Braess's Paradox in Epidemic Game: Better Condition Results in Less Payoff

Zhang, Hai-Feng; Yang, Zimo; Wu, Zhi-Xi; Wang, Bing-Hong; Zhou, Tao

ases. As shown in Fig. 2(d) , only selfprotective and laissez-faire individuals coexist in the lattice. With further increase the value of d, though the self-protection strategy is more efficient, the laissez-faire strategy is more attractive since successful self-protective individuals becomes more and thus for susceptible individuals, the risk of being infected becomes smaller. This is the reason why the fraction of laissez-faire individuals become larger as d goes approaching to 1. In fact, when d is very large, the uninfected laissez-faire individuals again form a percolating cluster since the externality effect from the successful self-protective individuals makes laissez-faire individuals to be free-riders. Please see Previous studies have shown that the contact patterns can dramatically impact the disease dynamics and the individual's decision makings 16, 17 , so it is necessary to further check our results on other types of networks. To this end, we implement the model on disparate networks including the Erdös-Rényi (ER) networks 23 , the Barabási-Albert (BA) networks 24 and the well-mixed networks (also called fully connected networks or complete networks). Figure 3 demonstrates that, in despite of the quantitative difference, the counterintuitive phenomenon can be observed for all kinds of networks. Figures S2-S5 present systematical simulation results about the effects of different parameters for different kinds of networks and one can always observe the counter-intuitive phenomenon when the condition 0 , b , c , 1 is hold.