A COVID-19 Twist on the Prisoner’s Dilemma
While the concepts of game theory from lecture at first may seem foreign when applied to the ways we think about the real world, in reality many of our real-life problems can be reimagined in terms of a “game”. As a result of this problem restructuring, we can begin to better understand the reasons people (certain players) choose to take certain actions. We can interpret this as the result of all players of a game acting upon their given payoffs (the utility they get from their choices in the games) and each deciding on their mutual Best Response functions (their dominant strategy which they use no matter what they believe the other player might decide). The intersection between players best response functions is often referred to as the Nash Equilibrium, which is a solution, such that no players have any profitable deviations (any better incentives to opt for a different action).
A classic example to simplify all these economic concepts and terms previously described, would be a game commonly referred to as the “Prisoner’s Dilemma”. The well-known version often involves two prisoners being questioned by the police. Since the police do not actually have enough evidence to incriminate both prisoners for a larger crime, they devise the following scheme. Each prisoner is questioned separately and told that if they confess to the crime and their partner doesn’t then they will be set free. However, if they choose to keep quiet, they could end up with 1 year of jail time or even worse, life imprisonment if their partner confesses and they don’t. If both confess, then they still end up with a less optimal result of each getting 10 years of jail time.
Upon writing out a game matrix and solving the optimal Nash Equilibrium, the surprising result is that the optimal solution ends up being that both players defect (confess to the crime). This is surprising to hear as if they both cooperated and kept quiet they would have each only had 1 year of jail time instead of 10 years each. We can conclude from this that each player’s desire to act in their own interests ultimately leads to greed and distrust which results in more overall jail time.
Image Source: https://roughdiplomacy.com/game-theory-prisoners-dilemma-2/
While dealing with actual prisoners is a more extreme and idealized example, Mulaney’s article “A COVID-19 Prisoner’s Dilemma” discusses an excellent real-life application of the classic cooperation and defect prisoner’s dilemma discussed above. Mulaney discusses the hypothetical but very likely case of two governors (one of California, one of Arizona) simultaneously deciding whether to continue the lock down of their state or to ease restrictions. While easing restrictions generates more revenue for the states, it also wreaks havoc if both states decide to lift restrictions and COVID-19 were to spread to high levels which would end up causing more losses as opposed to gains as deaths increase. While the optimal cooperation strategy would be for both to continue their shelter-in-place orders, we find the Nash Equilibrium of both re-opening their states to fall in line with the prisoner’s dilemma’s solution due to each Governor’s selfish interest to protect their own state’s economy.
Beyond the two governor scenario outlined in Mulaney’s article, one can easily imagine other pandemic related scenarios whose outcomes can be simply explained by the classic Prisoner’s Dilemma Nash Equilibrium. One particularly concerning example might be between two individuals deciding whether or not to get their COVID-19 vaccines. Following the examples above, both individuals could both potentially choose not to vaccinate out of their own selfish interests to avoid pain or unknown side effects. However, a positive outlook is that an individual’s payoffs are the key to solving Best Response functions for a Nash Equilibrium. Hopefully, in this case we find that people’s fear of catching COVID-19 will sway their actions to the socially desired optimum of everyone being vaccinated.
Article Source: https://www.stanforddaily.com/2020/06/21/a-covid-19-prisoners-dilemma/