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 language | English (US) |
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Pages (from-to) | 49-81 |
Number of pages | 33 |
Journal | Dynamic Games and Applications |
Volume | 12 |
Issue number | 1 |
DOIs | |
State | Published - Mar 2022 |
Externally published | Yes |
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