In this paper, we introduce a game that allows one to assess the potential loss of efficiency induced by a decentralized control or local management of a global epidemic. Each player typically represents a region or a country which is assumed to choose its control action to implement a tradeoff between socioeconomic aspects and the health aspect. We conduct the Nash equilibrium analysis of this game. Since the analysis is not trivial in general, sufficient conditions for existence and uniqueness are provided. Then we quantify through numerical results the loss induced by decentralization, measured in terms of price of anarchy (PoA) and price of connectedness (PoC). These results allow one to clearly identify scenarios where decentralization is acceptable or not regarding to the retained global efficiency measures.
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