Efficiency of Nash equilibria in Epidemic models with Confinements

C. Carballo Lozano, J. Doncel

We formulate a game in an epidemic model with N objects that evolve in discrete time. More precisely, we consider the SIRS model where the players are the objects of the epidemic system and the strategy of the players is the level of exposure to the epidemic (or equivalently, the confinement level). We consider that each infected player incurs a cost and that there is also a cost that is decreasing with the exposure strategy of the players. We formulate the best response of one player as a Markov Decision Process and we provide an algorithm to find a symmetric Nash equilibrium. The obtained result is compared with the global optimum strategy, i.e., with the strategy that must follow the whole population so as to minimize the total cost in the system. According to our numerical work, the Nash equilibria is an almost-efficient strategy and it confines less than the global optimum strategy.

Keywords: SIRS model,Markov Decision Process,Nash equilibrium

Game practice and OR Games I
June 12, 2025  3:30 PM
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