Several multiagent systems exemplify the need for establishing distributed control laws that ensure the resulting agents' collective behavior satisfies a given coupled constraint. This technical note focuses on the design of such control laws through a game-theoretic framework. In particular, this technical note provides two systematic methodologies for the design of local agent objective functions that guarantee all resulting Nash equilibria optimize the system level objective while also satisfying a given coupled constraint. Furthermore, the designed local agent objective functions fit into the framework of state based potential games. Consequently, one can appeal to existing results in game-theoretic learning to derive a distributed process that guarantees the agents will reach such an equilibrium.