Game Theory on Getting Vaccination for the Flu
Link: http://news.rutgers.edu/medrel/research/rh-2012/gaming-the-flu-how-w-20120801
While vaccination against the flu is generally perceived as a positive practice, some people—namely youngsters—actually view it as not worthwhile because they are less likely to become severely ill or die from the disease. Unfortunately, young people are also more likely than old people to spread influenza, which creates an interesting health dilemma: how can they be swayed so that the overall health of the population improves?
In the article “Gaming the Flu: How We Decide to Get Vaccinated, or Not,” the author describes how Professor Gretchen Chapman modeled this dilemma with game theory: she “divided 287 undergraduate students into groups labeled ‘young’ and ‘old.’ Everyone started the game with 4,000 points and gained or lost points, based on the decisions they made about vaccination. At the end, the researchers paid the students based on their number of points. Students in half the groups were paid according to how many points they earned individually; in the other half, students were paid based on how many points the group earned. Getting vaccinated cost points; getting infected cost points.” Both types of groups can be represented with payoff tables that we have learned in class.
First type (individual performance):
The numbers used are arbitrary, with vaccination costing 100 points, but they reflect the essence of the model (I’ve also left out the starting 4000 points). The payoffs for (no vaccination, no vaccination) are a bit higher than regular for each case since neither players are vaccinated, so their payoffs are negatively amplified. The first player is young, and the second player is arbitrary (we’re only concerned with the individual payoff of the first, young player). As you can see, the young player has a dominating strategy: no vaccination. Any possible Nash equilibrium would also have the young player choosing no vaccination. These results show that if young people are solely concerned with their own wellbeing, then they tend to not get vaccination.
Second type (group performance):
What’s different from the first table is that now the payoff for each player is the total sum of the group. The table above only considers two young players, but it reflects the payoffs of a “young” group. There is no longer a dominating strategy for either young players, but there are two Nash equilibria: (vaccination, no vaccination), (no vaccination, vaccination). This result is a significant improvement from the first case, where all young players would rationally not vaccinate to maximize their payoff.
Based on these results, it can be seen that to sway young people into getting vaccination, you must “make it worth their while.” Their wellbeing must be strongly tied to the overall community’s such that by helping the community (through getting vaccination), they help themselves greatly as well.
-jf