A Dartmouth study is the first to map the interplay of personal choice and social networks that has led to the United States being one of the world’s most heavily armed countries, with 120 firearms for every 100 people.

The researchers describe in Science Advances how individual incentives to buy firearms can lead to a phenomenon they call “overarming.” In an overarmed society, the collective cost of firearm ownership outweighs the individual benefits of possessing a gun. 

The team developed an evolutionary game theory model of how social factors drive someone to buy a firearm, how their choice influences other people’s decision to arm, and whether everyone’s choices ultimately lead to overarming. Grounded in mathematics and social science, evolutionary game theory analyzes collective outcomes based on individual actions.

“Our work is not an argument against guns—there are benefits of firearm ownership, and we find that a socially optimal level of ownership is often greater than zero,” says Feng Fu, the study’s corresponding author and an associate professor of mathematics.

“The problem is systematic overarming, which leads to a misalignment of individual and societal interests,” Fu says. “The gap between the individual equilibrium and the social optimum is not just theoretical. It maps onto the well-documented correlation between gun ownership rates and gun-related deaths. Overarming costs lives.”

In the researchers’ model, overarming happens when people perceive that the risk of future confrontations with other armed individuals is disproportionately high, says Daniel Rockmore, a professor of mathematics and computer science who co-authored the study with Fu and Michael Herron, a professor of quantitative social science. 

As more people arm, others feel increasingly compelled to do the same as the chances of confronting someone with a gun increases. The model, which Fu, Rockmore, and Herron began developing in 2022, shows the result is that people “perceive the world as more threatening, which drives still more gun purchases as a protection response,” Rockmore says.

The team incorporated data on firearm sales during the COVID-19 pandemic—the highest rate of gun sales in American history—and observed how an arming-and-fear feedback loop played out with “striking accuracy,” Rockmore says. People driven by concerns about personal safety, social unrest, and the pandemic’s trajectory rushed to arm themselves. 

The result is a society in which everyone bears the costs of firearm ownership but not necessarily the individual benefit, Herron says. There are similarities between this and the nuclear weapons strategy of “mutually assured destruction,” or MAD, that the United States and the Soviet Union adopted during the Cold War.

Based in game theory, MAD evolved as the two superpowers stockpiled more and more nuclear weapons to deter the other from using them. MAD exemplifies a Nash equilibrium—named after the late mathematician John Nash—wherein neither side in a competition has an incentive to change their actions. In the case of nuclear weapons, neither the U.S. nor the USSR were inclined to stop acquiring more.

“Just as nations can get locked into a nuclear arms race that leaves everyone less secure, individuals can get locked into a personal arms race for the same reason—rational self-interest that is collectively suboptimal,” Herron says.

“The fear of being the only unarmed person in a confrontation is enough, on its own, to push gun ownership well past the social optimum, regardless of whether people intrinsically need or want to own guns,” he says. 

The team examined three real social networks to understand how the individual choice to arm influences, and is influenced by, the prevalence of firearms in a larger group. They considered an intergang network among Montreal street gangs, peer-influence networks in close-knit rural villages in Honduras, and social ties on an American college campus. 

“Our model generally depends on the frequency with which people run into each other and the chances of confrontation. These networks reflect the actual way that people in small collectives encounter each other,” Rockmore says. 

Social networks are made up of smaller “clusters of interaction,” Rockmore says. Local behavior can spread to the whole network. “The structure of social networks can locally exaggerate or diminish fear, and somebody in one cluster might be a bridge to another,” he says. 

The double-edged sword of connectivity in most social networks also offers a way out of overarming, the research team reports. Their model shows that in calm environments where the perceived threat of confrontation is lower, having highly connected pockets within a social network can dampen firearm possession.

Connectivity patterns also suggest that overarming could be reduced through public information campaigns that help people more accurately assess the real risk of confrontation, breaking the cycle of fear and even more gun purchases. Targeted interventions within social networks may be able to use the structure of community ties to reduce overarming from within.

“Both approaches work with individual rationality rather than against it. This, we hope, is precisely what makes them worth pursuing,” Rockmore says.

“Our hope is that our model can play a role in a thoughtful data-driven conversation about one of the most societally and personally important decisions any person can make,” he says.