Pandemic Chronicles: Vaccination and the Tipping Point to Herd Immunity

Society is at a tipping point with two critical issues: climate change and the COVID-19 global pandemic. A tipping point is a phenomenon where enough people have collectively changed their social behavior to push society towards either a positive or negative direction. The climate change crisis is similar to the current public health pandemic in that it requires coordination among individual members of society in order to avert a disaster.

Ideally, countries would make good on their treaty commitments by investing in clean energies and take steps to meet greenhouse gas reduction targets. But since the Paris climate change treaty is voluntary and non-legally binding, what actually happens is some countries set meaningful national targets and takes steps to get there while other countries free ride by staying their current course.

In a Nature article “Tipping Climate Cooperation,” the authors use game theory to explain the global coordination dilemma between nations to address a problem that might become dangerous some day but not immediate.Their insight shows that When the uncertainty is small, however, societies are much more likely to coordinate efforts and avoid the tipping point.

In climate change forums, countries like America and China are strategic actors who weigh the choice of cutting or not cutting greenhouse gases depending on their payoffs. Each country’s pay-off (or expected benefits) in treaty adoption are dependent on the other country’s choice. As the payoff matrix above shows, there are two states of the world that represents Nash equilibria. A Nash equilibrium is a condition where neither country can improve its payoff or outcome by changing its strategy.

One Nash equilibrium captures the ideal scenario in which both countries don’t renege on their treat commitments and take actions at home to cut CO2 emissions. But the other state of the world (i.e. Nash equilibrium) is where neither country chooses to invest in clean energy or measures to cut carbon emissions. That’s a less desirable scenario because society is worse off. Yet, given then uncertainty around climate change risks in the short term, there is no immediate pending disaster.

Because of short-sightedness or lack of domestic support, free rider countries are less likely to jump on the bandwagon. To reach the ideal scenario, several things need to happen, including directly observing the real catastrophic impact of extreme weather patterns, or improving scientific research to reduce the uncertainty about the tipping point. These social, political, and economic considerations are similar to the current state of the COVID-19 pandemic.

Herd Immunity – Coordination Problem

At the beginning of May 2021 the U.S. government and the Centers for Disease Control and Prevention updated its guidance to allow Americans to go about their daily lives without a mask if they are fully vaccinated while calling out those unvaccinated to get vaccinated in order to get the same treatment in common public squares. After an intensive COVID-19 vaccination campaign to reach millions of Americans, experts believe America is at an inflection or tipping point to averting the raging pandemic. Previously, there were a lot of uncertainty whether we would reach the end of the tunnel on this dark chapter in the modern public health crisis. But since vaccinations and aggressive public health measures have taken place, more people will have an incentive to get vaccinated. Why? The tipping point.

Tipping point in collective behavior: over half of the U.S. are vaccinated. The unvaccinated are now the minority. Monthly cases and deaths are trending down. Society, governments, and organizations are rewarding the vaccinated to prompt social change in the unvaccinated population.

There are places that people would like to attend, like places of worship, grocery stores, and night clubs. These places have different levels of restrictions for those who are not vaccinated while allowing those who are vaccinated to enter without wearing a mask.

Chart: CDC's New Mask Guidance for Vaccinated, Unvaccinated People
Source: CDC Guidance

For churches, since it’s a place of faith, those centers recommend attendees who aren’t vaccinated to follow health guidelines by wearing masks and maintaining social distance. Worship centers tend to not impose hard requirement to show attendees are vaccinated, rather it’s an honor system.

Church Mask Policy Change

Nightclubs and Ride Shares

Nightclubs, on the other hand, are social spaces that attract people of all backgrounds. People interact closely and crowds tend to be more concentrated. Those places have an incentive to impose a requirement for people to show evidence of vaccination to enter. For example, Rumi is a nightclub in New York City populated with millenials and Genzers. To enter, customers go through two checkpoints: (1) age verification and temperature check; (2) vaccination card. These same people often commute using ride sharing services including Uber and Lyft, both of which have stated that they will maintain current mask restrictions for all customers (or no service).

Shopping Centers

Grocery stores approach the new government guidance in different ways, ranging from requiring all shoppers to still wear masks and maintain social distance to allowing the vaccinated to be maskless. Because of either hard requirements or public pressures from a large number of people who are vaccinated, people who are unvaccinated will have an incentive to get vaccinated. The combination of these policies carried out by private organizations, accompanied by local ordinances and requirements, as well as sustained commitment and guidance by the government to end the pandemic, will help push American society over the tipping point.

Consider the scenario below, where each Customer can choose to get vaccinated or not get vaccinated. Their individual choices and payoffs are dependent on what the other Customer do. If Customer 1 takes an effort to vaccinate, Customer 2 could be a free rider and not vaccinate. Why? Customer 2 may not want to take the effort, and may want to take advantage of others getting vaccinated and free ride off a perceived herd immunity. The expected payoff for C1 and C2 is (1,2), respectively.

There are two important outcomes from this decision matrix. The first is where both Customer 1 and Customer 2 vaccinate, which is the desired Nash Equilibrium, since neither Customer could increase its payoff by changing their strategy. Both Customers 1 and 2 choose to vaccinate after seeing a certain threshold of the population get vaccinated with minimal risk, while the vaccinated have the benefits of attending more more venues and activities. If unvaccinated customers wish to get the benefit accruing to vaccinated customers, then the unvaccinated have an incentive to get vaccinated. If enough unvaccinated people think that way, this establishes a tipping point in the health pandemic that inches us close to herd immunity. The other scenario, the undesirable Nash Equilibrium, is where Customer 1 and Customer 2 do not vaccinate. Here the expected payoffs are (2,2) for Customer 1 and 2, respectively. The social drivers for customers making this choice could be the following:

  1. if they’re skeptical of vaccines;
  2. if the unvaccinated don’t think there’s enough supply
  3. if they believe the pandemic will worsen (no light at the end of the tunnel)
  4. if the unvaccinated think their other people will also stay unvaccinated.

If the above drivers are strong enough, then it pushes society away from the tipping point and further away from herd immunity. The choices that we as individuals make based on our own expected payoff can put our friends, neighbors and overall society at risk.


Lenton, Timothy M. 2014. Game Theory: Tipping Climate Cooperation. Nature Climate Change 4 (1): 14–15

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