Abstract
We consider a non-cooperative game in the SIR model with confinements. Each member of the population is a player whose strategy is her probability of being protected from the epidemic. We assume that for each player, there is a cost of infection per unit time and a cost of being confined, which is linear and decreasing on her confinement strategy. The total cost is defined as the sum of her confinement and infection costs. We present a method for computing a symmetric Nash equilibrium for this game and study its efficiency. We conclude that the Nash equilibrium we obtain leads to fewer confinements than the strategy that minimizes the cost of the entire population.
This work has been partially supported by the Department of Education of the Basque Government, Spain through the Consolidated Research Group MATHMODE (IT1294-19) and by the Marie Sklodowska-Curie grant agreement No 777778.
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Notes
- 1.
The code to reproduce the experiments of this section is available at https://github.com/josudoncel/StudentsCode/tree/main/MaiderSanchezJimenez.
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Sanchez, M., Doncel, J. (2024). Efficiency of Symmetric Nash Equilibria in Epidemic Models with Confinements. In: Kalyvianaki, E., Paolieri, M. (eds) Performance Evaluation Methodologies and Tools. VALUETOOLS 2023. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 539. Springer, Cham. https://doi.org/10.1007/978-3-031-48885-6_4
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