We study decentralized protection strategies by human decision-makers against Susceptible-Infected-Susceptible (SIS) epidemics on networks. Specifically, we examine the impact of behavioral (mis)-perceptions of infection probabilities (captured by Prospect theory) on the Nash equilibrium strategies in two classes of games. In the first class of games, nodes choose their curing rates to minimize the steady-state infection probability under the degree-based mean-field approximation plus the cost of their selected curing rate. We establish the existence of pure Nash equilibria under both risk neutral and behavioral decision-makers. When the per-unit cost of curing rate is sufficiently high, we show that risk neutral players choose the curing rate to be zero at the equilibrium, while curing rate is nonzero under behavioral decision-making for any finite cost. In the second class of games, the nodes choose whether or not to vaccinate themselves. We establish the existence of unique threshold equilibria where nodes with degrees larger than a certain threshold vaccinate. When the vaccination cost is sufficiently high, fewer behavioral players vaccinate compared to risk neutral players, and vice versa. Finally, we provide a rigorous comparison of the equilibrium thresholds under behavioral and risk neutral players in networks with power-law degree distributions.
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