Shared knowledge structures, such as cognitive categories and relationships, are central to the interpretation of a complex social environment and thus play an important role in mediating between individual preferences and group outcomes. This article defines a "knowledge-induced equilibrium" that applies to both cooperative game theory, such as social choice and voting, and to non-cooperative game theory, such as coordination games. This equilibrium concept bridges between interpretive approaches, which emphasize cognitive structures or frames, and positive approaches, which focus on preferences, choice, and the stability of collective outcomes.