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

Human-activated systems are usually much more complex than our expectation, since people's choices and actions are influenced by the environment and at the same time their choices and actions have changed the environment. This kind of interplay leads to many unexpected collective responses to both emergencies and carefully designed policies, which, fortunately, can still be modeled and analyzed to some extent. This work raises an unprecedent challenge to the public health agencies about how to lead the population towards an epidemic. The government should take careful consideration on how to distribute their resources and money on popularizing vaccine, hospitalization, self-protection, self-treatment, and so on. Quantitatively, the delocalization reduces the advantage of the laissez-faire strategy, which leads to a larger fraction of self-protective individuals. When A is large enough, self-protection becomes the dominating strategy for a certain range of d. Overall speaking, the epidemic size is smaller at larger A. Parameters are the same as in Fig. 1 . The meanings of different colors are the same to Methods Model. Considering a seasonal flu-like disease that spreads through a social contact network 38, 39 . At the beginning of a season, each individual could choose one of the three strategies: vaccination, self-protection or laissez faire. If an individual gets infected during this epidemic season, she will pay a cost r. A vaccinated individual will pay a cost c that accounts for not only the monetary cost of the vaccine, but also the perceived vaccine risks, side effects, long-term healthy impacts, and so forth. We assume that the vaccine could perfectly protect vaccinated individuals from infection in the following epidemic season. A self-protective individual will pay a less cost b, while a laissez-faire individual pays nothing. Denote d be the successful rate of selfprotection, that is, a self-protective individual will be equivalent to a vaccinated individual with probability d or be equivalent to a laissez-faire individual with probability 1 2 d. This will be determined right after an individual's decision for simplicity. Obviously, r . c . b . 0. Without loss of generality, we set the cost of being infected as r 5 1. Table 1 presents the payoffs for different strategies and outcomes.