In this paper, we study the effects of industrial policies on international convergence using a multi-country agent-based model which builds upon Dosi et al. (2019b). The model features a group of microfounded economies, with evolving industries, populated by heterogeneous firms that compete in international markets. In each country, technological change is driven by firms’ activities of search and innovation, while aggregate demand formation and distribution follows Keynesian dynamics. Interactions among countries take place via trade flows and international technological imitation. We employ the model to assess the different strategies that laggard countries can adopt to catch up with leaders: market-friendly policies; industrial policies targeting the development of firms’ capabilities and R&D investments, as well as trade restrictions for infant industry protection; protectionist policies focusing on tariffs only. We find that markets cannot do the magic: in absence of government interventions, laggards will continue to fall behind. On the contrary, industrial policies can successfully drive international convergence among leaders and laggards, while protectionism alone is not necessary to support catching up and countries get stuck in a sort of middle-income trap. Finally, in a global trade war, where developed economies impose retaliatory tariffs, both laggards and leaders are worse off and world productivity growth slows down.