The management of fish aggregating devices (FAD) creates heated debates in tuna fishery management organizations striving to reduce the number of deployed floating objects. Through several econometric models and a machine learning approach, we evaluate the consequences of three management scenarios on the catch and profit of the French purse‐seine fleet operating in the Indian Ocean: (1) a half reduction in the number of authorized buoys per vessel, (2) a 72‐day closure of FAD fishing with and (3) without re‐allocation of effort on free schools. The results show a significant decrease of fleet profits by 7%, 10% and 18% respectively. We hypothesize an “economic trap” of FAD fishing caused by the far greater efficiency of this harvesting technique for larger vessels searching for economies of scale, and by the overfished status and catch limitation of yellowfin ( Thunnus albacares ) and bigeye ( Thunnus obesus ) tunas in the Indian Ocean. The results are compared with other studies looking at the impact of FAD management measures in other oceans.