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

Strikingly, we found a counter-intuitive phenomenon that a better condition (i.e., larger successful rate of self-protection) may unfortunately result in less system payoff. It is because when the successful rate of self-protection increases, people become more speculative and less interested in vaccination. Since a vaccinated individual indeed brings the 'externality' effect to the system: the individual's decision to vaccinate diminishes not only their own risk of infection, but also the risk for those people with whom the individual interacts 13 , the reduction of vaccination can remarkably enhance the risk of infection. Qualitatively speaking, the counter-intuitive phenomenon is insensitive to the network topology, while quantitatively speaking, networks with delocalized structure (e.g., ER, BA and well-mixed networks) have more self-protective individuals and less laissez-faire individuals than networks with localized structure (e.g., square lattices), and the epidemic size is larger in the latter case. Without the diverse behavioral responses of individuals, epidemic in delocalized structure usually spreads more quickly and widely than in localized structure 32, 33 . The opposite observation reported in the current model again results from more and more speculative choices (i.e., to be laissez-faire) at a low-risky situation. Therefore, this can be considered as another kind of ''less payoff in better condition'' phenomenon.