Collective intelligence in our highly-connected world is a topic of interdisciplinary interest. Previous research has demonstrated that social network structures can affect collective intelligence, but the potential network impact is unknown when the task environment is volatile (i.e., optimal behavioral options can change over time), a common situation in modern societies. Here, we report a laboratory experiment in which a total of 250 participants performed a “restless” two-armed bandit task either alone, or collectively in a centralized or decentralized network. Although both network conditions outperformed the solo condition, no sizable performance difference was detected between the centralized and decentralized networks. To understand the absence of network effects, we analyzed participants’ behavior parametrically using an individual choice model. We then conducted exhaustive agent-based simulations to examine how different choice strategies may underlie collective performance in centralized or decentralized networks under volatile or stationary task environments. We found that, compared to the stationary environment, the difference in network structure had a much weaker impact on collective performance under the volatile environment across broad parametric variations. These results suggest that structural impacts of networks on collective intelligence may be constrained by the degree of environmental volatility.