Game Theory on Herd Immunity
The outbreak of COVID-19 caused overwhelming chaos. Although most countries took action as soon as possible, it was very hard for the world to properly react to a new, powerful, and widely spread disease. Even after the vaccine was invented and put into use, many problems still emerged. Some believe the effect of vaccination while others do not, and there are even protests. Also, the vaccine is scarce, with higher demand than support. As a result, policymakers thought about a method that requires less vaccination and was implemented in pandemics before: Herd immunity. In other words, it is possible to reduce the infection rate by vaccinating a certain percentage of people, while those who are not vaccinated are left to the natural contagion.
In the study, researchers decided to make a nonlinear game based on people’s vaccination choices. Using game theory and experiments, they tried to figure out whether people would voluntarily obtain herd immunity. There were 8 players in the game, each independently decided whether to get the injection or not, so that they could optimize their health assets. The result indicates a mixed-strategy equilibrium: the player did not stay in only one definite choice. Instead, they choose according to a probability distribution, which can be a more personal reason. In this case, they chose with the payoff in mind: a nonlinear probabilistic benefit of vaccination and deterministic cost of vaccination. With a higher relative benefit of vaccination, there was higher vaccination coverage. Thus, herd immunity was more likely to be achieved through private and voluntary choice.
It is the first time making a vaccination game considering game theory. The research does help to elaborate on the rate of vaccination choices and possible reasons. It is also a new discovery that the unpredictability in immunization leads to randomized choices to take the vaccination, which makes the players more independent and the experiment more objective. However, eight players are a limited number. The reality must be far more complex. There are various factors to affect the vaccination choice, for example, their jobs, the education they received, and their political bias.
Source:
Lim W, Zhang P (2020) Herd immunity and a vaccination game: An experimental study. PLoS ONE 15(5): e0232652. https://doi.org/10.1371/journal.pone.0232652
Written by Weilin Pan