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

Under such complicated environment, an individual's strategy usually results from a tradeoff between cost and risk. For instance, people may be laissez-faire to the spreading of common flu, while they will take vaccination for hepatitis B since the vaccines are very effective and hepatitis B is very difficult to cure. In contrast, people prefer to take self-protection against HIV since its consequence is terrible while the effectivity and side effects of vaccines are both unknown. Accordingly, game-theoretic models may be suitable to characterize these decision-making processes 3, 4, [12] [13] [14] [15] [16] [17] . Bauch et al. 3, 4 analyzed population behavior under voluntary vaccination policies for childhood diseases via a game-theoretic framework, and they found that voluntary vaccination is unlikely to reach the population-level optimum due to the risk perception in vaccines and the effect of herd immunity. By coupling game models and epidemic models, Bauch 12 and Reluga et al. 13 demonstrated that the self-interested behaviors of individuals can lead to oscillations in vaccine uptake over time. Vardavas et al. 14 considered the effects of voluntary vaccination on the prevalence of influenza based on a minority game, and found that severe epidemics could not be prevented unless proper incentives are offered. Basu et al. 15 proposed an epidemic game model for HPV vaccination based on the survey data on actual perceptions regarding cervical caner, showing that the actual vaccination level is far lower than the overall vaccination goals. Perisic and Bauch 16 studied the interplay between epidemic spreading dynamics and individual vaccinating behavior on social contact networks. Compared with the homogeneously mixing model, they found that increasing the neighborhood size of the contact network can eliminate the disease if individuals decide whether to vaccinate by accounting for infection risks from neighbors. Under the assumption that people make decisions based on the information of the prior seasonal epidemic, Cornforth et al. 17 found that both the flu vaccination rate and the disease prevalence are erratic due to the shortsighted behavior of individuals in contact networks. More recent progresses in this field are summarized in Refs 18, 19 .