We investigate the interactions between anthropogenic climate change, socioeconomic developments and tuna fishery management strategies. For this purpose, we use the APECOSM-E model to map the effects of climate change and commercial fishing on the distribution of skipjack tuna biomass in the three oceans, combined with a new bioeconomic module representing the rent or profit of skipjack fisheries. For forcing, we use Representative Concentration Pathway (RCP) 8.5, the highest emission scenario for greenhouse gas concentrations presented in the IPCC's Fifth Assessment Report (AR5), and the IPCC Socioeconomic Shared Pathway (SSP) 3, which is characterized by low economic development and a strong increase in the world population. We first investigate the impact of climate change on regional skipjack abundance, catches and profits in three oceans (Atlantic, Indian and Pacific) in 2010, 2050 and 2095. We then study the effects of three management strategies (maximum sustainable yield or MSY, maximum economic yield or MEY, and zero rent or ZR) on the future distribution of fishing fleets between oceans and on global economic rent. Our model projections for 2050 and 2095 show an increase in global skipjack biomass compared to 2010 and major changes in its distribution, impacting local and regional fishing efforts. The Pacific Ocean will continue to dominate the skipjack market. In our modeling of management strategies, the currently predominant MSY strategy would have been unprofitable in 2010, due to a decreased catch per unit effort (CPUE). In the future, however, technological developments should increase fishing efficiency and make MSY profitable. In all the scenarios, a MEY strategy is more profitable than MSY but leads to the lowest catches and the highest prices. This raises ethical questions in a world where food security may become a top priority. In the scenarios where MSY generates an economic loss (e.g. 2010), a ZR strategy allows global stocks to be exploited at high but still profitable levels. Conversely, in the scenarios where MSY is profitable, (e.g. 2095) ZR leads to overfishing and smaller global catches. We conclude that the most appropriate management strategy at any time is likely to change as environmental and socioeconomic conditions evolve. The decision to follow one or other strategy is a complex one that must be regularly reviewed and updated.