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

The observed counter-intuitive phenomenon reminds us of the well-known Braess's Paradox in network traffic 20,21 . Zhang et al. 34 showed that to remove some specific edges in a network can largely enhance its information throughput, and Youn et al. 35 pointed out that some roads in Boston, New York City and London could be closed to reduce predicted travel times. Actually, Seoul has removed a highway to build up a park, which, beyond all expectations, maintained the same traffic but reduced the travel time 36 . Very recently, Pala et al. 37 showed that Braess's Paradox may occur in mesoscopic electron systems, that is, adding a path for electrons in a nanoscopic network may paradoxically reduce its conductance. This work provides another interesting example analogous to Braess's Paradox, namely a higher successful rate of self-protection may eventually enlarge the epidemic size and thus cause system loss. Let's think of the prisoner's dilemma, if every prisoner stays silent, they will be fine, while one more choice, to betray, makes the situation worse for them. Analogously, if the successful rate d is small, few people will choose to be self-protective, while for larger d, people have more choices, which may eventually reduce the number of vaccinated people and thus enlarge the epidemic size. Basically, both the original Braess's Paradox and the current counter-intuitive phenomenon are partially due to the additional choices to selfish individuals. This is easy to be understood in a simple model like the prisoner's dilemma game, but it is impressive to observe such phenomenon in a complex epidemic game.