Braess’s Paradox in Epidemic Game: Better Condition Results in Less Payoff
Hai-Feng Zhang, Zimo Yang, Zhi-Xi Wu, Bing-Hong Wang, and Tao Zhou studied evolutionary epidemics coupled with human behaviors as a game. Individual humans are their players with 3 strategies: vaccination, self-protection, and laissez faire. They may change strategies at the beginning of each new season of epidemic spreading, basing this decision on the aggregate decisions of the larger population.
The choice of an individual strategy is influenced by cost and risk. The authors of this study give the example of popular response strategies to 3 well-known ailments. People tend to choose laissez faire or do nothing to prevent the common flu. The reason why is that the cost of contracting the common cold is relatively low to other diseases, so taking prevention methods against it seems like a needless cost. People often choose vaccination for hepatitis B because the risk of contracting the disease is high and the vaccination has proven to be effective, which lowers the cost of vaccinating. The authors consider not only monetary costs of vaccination but also inconvenience, perceived risks, potential side effects, etc. Finally, people usually employ self-protection for HIV because the consequence is terrible but the side effects and effectiveness of vaccines are unknown, making them costly.
Herd immunity is the concept that if enough of a population is vaccinated against a disease, the unvaccinated are protected against the disease. Vaccinated individuals act as a “firewall” to prevent the disease from spreading. The authors argue that because of self-interest and Braess’s Paradox, the amount of vaccinated individuals will not reach this optimal level that creates herd immunity.
The authors explain that when more people choose vaccination, the advantage of self-protection appears. The large population that has vaccinated protects individuals who do not vaccinate. Laissez faire is still risky, but self-protection is appealing because it provides a sufficient level of protection without incurring the costs of vaccination. Thus, in the next round, more people choose self-protection. However, the low efficiency of self-protection is realized when there are also fewer vaccinated individuals, and this increases the size of the epidemic. As in Braess’s paradox, the option that was individually beneficial creates a system with a smaller payoff, making the entire population worse off.
Source: http://www.nature.com/articles/srep03292#abstract