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Ecosystem-based fisheries management (EBFM) has emerged as a promising framework for understanding and managing the long-term interactions between fisheries and the larger marine ecosystems in which they are nested. However, successful implementation of EBFM has been elusive because we still lack a comprehensive understanding of the network of interacting species in marine ecosystems (the food web) and the dynamic relationship between the food web and the humans who harvest those ecosystems. Here, we advance such understanding by developing a network framework that integrates the complexity of food webs with the economic dynamics of different management policies. Specifically, we generate hundreds of different food web models with 20–30 species, each harvested by five different fishers extracting the biomass of a target and a bycatch species, subject to two different management scenarios and exhibiting different information in terms of avoiding bycatch when harvesting the target species. We assess the different ecological and economic consequences of these policy alternatives as species extinctions and profit from sustaining the fishery. We present the results of different policies relative to a benchmark open access scenario where there are no management policies in place. The framework of our network model would allow policymakers to evaluate different management approaches without compromising on the ecological complexities of a fishery. This article is part of the theme issue ‘Connected interactions: enriching food web research by spatial and social interactions’.