As any economist well versed in game theory will tell you, there are plenty of good reasons to cooperate—and plenty of good reasons not to do so. (Of course, any self-respecting kindergartner could tell you the same thing.)

The fundamental problem with cooperation is that the incentives are askew. While the act of cooperating results in the best collective outcome, it’s not always clear whether it will yield the best individual outcome. There’s tricky cost/benefit analysis involved: If I cooperate and you don’t, you get a benefit and I pay a cost. If you cooperate and I don’t, I gain the advantage and you pay a cost. The prisoner’s dilemma is the most famous example of this predicament.

Certain groups and societies are structured in ways that promote cooperation. Others are not. In these societies, spite can become the norm: individuals are willing to pay a cost for others to lose.

Since cooperation is optimal—if everyone cooperates for the greater good, everyone is better off—we are left with the question: what will it take to promote cooperation in an otherwise uncooperative society?

My colleagues Babak Fotouhi and Martin A. Nowak at Harvard University and Benjamin Allen at Emmanuel College and I set out to find the answer. Through mathematical analysis, simulations and examples from real-world social networks, we found that the key to cultivating cooperation lies in the creation of sparse connections—similar to bridges and brokers—between disparate groups. Our study is published in the July issue of Nature Human Behavior.

My colleagues and I have long been intrigued by this topic. Last year, we conducted and published research that examines how and when cooperative behaviors spread across a network via natural selection. We found that cooperation thrives when there are strong pairwise connections between individuals. In other words, if all individuals are evenly connected to all others, then selfish behaviors can come to the fore. But if each individual has a small number of close pairwise ties, cooperation can quickly spread from one person to another.

In this new study, we use an adapted branch of mathematics known as evolutionary graph theory, which makes it possible to study biological and social evolutionary dynamics on networks, to look at population structures where cooperation falters. These include: cliques, which are clusters of nodes that are all connected to each other; star networks, which are comprised of a central node that serves as a hub or conduit between other nodes; and rich club networks, which comprise a cohesive core of several nodes connected to many peripheral nodes.

Each of these population structures has an analogous real-world counterpart: cliques are like crowded groups; star networks are like hierarchal organizations; and rich clubs are like the social network of company executives and directors. For a variety of reasons, cooperation is hard to come by in each of these structures alone.

However, circumstances change once these uncooperative groups and societies become thinly connected together, which can be done by a broker, for instance. When two or more cliques or rich clubs become conjoined, the critical benefit-to-cost ratio of cooperation goes from negative to positive. When two stars become sparsely connected, the effect on the community is dramatic: conjoined stars can build super-promoters of cooperation.

Our study also included real-life examples: a fourth-grade class, for instance. The class, which had about 25 students, was one large community. Within that community, we detected two sub-communities. Overall, unlike the sub-communities, the class exhibited cooperative behaviors. This is mainly due to the small connections between these subgroups and small groups.

Based on our findings, it’s clear that cooperation does not require connections between each and every individual in the group. In the case of the fourth-grade class, the sparse connections served as olive branches that promoted an atmosphere of harmony and collaboration. In all of the examples, conjoining the groups through even just a few representatives, brokers or bridges had a tremendous effect on outcomes.

To be sure, sparse connections are not the only way to promote cooperation in fragmented societies. There are many tried and true mechanisms, such as increasing social incentives, which revolve around status, reputation and indirect reciprocity. It’s likely that combining sparse connections with these other means might make this cooperative effect even more pronounced.

Our findings have important implications. The key to encouraging and cultivating cooperation is to increase interconnections between segregated groups to an optimal level, which sews the groups together into a cooperative whole.