The Hawk-Dove Game and Covid Guideline Compliance
Game theory has applications across a wide range of topics with political strategy, the stock exchange and sports strategy being just a few examples. However, perhaps the most relevant in today’s world is its direct applications to Covid 19. From small, everyday decisions, like whether one should wear a mask at any given time, to larger decisions such as getting a vaccination, game theory can be used to model human behavior. This is exactly what Drs Madhur Anand and Chris Bauch did during the pandemic. In a research paper written by their graduate student Mr. Jentsch, their team showed that human behavior with respect to the pandemic could be modeled using game theory. These models were used to determine who should get vaccinated, and when, in order to provide the greatest benefit to society. They determined that different populations should be prioritized depending on timeline, with more at risk people getting vaccinated if the pandemic is still in early stages, but younger populations who are more likely to spread the disease being prioritized if natural immunity has already started to build.
Perhaps their most interesting finding, however, is that a model similar to the prisoner’s dilemma could predict fluctuations in cases and transmission rate. In this game, the two strategies available to players are to behave (follow Covid guidelines, ie. get vaccinated, wear a mask, social distance, etc.) or to misbehave (opt out of the vaccine, party, etc.), and the payoffs are the perceived benefits of being able to live life as normal, minus the perceived risk of infection. The first player is the individual, and the second is the rest of society on average.
The game looks something like this (likely with slightly different payoffs):
| P2 Behaves | P2 Misbehaves | |
| P1 Behaves | -1, -1 | -4, 1 |
| P1 Misbehaves | 1, -4 | -5, -5 |
Behaving is somewhat unpleasant. Masks can be uncomfortable, the long-term effects of the vaccine are unknown, and you don’t get to hang out with your friends. But the risk is also low, so we only have a small negative payoff. This payoff becomes slightly more negative if the rest of society chooses to misbehave because that allows the virus to spread more easily, so despite following guidelines, the risk is a little higher. However, the payoff of misbehaving while the rest of society follows the rules is high. You get to visit friends, avoid unknown risks of vaccination, and not worry about wearing a mask, while also reaping the benefits of herd immunity that come from the rest of society getting the vaccine. This is a great option, until the rest of society start to misbehave as well, at which point transmission rate increases enough that the risks far outweigh the benefits of misbehaving, and the individual is better off following the rules even though they can at times be bothersome.
This game has two pure Nash equilibrium and is essentially equivalent to the Hawk-Dove game. If one player behaves, the other rational player will choose to misbehave. This is exactly what happened with the pandemic as vaccines started to become available. As more people began to get vaccinated (P2 chose to behave with more likelihood), it became more and more beneficial for the individual to ignore Covid guidelines (P1 misbehaves). When this happened however, the virus would spread more rapidly, and infection rates would increase. This would change the payoffs, making it riskier to misbehave. The game would then look something like this:
| P2 Behaves | P2 Misbehaves | |
| P1 Behaves | -1, -1 | -4, -2 |
| P1 Misbehaves | -2, -4 | -5, -5 |
The new payoffs create a pure Nash equilibrium where both players behave, and transmission rates decrease until the game transitions back to what it was above. This oscillation between equilibria is what caused waves to form in the pandemic as the population shifted between behavior and misbehavior along with perceived risk. This is a great example of how Nash equilibria are observed in human behavior even when there is an option that is overall better for everyone. (If everyone behaves in the first place, the net payoff is the least negative)
source: https://www.nytimes.com/2020/12/20/health/virus-vaccine-game-theory.html