Inequality and cooperation in social networks

www.nature.com/scientificreports OPEN Inequality and cooperation in social networks David Melamed1,2*, Brent Simpson3*, Bradley Montgomery1 & Vedang Patel4 Social networks are fundamental to the broad scale cooperation observed in human populations. But by structuring the flow of benefits from cooperation, networks also create and sustain macro-level inequalities. Here we ask how two aspects of inequality shape the evolution of cooperation in dynamic social networks. Results from a crowdsourced experiment (N = 1080) show that inequality alters the distribution of cooperation within networks such that participants engage in more costly cooperation with their wealthier partners in order to maintain more valuable connections to them. Inequality also influences network dynamics, increasing the tendency for participants to seek wealthier partners, resulting in structural network change. These processes aggregate to alter network structures and produce greater system-level inequality. The findings thus shed critical light on how networks serve as both boon and barrier to macro-level human flourishing. Both cooperation1–5 and resource i nequality6,7 are universal but variable across human societies. Although several studies have suggested that variation in material wealth inequality and cooperation may be linked2,8–10, we currently know little about how inequality in material wealth or endowments impacts cooperation8 or how cooperation, in turn, influences i nequalities11. We study the bidirectional effects of cooperation and inequality in dynamic networks, where ties between alters represent opportunities to cooperate8,12–14. Two interrelated bases of inequality are likely fundamental for cooperation in social networks. First, inequality in wealth may lead to differences in self-reliance, which decreases the tendency for the wealthy to cooperate or form ties to new partners, especially with the poor. Some evidence supports the contention that visible inequality results in the wealthy being less c ooperative8,9. Alternatively, wealth may lead to noblesse oblige, leading the rich to be more generous in their interactions with their less fortunate network partners. There is theory and evidence supporting this view as w ell10. We refer to any tendency for greater wealth to affect one’s behavior as baseline wealth effects. We argue that wealth will affect both cooperation and network dynamics beyond its effects on the holder of wealth. Here we test the argument that the tendency for people to derive greater benefits from interactions with wealthy partners10,15 can generate differences in cooperation, altering network dynamics and exacerbating existing inequalities in networks. That is, a key starting point for our investigation is that cooperators who possess more material wealth (or other valuable resources like technology or knowledge) can generate larger material benefits for their network partners than cooperators with access to less material wealth. Thus, collaborations with individuals with more wealth or other valuable resources (e.g., greater human capital) generally result in higher overall outcomes. For example, one will likely benefit more from investing in a business venture with a wealthy partner than a poor partner, or by working on a project with an experienced vs. inexperienced collaborator. Following related work, we refer to this second aspect of inequality as wealth productivity effects10. Critically, however, interactions with the wealthy are only more productive if the wealthy are cooperative. One does not benefit from collaborating with a wealthy or experienced partner who freerides on one’s efforts while contributing nothing of their own. We expect that wealth productivity effects will lead to more cooperation with the wealthy, both to maintain ties to them and to bring about higher levels of cooperation from them. Thus, when we account for wealth productivity effects, we expect that these higher levels of preferential attachment to the rich and cooperation with them will lead to “rich-get-richer effects.” This, in turn, will result in increased network-level inequality. This is consistent with recent w ork16 showing that the greater resources of the wealthy allow them to produce larger benefits for interaction partners for any given level of cooperation. Those interaction partners, in turn, attribute higher levels of cooperativeness to the wealthy than their (equally cooperative) poorer counterparts, leading the wealthy to gain more reputational benefits, which can then lead to increased monetary rewards in downstream interactions. 1 Department of Sociology, The Ohio State University, Columbus, OH 43210, USA. 2Core Faculty, Translational Data Analytics Institute, The Ohio State University, Columbus, OH 43210, USA. 3Department of Sociology, University of South Carolina, Columbia, SC 29208, USA. 4Microsoft, Redmond, WA 98052, USA. *email: ; Scientific Reports | (2022) 12:6789 | https://doi.org/10.1038/s41598-022-10733-8 1 Vol.:(0123456789) www.nature.com/scientificreports/ 120 Cost to Alter 10 1000 1500 30 50 Ego Payoff 100 80 60 40 20 500 2000 Alter Endowment 2500 3000 Figure 1.  Illustration of our wealth productivity manipulation. As alters endowment increases, so does the amount ego receives from varying levels of alter’s cooperation (10, 30, and 50). Summing up, we study not only the effects of wealth inequality and productivity on cooperation in dynamic networks, but also how those factors lead to concentration of both material wealth and social wealth (i.e., social ties). More specifically, we conducted a large-scale behavioral experiment using human subjects to answer several interrelated questions about how inequality shapes cooperation, network dynamics, and macro-level inequalities: (1) How do baseline wealth and wealth productivity affect cooperation in networks? (2) Does wealth productivity increase cooperation because participants give more to wealthy partners? (3) Does wealth productivity lead to preferential attachment to the rich? If so, does inequality in network degree increase? And, (4) Do the effects of inequality on cooperation and network dynamics combine to increase network-level inequality? That is, does wealth productivity lead to “rich get richer” effects by shaping who cooperates with whom? A total of 1080 participants were embedded in 40 dynamic networks (average initial network size = 27; “Methods”). Initial networks were random (Erdös-Rényi) graphs, with a density of 0.167 or about 4 ties each. Each network tie represented an opportunity to interact in an iterated prisoner’s dilemma (PD). In each round, each participant made a single decision to give 0 to 50 monetary units (MUs; in ten-unit increments) to all of their alters8,12,13, where 0 represented full defection and 50 represented maximal cooperation. Specifically, consistent with a PD incentive structure, any given person in an interaction benef (...truncated)