A game theory analysis of decentralized epidemic management with opinion dynamics

In this paper, we introduce a static game that allows one to numerically assess the loss of efficiency induced by decentralized control or management of a global epidemic. Each player represents a region, which is assumed to choose its control to implement a tradeoff between socio-economic aspects and health aspects; the control comprises both epidemic control physical measures and influence actions on the region's opinion. The Generalized Nash equilibrium (GNE) analysis of the proposed game model is conducted. The direct analysis of this game of practical interest is non-trivial but it turns out that one can construct an auxiliary game which allows one: to prove existence and uniqueness; to compute the GNE and the optimal centralized solution (sum-cost) of the game. These results allow us to assess numerically the loss (measured in terms of Price of Anarchy (PoA) induced by decentralization with or without taking into account the opinion dynamics.