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A city-state is a self-governing political entity that consists solely or chiefly of a single metropolitan area. City-states are not precluded from possessing colonies or dependencies but are defined instead by the fact that the chief city or capital also functions as the primary government of the entire state, with no distinction between local government or the one that rules the entirety of the state.
Several states along both the Sword Coast and Dragon Coast are city-states. Some examples include Baldur's Gate, Waterdeep, or Westgate. Athkatla, the capital of Amn, while rich and powerful, is not a city-state by virtue of its role as a component piece of a greater state, the nation of Amn.