The Relationship Between Game Theory and COVID Guidelines
Amidst a growing number of COVID-19 cases and elevated uncertainty surrounding the trajectory of the pandemic, municipalities across the US are reinstating lockdown restrictions. Heated criticism comes from every direction, as both lockdown-proponents and opponents contest the best method for managing the virus. While everyone has different opinions on the matter, a familiar question has resurfaced: will people adhere to stay-at-home orders? Enforcing lockdown measures has proved to be difficult. Despite safety guidelines, many people continue to ignore recommended precautions, and the question of “why?” arises. While the answer is often reduced to saying that deviators simply don’t care about public welfare, this generalization doesn’t capture all the factors at play. Behavioral economics can explain why many people deviate from COVID recommendations; the pandemic can be treated as a game, and as such, game theory can elucidate why public consensus on how to handle the pandemic is not uniform. Examination under the lens of game theory shows that individuals often benefit more by not following guidelines. From this conclusion, the added benefit of further lockdowns becomes questionable.
In essence, game theory examines how decision-makers act in various circumstances where there are multiple participants. They are referred to as “players” and the situation is the “game”. Many different types of games are created and studied in an effort to model reality and understand human behavior (Ross, 2019). Perhaps the most well-known and simple example of game theory is the Prisoner’s Dilemma: two individuals are arrested for a suspected robbery and put in separate interrogation rules. The detective gives the same option to each: confess or stay silent. If one individual confesses while the other stays silent, the confessor goes free and the other gets ten years in prison, and vice versa. If both confess, they each get five years. If both stay silent, they each get one year in prison. The dilemma produces the following decision matrix:
As the figure shows, the optimal outcome for the pair would be for each to serve one year, so both would remain silent. However, because the prisoners make their decisions separately, they prioritize their own freedom and wellbeing over the other person’s. Each player can anticipate the other’s move, but cannot be certain in their guess of what the other will do. Therefore, each individual analyzes the possibilities their accomplice may choose and what they should do in response. The player first considers what to do if their partner confesses: they would also confess, so as to get only five years jail time instead of ten. If the partner stays silent, they would also confess, to get no jail time instead of one year. In both situations it’s best for that player to confess, so it doesn’t matter what they think their partner will choose: the final decision is to confess. Both players reach this conclusion and confess, leading to each receiving a five-year sentence. Although both individuals are making the optimal decision for themselves, the end result is not the ideal outcome. If both stayed silent, they would only get one year each, but this doesn’t happen. Neither want to risk the outcome of getting ten years while the other goes free, so they prioritize their own freedom and always choose to confess (Davis & Brams, 2020). The disconnect between the best result and the real result can be explained by the irrational and selfish nature of humans. If the players were to unselfishly cooperate, they would both remain silent, but this is not the case.
A similar game can be applied to the current pandemic to examine how individuals make choices. This game focuses on the individual’s perspective, so the players are you and everyone else around you. The decision or “move” that must be made is whether or not to follow COVID safety guidelines, like wearing a mask, social distancing, and being in close proximity with people outside their family unit. The results that occur are more complex than the prisoner’s dilemma, and there are more, including the individual’s happiness, their likelihood of sickness, and the overall pandemic trajectory. The following decision matrix shows the game and different outcomes for each possibility:
The optimal result for every person in the country is for the pandemic to end by everyone following guidelines, but this has not happened. So why not? Why doesn’t everyone stay at home so we can end the pandemic? The same answer from the Prisoner’s Dilemma applies here: people’s own selfishness influences their choice. Put yourself in the shoes of the individual in this game and walk through both scenarios: one where others follow restrictions and one where others don’t. If people follow restrictions, the pandemic likely ends and you likely stay healthy, so it’s in your best interest to maximize your enjoyment by carrying on with your life as normal and not following guidelines. If others don’t follow restrictions, the pandemic will continue regardless of your own efforts, and you’re more likely to get sick either way. So rather than stay at home and watch others have fun without you, you maximize your joy by joining the crowd and deviating from guidelines. In either case you are better off not following guidelines, even though this leads to the non-optimal result.
As needed for useability, the game makes simplifications. For instance, the tradeoff between staying in and getting sick is different for different people. Particularly, young people likely value social enjoyment over protection from getting sick, while older people do the opposite. Furthermore, stay-at-home orders are more disruptive for some than others; those with a higher opportunity cost of sheltering in place are less likely to follow guidelines (Kabir & Tanimoto, 2020). The game’s simplifications make it impossible for the model to capture all facets of reality, but the results do explain why many choose to not follow guidelines: it’s the seemingly rational choice.
Viewing health as a public good may also explain why restrictions are less effective over time. A public good is something that is provided to everyone and benefits all equally, and one person enjoying the benefits cannot inhibit another from doing the same. In the case of COVID, herd immunity and low infection transmission can be thought of as public goods. A public good game (PGG) is useful to examine behaviors in the pandemic surrounding the public good of health. One PGG asks players to invest any number of given tokens in the public good, and after each player has done so, the pot is split evenly between all players. Those who donated very few or no tokens receive just as much of the public good as those who donated many. For COVID, the tokens can be thought of as precautions against the virus, meaning those who invest a lot of tokens take health guidelines seriously compared to those who invest few. The game is performed repeatedly, and eventually players catch on to the drift and begin investing fewer and fewer tokens. They know that the pot is split evenly at the end, so even if they donated nothing, they would still receive some of the public good. Almost every player adopts this strategy, and after many plays, the pot shrinks and the resulting amount of public good each player receives is significantly smaller than in the beginning (Brüne & Wilson, 2020). In the real world, this is akin to fewer people following COVID guidelines as time goes on, leading to the virus spreading more. The PGG explains why stay-at-home benefits diminish over time, as fewer people continue to follow them.
While many are quick to dub COVID restriction deviants as irrational and thoughtless, game theory shows a different perspective, possibly that they are actually acting rationally. Humans naturally put their own best interests first, and as both games showed, their interests are preserved when they don’t follow COVID guidelines. Both games are simple models and thus cannot capture all nuances at play, but the basic relationships that create the results are sound. When one who doesn’t follow COVID guidelines is asked why, the common responses echo those that result from game theory: They don’t see how their individual actions will affect the overall trajectory of the pandemic, or they believe others are out having fun and they don’t want to be left out. While these reasonings may work for the individual, the problem arises when many individuals use this thinking, and consequently, the masses don’t follow COVID rules. It’s common for individuals to see their being as separate from the public, failing to realize that they are the public. For the pandemic to die out naturally, each person must adopt a group mentality and view their own actions as impactful. Until a new approach to tackling COVID is achieved, lockdowns will continue to be ineffective; some people will ignore guidelines from the get-go, and others will follow this deviation as time goes on. While the best solution is unclear, so long as lockdowns follow the same formula they have since March, little progress will likely be made in protecting the health of our nation. While the intuitions of human nature often serve the individual well, crises like COVID-19 show how the individual acting in their best interests can result in the group being worse off. For national and state leaders to fight the pandemic successfully, understandings of human nature and rational thought must be considered and built into COVID responses. Game theory may highlight the pitfalls of individual decision-making, but policymakers can use these insights to work for them, rather than against.
References
Brüne, M., & Wilson, D. R. (2020). Evolutionary perspectives on human behavior during the Coronavirus pandemic: insights from game theory. Evolution, Medicine, and Public Health, 2020(1), 181-186.
Davis, Morton & Brams, Steven. (2020, August 6). Game Theory. Encyclopaedia Britannica. https://www.britannica.com/science/game-theory
Kabir, K. A., & Tanimoto, J. (2020). Evolutionary game theory modelling to represent the behavioural dynamics of economic shutdowns and shield immunity in the COVID-19 pandemic. Royal Society open science, 7(9), 201095.
Ross, Don, "Game Theory", The Stanford Encyclopedia of Philosophy (Winter 2019 Edition), Edward N. Zalta (ed.), https://plato.stanford.edu/archives/win2019/entries/game-theory/.
