Technologically enabled sharing-economy networks are changing the way humans trade and collaborate. Here, using a novel ‘Wi-Fi sharing’ game, we explored determinants of human sharing strategy. Subjects (N = 1,950) participated in a networked game in which they could choose how to allocate a limited, but personally not usable, resource (representing unused Wi-Fi bandwidth) to immediate network neighbors. We first embedded N = 600 subjects into 30 networks, experimentally manipulating the range over which subjects could connect. We find that denser networks decrease any wealth inequality, but that this effect saturates. Individuals’ benefit is shaped by their network position, with having many partners who in turn have few partners being especially beneficial. We propose a new, simplified “sharing centrality” metric for quantifying this. Further experiments (N = 1,200) confirm the robustness of the effect of network structure on sharing behavior. Our findings suggest the possibility of interventions to help more evenly distribute shared resources over networks.