‘The Pandemic Is a Prisoner’s Dilemma Game’

Madhur Anand, an ecologist, and her husband, Chris Bauch, a mathematical biologist, were optimally situated during the spring lockdown, working from home in Guelph, Ontario, to watch the pandemic play out — and to discuss patterns of behavior, within their community and beyond, as we all tried to keep safe and carry on.

Their offices at home are separated only by a wall, rather than a 45-minute drive. Dr. Anand is the director of the new Guelph Institute for Environmental Research at the University of Guelph, and Dr. Bauch runs a lab at the University of Waterloo. The couple’s collaborative research usually focuses on the interplay between human behavior and environment systems — for instance, with pollution, deforestation and climate change. Whereas those dynamics unfold slowly, the pandemic provided an acute example of rapid change.

“Societal change is not the kind of thing you can easily experiment with,” Dr. Anand said. “But here we were in the middle of a huge social experiment.”

Like many scientists, they redirected their research to Covid-19. The resulting study, led by their doctoral student Peter Jentsch and currently under peer review, looked at vaccination prioritization: To save the most lives, who should get the vaccine first?

As infectious disease studies go, their methodology was somewhat atypical because it applied game theory, a mathematical way of modeling how people make strategic decisions within a group. Each individual has choices, but the payoff for each choice depends on choices made by others. This is what’s called a “prisoner’s dilemma game” — players weigh cooperation against betrayal, often producing a less than optimal outcome for the common good.

The pandemic presents an everyday complexity of such choices. Imagine, Dr. Bauch said, if everyone followed public health recommendations: They wore masks, socially distanced, washed their hands, followed stay-at-home orders. “In that case there is a significantly reduced risk of infection,” he said.

But there are always trade-offs and temptations to defect from the regimen. Masks are annoying. Hand-washing is tedious. You need a hug.

“The pandemic is a prisoner’s dilemma game played out repeatedly,” Dr. Bauch said. In lectures, he invokes a comparison between Ayn Rand, who made a virtue of selfishness, and the “Star Trek” character Spock, who said, “The needs of the many outweigh the needs of the few.”

Now the vaccine adds one more protective layer. The perceived benefits and costs of vaccination are often expressed as concerns about safety and side effects. If you are on the fence about vaccination, you might decide — noticing lower infection rates as vaccination campaigns gain speed — that it no longer seems so critical to get the jab.

“Some people might play a ‘wait-and-see game,’” Dr. Bauch said. People who choose not to be vaccinated effectively get a free ride, reaping the benefits of reduced virus transmission generated by the people who do opt for vaccination. But the free rides generate a collective threat.

“That is the prisoner’s dilemma,” Dr. Bauch said. When infection levels are low, people feel less at risk, let down their guard, and then infection levels again rise; the ebb and flow between our behavior and the virus causes the pandemic waves. “We end up in this unhappy medium,” he said.

Tragedy of the commons

The origins of game theory can be found in the 1944 book “Theory of Games and Economic Behavior,” by the mathematician John von Neumann and the economist Oskar Morgenstern. The applications range from evolution to psychology to computer science; there’s even a book called “The Game Theorist’s Guide to Parenting.”

Dr. Bauch did pioneering work combining game theory and epidemiological modeling, with colleagues including Alison Galvani, an epidemiologist and the director of the Yale Center for Infectious Disease Modeling and Analysis.

“Vaccination decisions based purely on self-interest can lead to vaccination coverage that is lower than what is optimal for society overall,” Dr. Galvani said in an email.

The self-interest strategy maximizing individual payoff is called the Nash equilibrium. Dr. Galvani’s later research included psychological data and demonstrated that vaccination decisions can be influenced by altruism, thereby boosting uptake beyond the Nash equilibrium and serving the common good.

She noted, however, that game theory assumes people are rational in their decision-making. Fear can suppress vaccination “to precarious levels insufficient to prevent the spread of an outbreak,” she said.

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Answers to Your Vaccine Questions

With distribution of a coronavirus vaccine beginning in the U.S., here are answers to some questions you may be wondering about:

    • If I live in the U.S., when can I get the vaccine? While the exact order of vaccine recipients may vary by state, most will likely put medical workers and residents of long-term care facilities first. If you want to understand how this decision is getting made, this article will help.
    • When can I return to normal life after being vaccinated? Life will return to normal only when society as a whole gains enough protection against the coronavirus. Once countries authorize a vaccine, they’ll only be able to vaccinate a few percent of their citizens at most in the first couple months. The unvaccinated majority will still remain vulnerable to getting infected. A growing number of coronavirus vaccines are showing robust protection against becoming sick. But it’s also possible for people to spread the virus without even knowing they’re infected because they experience only mild symptoms or none at all. Scientists don’t yet know if the vaccines also block the transmission of the coronavirus. So for the time being, even vaccinated people will need to wear masks, avoid indoor crowds, and so on. Once enough people get vaccinated, it will become very difficult for the coronavirus to find vulnerable people to infect. Depending on how quickly we as a society achieve that goal, life might start approaching something like normal by the fall 2021.
    • If I’ve been vaccinated, do I still need to wear a mask? Yes, but not forever. Here’s why. The coronavirus vaccines are injected deep into the muscles and stimulate the immune system to produce antibodies. This appears to be enough protection to keep the vaccinated person from getting ill. But what’s not clear is whether it’s possible for the virus to bloom in the nose — and be sneezed or breathed out to infect others — even as antibodies elsewhere in the body have mobilized to prevent the vaccinated person from getting sick. The vaccine clinical trials were designed to determine whether vaccinated people are protected from illness — not to find out whether they could still spread the coronavirus. Based on studies of flu vaccine and even patients infected with Covid-19, researchers have reason to be hopeful that vaccinated people won’t spread the virus, but more research is needed. In the meantime, everyone — even vaccinated people — will need to think of themselves as possible silent spreaders and keep wearing a mask. Read more here.
    • Will it hurt? What are the side effects? The Pfizer and BioNTech vaccine is delivered as a shot in the arm, like other typical vaccines. The injection into your arm won’t feel different than any other vaccine, but the rate of short-lived side effects does appear higher than a flu shot. Tens of thousands of people have already received the vaccines, and none of them have reported any serious health problems. The side effects, which can resemble the symptoms of Covid-19, last about a day and appear more likely after the second dose. Early reports from vaccine trials suggest some people might need to take a day off from work because they feel lousy after receiving the second dose. In the Pfizer study, about half developed fatigue. Other side effects occurred in at least 25 to 33 percent of patients, sometimes more, including headaches, chills and muscle pain. While these experiences aren’t pleasant, they are a good sign that your own immune system is mounting a potent response to the vaccine that will provide long-lasting immunity.
    • Will mRNA vaccines change my genes? No. The vaccines from Moderna and Pfizer use a genetic molecule to prime the immune system. That molecule, known as mRNA, is eventually destroyed by the body. The mRNA is packaged in an oily bubble that can fuse to a cell, allowing the molecule to slip in. The cell uses the mRNA to make proteins from the coronavirus, which can stimulate the immune system. At any moment, each of our cells may contain hundreds of thousands of mRNA molecules, which they produce in order to make proteins of their own. Once those proteins are made, our cells then shred the mRNA with special enzymes. The mRNA molecules our cells make can only survive a matter of minutes. The mRNA in vaccines is engineered to withstand the cell’s enzymes a bit longer, so that the cells can make extra virus proteins and prompt a stronger immune response. But the mRNA can only last for a few days at most before they are destroyed.

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