Game Theory and its Applications to the Vaccine Rollout
Ever since the Covid-19 vaccine became available for public use, there have been several hurdles to clear on the way to reaching herd immunity. Unfortunately, the rollout has been mostly left to local health officials, which has resulted in issues ranging from too long of lines to expiring vaccines. It can be argued that state officials should have taken a more mathematical approach to solve these dilemmas: this is where game theory comes into play.
Game theory is defined by the Oxford Dictionary as “the branch of mathematics concerned with the analysis of strategies for dealing with competitive situations where the outcome of a participant’s choice of action depends critically on the actions of other participants.” From this definition, it is clear that game theory can be applied to an individual’s decision whether or not to get vaccinated, as many will take into account the actions of others. While a Rand article describes it as “players would be individuals seeking care; the actions would be the individuals’ selection of a facility; and the payoffs would be measured in terms of how individuals perceive the risk of vaccination, distance traveled, and level of service available at a chosen facility,” I will provide two simple examples of the application of game theory. The first simple example of this involves perceived wait time. If individuals expect a multiple-hour wait time at a particular vaccination site, they may be less likely to get the vaccine. To provide the simplest of examples, see the graph below.
|
Player 1 |
|||
|
Get Vaccine |
Do Not Get Vaccine |
||
|
Player 2 |
Get Vaccine |
1, 1
|
3, 2 |
|
Do Not Get Vaccine |
2, 3
|
2, 2 |
|
In this example, the numbers represent the perceived benefit of getting vaccinated, given what the other player has done. The key simplification we make is a significant increase in wait time if the other player also decides to get vaccinated. This renders outcomes where both players would rather not get the vaccine than wait in line. While this obviously does not tell the whole story, one can see that game theory is most definitely applicable.
The second specific example involves herd immunity. Again, depending on the individual, one may be more or less likely to get vaccinated if they believe herd immunity can be achieved. For example, one person who views many others getting vaccinated might be more like to get vaccianted as they think they can contribute to achieving herd immunity. Another individual, however, might be less likely to get vaccianted because they view herd immunity as obtainable without them getting the vaccine. In economics, this is called the free-rider problem. This is demonstrated in the game below, albeit a simplified one.
|
Player 1 |
|||
|
Get Vaccine |
Do Not Get Vaccine |
||
|
Player 2 |
Get Vaccine |
0, 5
|
0, 0 |
|
Do Not Get Vaccine |
5, 3
|
0, 3 |
|
We assume that both players are somewhat skeptical of the vaccine in this game, but both value herd immunity. Additionally, one player’s decision to get vaccianted indicates to the other that herd immunity is obtainable. Thus, the payoffs represent the benefits of getting or not getting the vaccine. Thus, in this example player, 1 is more likely to get vaccianted if they believe herd immunity is obtainable, and player 2 is indifferent whether or not they believe herd immunity is available.
Article Used: https://www.rand.org/blog/2021/03/how-game-theory-could-solve-the-covid-19-vaccine-rollout.html