We experimentally investigate coordination games in which cognition plays an important role, i.e. where outcomes are affected by the agents level of understanding of the game and the beliefs they form about each others understanding.We ask whether and when repeated exposure permits agents to learn to improve cognition in a strategic setting.We find evidence for strategic sophistication being learned, generalized and promoted.Agents acquire strategic sophistication in simple settings.They may fail to do so in similar but more demanding settings.Given the opportunity, they transfer learning from the simple to the more demanding task.There is heterogeneity in sophistication.We find some evidence for sophisticated agents trying to spread sophistication early in the game, provided there is a long enough time horizon.