From small communities to entire nations and society at large, inequality in wealth, social status, and power is one of the most pervasive and tenacious features of the social world. What causes inequality to emerge and persist? In this study, we investigate how the structure and rules of our interactions can increase inequality in social groups. Specifically, we look into the effects of four structural conditions-network structure, network fluidity, reputation tracking, and punishment institutions-on the distribution of earnings in network cooperation games. We analyze 33 experiments comprising 96 experimental conditions altogether. We find that there is more inequality in clustered networks compared to random networks, in fixed networks compared to randomly rewired and strategically updated networks, and in groups with punishment institutions compared to groups without. Secondary analyses suggest that the reasons inequality emerges under these conditions may have to do with the fact that fixed networks allow exploitation of the poor by the wealthy and clustered networks foster segregation between the poor and the wealthy, while the burden of costly punishment falls onto the poor, leaving them poorer. Surprisingly, we do not find evidence that inequality is affected by reputation in a systematic way but this could be because reputation needs to play out in a particular network environment in order to have an effect. Overall, our findings suggest possible strategies and interventions to decrease inequality and mitigate its negative impact, particularly in the context of mid- and large-sized organizations and online communities.