A vaccine only protects a whole community if enough people get it, including those who would stay safe anyway once their neighbors are covered. The same tension runs through climate action and social movements: the shared payoff arrives only when enough people pitch in.
In a new study published in the Proceedings of the National Academy of Sciences, two Dartmouth researchers find that rewarding the people who consistently cooperate does more to sustain that cooperation than punishing the ones who don’t.
“Getting people to cooperate is crucial to social well-being; a society’s prosperity hinges on the willingness of people to work together for the public good,” says Feng Fu, a professor of mathematics who chairs Dartmouth’s Quantitative Social Science Program.
The study, by Fu and Alina Glaubitz, Guarini ’24, set out to understand why some people become steady cooperators while others consistently free-ride, and how incentives shape that split.
“People may be tempted to act selfishly and ‘free-ride’ on the contributions of others, but it is only through widespread cooperation that we can achieve outcomes such as herd immunity, reduced carbon emissions, and fair elections that represent what the public wants,” Glaubitz says.
Most earlier research stops at a single decision. “There is a lot of research that explores this issue, but that research typically focuses on how to encourage cooperation one time,” says Fu.
“Our contribution is that we’ve looked at how incentive structures affect cooperation when there are multiple rounds. In other words, what makes people more willing to consistently cooperate over and over again?”
To get at that, Glaubitz and Fu built mathematical models grounded in game theory. They used a method called adaptive dynamics, which tracks how people adjust their choices as conditions shift, and set it inside a “threshold” version of the game, where the group reaps a benefit only once contributions clear a certain bar. Vaccines work this way: protection kicks in for everyone only once enough people have gotten the shot.
“Adaptive dynamics is a well-established technique that can offer insights into human behavior and how people respond to changing conditions in order to optimize outcomes for themselves,” says Fu.
The researchers ran a range of incentive structures across many rounds, mixing rewards and punishments in different combinations, alongside a control condition with no incentives at all.
How rewards split the crowd
One pattern stood out. “We found that when players who have consistently cooperated are rewarded, people branch into two distinct groups: ‘volunteers’ who consistently cooperate, and ‘free-riders,’ who do not,” Fu says.
That split grew sharper under an “all or nothing” structure, where steady cooperators earned the largest rewards, while anyone who slipped even once got nothing.
The size of the reward mattered too. “You can also get more people to cooperate by increasing the size of the reward,” Fu says. “And rewarding consistent volunteers leads to widespread adoption of cooperative behavior once a certain reward threshold is reached.”
Bigger, consistency-based rewards pushed more people into the reliable-volunteer group. Punishing the free-riders never produced that same steady split, no matter how the researchers tuned it.
“This work suggests that it would be useful to incorporate rewards into social structures where cooperation is necessary, and that those rewards need to be contingent on consistent cooperation over time,” says Fu.
The next question is whether the models hold up with real people. “One next step for this work is to find collaborators and conduct a rigorous behavioral study to see the extent to which these theoretical findings align with practice,” says Fu. “On a practical level, we also need to understand the benefit of cooperation, because providing rewards, or enforcing punishments, comes with a cost. You need to know the value of cooperation in order to determine whether the cost is worth it.”
The work was supported by a Dartmouth Scholarly Innovation and Advancement Award.