![[Adobe Stock]](https://sp-ao.shortpixel.ai/client/to_webp,q_glossy,ret_img,w_750,h_375/https://www.psypost.org/wp-content/uploads/2026/11/team-rowing-750x375.jpg)
A small band of unconditionally cooperative individuals can make it much easier for a group to get a shared effort off the ground, yet their reliability may also encourage others to slack off over the long run. According to a new mathematical modeling study published in Proceedings of the Royal Society B, unwavering cooperators act as a double-edged sword in group tasks that require a minimum number of contributors to succeed. The findings suggest that committed minorities can help spark collective action while simultaneously reducing overall participation once coordination takes hold.
Cooperation allows living things, from bacteria building protective films to humans funding public infrastructure, to achieve together what no single individual could manage alone. Yet pitching in carries a personal cost in time, energy, or resources, leaving contributors vulnerable to free-riders who enjoy the shared benefits without doing any of the work.
To study when helpful behavior survives or dies out under these pressures, scientists often turn to evolutionary game theory, a mathematical framework that tracks how competing strategies spread or shrink in a population depending on the payoffs they earn. Even in anonymous, one-time encounters where people cannot reward helpers or punish slackers, outcomes can shift in the presence of what game theorists call zealots: committed individuals who always cooperate and never change their strategy, regardless of what others do.
Earlier research suggested that a small fraction of these steadfast contributors could nudge an entire group toward helpfulness. For example, a 2012 mathematical modeling study indicated that ordinary players often copy unwavering cooperators and tip an entire population into cooperating, provided individuals do not base their choices strictly on maximizing payoffs. Committed minorities can similarly reshape group consensus in real human interactions, as demonstrated by a 2018 behavioral experiment in which planted group members who consistently promoted an alternative name overturned an established naming convention once they made up roughly 25 percent of the group.
Don’t miss the next big psychology finding
Every morning, PsyPost sends a short briefing on the most interesting new peer-reviewed research in psychology and neuroscience.
Newer work indicates that unconditional generosity does not always boost group participation, especially when individuals strongly favor whichever behavior yields the highest personal return. When researchers simulated spatial group resource games in networked populations in a 2023 modeling study, a moderate share of zealous cooperators actually lowered overall cooperation by giving nearby free-riders easy rewards and blocking local clusters of ordinary cooperators from expanding. Still, most prior research on zealots focused on classic social dilemmas such as the prisoner’s dilemma, where acting selfishly always pays better for an individual and universal defection is typically the sole stable outcome.
Many real-world collective challenges, such as pack hunting in animals or international climate negotiations, instead operate as multiplayer coordination dilemmas. Often modeled as a multiplayer stag-hunt game, these situations generate shared rewards only if at least a minimum critical number of group members contribute; if participation falls short of that threshold, the effort fails and contributors lose what they put in. To see how committed minorities affect these threshold-based challenges, Yuting Dong and Lei Shi of Yunnan University of Finance and Economics in China, working with Chen Shen of Kyushu University in Japan and a colleague, modeled multiplayer stag-hunt games containing a minority of zealots.
Rather than recruiting human participants, the researchers relied on mathematical equations and computer simulations, posting the code for their numerical calculations publicly on Zenodo. They examined anonymous, single-round interactions in a well-mixed population, meaning every player had an equal chance of being randomly grouped with anyone else.
“We wanted to understand how a minority of committed cooperators influences collective cooperation in social dilemmas,” study co-author Chen Shen, a research associate professor in the Faculty of Engineering Sciences at Kyushu University in Japan, told PsyPost. “Previous studies have shown that such individuals, known as ‘zealots,’ can promote cooperation in two-player social dilemma games in well-mixed populations. However, much less was known about their influence in multiplayer settings, where success requires a minimum number of individuals to cooperate. We therefore asked whether zealots are equally beneficial in these settings.”
In each round, a fixed number of players formed a group and chose either to cooperate by contributing one unit to a shared pool or to defect by contributing nothing. Once the number of contributors met or exceeded the required threshold, the pooled contributions were multiplied by a productivity factor and divided equally among all group members, free-riders included; otherwise, no public reward was produced and contributors lost their investment. Alongside adaptable players who could switch strategies over time, the population included a minority of zealots who always contributed and never changed strategies.
In their first analysis, the authors modeled an idealized, infinitely large population to map out the game’s long-term equilibrium states, which are the stable outcomes a population naturally settles into over time. Using an evolutionary formula called replicator dynamics, they tracked how the share of cooperators among adaptable players grew or shrank under strong payoff sensitivity, where whichever strategy earned a higher average return steadily spread. Ordinary players could not tell zealots apart from other cooperators, so zealots shaped the dynamics only by changing the mix of contributors in each group.
Without zealots, once collective returns are high enough to make teamwork worthwhile, the game typically features an unstable tipping point known as a coordination barrier: if initial participation falls below that mark, cooperation collapses to zero. Starting above that mark, by contrast, leads adaptable players into either full cooperation or a stable coexistence mix of cooperators and free-riders.
Keeping zealots capped at no more than half of the total population, the researchers found that adding a small share of them, such as 0.2 zealots per adaptable player (about 17 percent of the total population) in a 15-person game requiring at least 5 contributors, pushed that barrier downward so fewer adaptable cooperators were needed to get collective action started. Under moderate collective returns, however, that same downward shift also lowered the stable coexistence point, meaning a smaller proportion of adaptable players cooperated in the long run than in a population with no zealots.
“Our main finding is that zealots can have two opposing effects: they can make it easier for cooperation to emerge, but they may also discourage others from cooperating in the long run,” Shen explained. “In other words, having individuals who always cooperate does not necessarily encourage others to do the same.”
Increasing the proportion of zealots past specific mathematical thresholds reshaped the menu of stable outcomes altogether, creating standalone endpoints that do not appear in the standard stag-hunt game. At a ratio of 0.5 zealots per adaptable player (one-third of the total population) in the same 15-person setup, the starting coordination barrier vanished completely. That shift ensured adaptable players reached stable coexistence under moderate returns or 100 percent cooperation under high returns, regardless of where participation began. Raising the ratio further to 0.9 zealots per adaptable player (roughly 47 percent of the total population) wiped out the coexistence state across part of the moderate-return range, leaving all adaptable players to defect.
The team also tested the two extreme versions of the threshold rule. When just one contributor was enough to generate a group reward, turning the scenario into a standard public goods game with no coordination hurdle, zealots did not change the stable outcomes at all. At the other extreme, when every single member of a group had to pitch in for the effort to succeed, zealots lowered and at higher densities eliminated the coordination barrier, provided each person’s payoff from group success exceeded their contribution cost.
Because real groups draw from finite populations where random chance affects who ends up together, the researchers ran a second analysis in populations of limited size. In this probabilistic model, adaptable players compared payoffs step by step under strong payoff sensitivity and tended to adopt higher-earning strategies, paired with a 0.1 percent chance of randomly switching strategies at each step to reflect occasional exploration. Using a probability method called a Markov chain, the scientists calculated the long-run share of time the population spent at each level of cooperation.
Simulating 10-person groups that required at least 5 contributors, with zealots accounting for 30 percent of the total population, showed that total population size shapes what committed cooperators achieve. In a tiny population of 10 players, where everyone landed in the same group, free-riding prevailed among adaptable players and zealots had almost no effect. At intermediate population sizes of 20 and 50 under moderate returns, populations without zealots spent nearly all their time near low cooperation, whereas adding 30 percent zealots helped overcome the coordination hurdle and shifted adaptable players into sustained coexistence.
As the finite population grew larger, the trade-off seen in the infinite model resurfaced. In a population of 500 players under moderate collective returns, having 30 percent zealots lowered the long-run share of adaptable cooperators compared with a 500-player population without zealots, a dual pattern that held up in additional checks across smaller zealot fractions and varied group sizes and thresholds.
That downside ran counter to initial intuition. “I initially expected zealots to promote cooperation because their consistent contributions bring groups closer to the minimum number of cooperators needed for success,” Shen noted. “What surprised me was that these same contributions could also weaken others’ incentives to cooperate.”
In the authors’ reading, this dual influence stems from how a guaranteed baseline of contributions alters incentives for everyone else. Zealots initially make it likelier that a group will pass its participation threshold, reassuring adaptable players that their contributions will not be wasted, yet once cooperation takes hold, that same cushion lets groups meet the target with fewer ordinary contributors and gives free-riders wider room to coast. The researchers propose that similar trade-offs could arise in other threshold challenges, from climate mitigation to the spread of group social norms, where dedicated advocates may ease initial coordination while inadvertently dampening broader participation.
“The effects of zealots depend on factors such as their proportion, coordination requirements, population size, and the benefits of collective cooperation,” Shen said. “These findings have potential implications for collective action challenges requiring coordinated efforts, ranging from addressing climate change to developing artificial intelligence. They suggest that relying on committed cooperators alone may not be sufficient for successful collective action.”
There are a few caveats to keep in mind when interpreting these findings. The work is based entirely on mathematical equations and computer models rather than experiments with people or animals. As a result, it boils behavior down to payoff-driven rules and leaves out real-world factors such as moral norms, leadership, and unequal wealth.
The models also assume that strangers are grouped at random for single, anonymous rounds, meaning individuals cannot recognize who the unconditional cooperators are, discuss plans beforehand, or build reputations over repeated encounters. Just as important, the equilibrium curves track cooperation among adaptable players alone, while overall participation in the population also includes the guaranteed contributions of the zealots themselves.
“Our findings should not be interpreted as suggesting that zealots are generally harmful to collective cooperation,” Shen cautioned. “Reduced cooperation among other individuals does not necessarily mean that overall cooperation declines. Moreover, our study is theoretical, and further research is needed to understand how these effects operate in real-world settings.”
Future studies could examine whether this dual effect persists in structured social networks, where people interact repeatedly with the same neighbors, coworkers, or friends. Incorporating pre-game communication, reputation systems, and behavioral experiments with human participants could help scientists determine when committed minorities sustain real-world teamwork and when they invite others to free-ride.
“Our long-term goal is to understand how committed individuals influence participation in real-world collective efforts, such as environmental campaigns and voluntary charitable initiatives,” Shen added. “We hope to investigate how social network structures shape these effects and explore the underlying behavioral mechanisms through experiments involving human participants or AI agents.”
The study, “Zealots lower coordination barriers but undermine cooperation in multiplayer games,” was authored by Yuting Dong, Hao Guo, Chen Shen, and Lei Shi.
