology |
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