People may be familiar with stories of long lines at vaccination centers in Los Angeles and New York City, but there are also examples of expiring vaccines being hastily administered to whoever happened to be near a health clinic, or even in the middle of traffic during a snowstorm. Instead of a single national strategy, the logistical responsibility of administering millions of vaccines has been pushed to local levels, forcing individual health systems to find solutions. The health systems behind the rollout of COVID-19 vaccinations are attempting to create order from chaos, sometimes with mixed results.
Rather than rely on improvisation and on-the-fly decision-making, state authorities should consider turning to mathematics for a tool that could prove to be the key to more efficient, faster vaccine distribution. That tool: the discipline known as game theory.
Game theory is a field of mathematics that models competitive and cooperative human interactions, where a “game” is composed of players, their actions, and the resulting payoffs. Often applied to competitive economic and political contexts, game theory can be valuable for predicting behavior and incentivizing decisions that improve a broader system. In the context of health care, it models individuals’ decision-making criteria when accessing health services.
In the COVID-19 vaccine rollout, the “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. The level of service might be captured in terms of the congestion of facilities or a supply-demand ratio.
In past research, game theory predicted whether or not individuals would vaccinate, if herd immunity could be achieved, potential vaccine accessibility, and how individuals select vaccination centers. Among other things, these analyses can help calculate how many vaccines need to be sent to each vaccination center. This approach has been proven valuable in after-the-fact analyses of the H1N1 vaccination campaign in 2009 and the response to Haiti’s cholera epidemic in 2010. In those scenarios it enabled the identification of “equilibrium solutions,” which represent how individuals may select vaccination centers when given the freedom to choose.
When equilibrium solutions involve overwhelmed vaccination centers, a city might offer free transportation from certain neighborhoods to more distant centers, incentivizing individuals to spread demand more evenly. Another opportunity might be to openly share data concerning the vaccine supply, wait times, and the likely demand at each center. This may enable people to make more informed choices. It also could benefit the overall system and lessen system stress, as nobody would be likely to knowingly select an overcrowded vaccine center.
The concept of equilibrium is also valuable when a centralized planner has the ability to assign individuals to facilities, because it allows the planner to implement equilibrium solutions, creating an assignment in which no individual can do better by switching facilities. Otherwise, the public may reject a health system’s proposed strategy, either by overwhelming some centers and underutilizing others, or by refusing vaccination altogether. In addition to finding equilibrium solutions, a centralized planner might wish to ensure these solutions minimize the scarcity of vaccines across centers, minimize the cumulative distance traveled and congestion at facilities, or maximize efficient and equitable access to vaccines.
As vaccine centers expand from health clinics and hospitals to stadiums and event centers, and administrators are encouraged not to stockpile vaccines, it is important to use the best management tools at our disposal—including game theory.
It’s time we stopped measuring “what could have been” scenarios and begin applying game theory to create what could be.
Luke Muggy is a full operations researcher focusing on humanitarian logistics systems at the nonprofit, nonpartisan RAND Corporation.
