Vaccination in a Large Population: Mean Field Equilibrium versus Social Optimum

Bruno Gaujal (1) , Josu Doncel (2) , Nicolas Gast (1)

1 POLARIS - Performance analysis and optimization of LARge Infrastructures and Systems
2 UPV / EHU - University of the Basque Country = Euskal Herriko Unibertsitatea

We analyze a virus propagation dynamics in a large population of agents (or nodes) with three possible states (Susceptible, Infected, Recovered) where agents may choose to vaccinate. We show that this system admits a unique symmetric equilibrium when the number of agents goes to infinity. We also show that the vaccination strategy that minimizes the social cost has the same threshold structure as the mean field equilibrium, but with a shorter threshold. This implies that, to encourage optimal vaccination behavior, vaccination should always be subsidized.

Domaines: Informatique et théorie des jeux [cs.GT]

Bruno Gaujal, Josu Doncel, Nicolas Gast. Vaccination in a Large Population: Mean Field Equilibrium versus Social Optimum. NETGCOOP 2020 - 10th International Conference on NETwork Games, COntrol and OPtimization, Sep 2021, Cargèse, France. pp.1-9. ⟨hal-02938850⟩