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Human interaction requires reasoning not only about other people’s observed behavior and mental states but also about their incentives and goals. The development of children’s strategic thinking is not well understood, leaving open critical questions about early human capacity for strategic interaction. We investigated strategic reasoning in 3- to 9-y-old children and adults in two strategic games that represent prevalent aspects of social interaction: incentives to mislead and competition. We find that despite strategic differences in the two games, by the age of 7 y, children’s behavior is similar to that of adults. Our findings also show an early sophisticated ability to think strategically about others in both static and repeated interactions.Human strategic interaction requires reasoning about other people’s behavior and mental states, combined with an understanding of their incentives. However, the ontogenic development of strategic reasoning is not well understood: At what age do we show a capacity for sophisticated play in social interactions? Several lines of inquiry suggest an important role for recursive thinking (RT) and theory of mind (ToM), but these capacities leave out the strategic element. We posit a strategic theory of mind (SToM) integrating ToM and RT with reasoning about incentives of all players. We investigated SToM in 3- to 9-y-old children and adults in two games that represent prevalent aspects of social interaction. Children anticipate deceptive and competitive moves from the other player and play both games in a strategically sophisticated manner by 7 y of age. One game has a pure strategy Nash equilibrium: In this game, children achieve equilibrium play by the age of 7 y on the first move. In the other game, with a single mixed-strategy equilibrium, children’s behavior moved toward the equilibrium with experience. These two results also correspond to two ways in which children’s behavior resembles adult behavior in the same games. In both games, children’s behavior becomes more strategically sophisticated with age on the first move. Beyond the age of 7 y, children begin to think about strategic interaction not myopically, but in a farsighted way, possibly with a view to cooperating and capitalizing on mutual gains in long-run relationships.