We analyze a model of agent based vaccination campaign against influenza with imperfect vaccine efficacy and limited persistence. We prove the existence of a Nash equilibrium by Kakutani's fixed point theorem in the context of non-persistent immunity. Subsequently, we propose and test a novel numerical method to find the equilibrium. Various issues of the model are then discussed, among which the dependence of the optimal policy with respect to the imperfections of the vaccine and the best vaccination timing.