Effect of noise-perturbing intermediate defense measures in voluntary vaccination games

Recently, a new vaccination game model was proposed, where an intermediate defense measure besides two fundamental strategies; committing vaccination that leads to a perfect immunity and not committing vaccination, was introduced as third strategy. We explore what happens if both effectiveness and cost of an intermediate defense measure stochastically perturbing on the viewpoint of whether or not the third strategy helping to improve total social payoff. We found that unlike resonance effect by adding noise to payoff matrix in case of spatial prisoner's dilemma (SPD) games, adding time-varying noise on both effectiveness and cost does not make difference from the default setting without perturbation to the third strategy. However, if the noise initially given to each agent is frozen, we found the third strategy becoming robust to survive. In particular, if the strategy updating rule allows a more advantageous third strategy can be more commonly shared among agents through copying, the total social payoff is significantly improved.