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We consider properties of constrained games, where the strategy set available to a player depends on the choice of strategies made by other players. We show that the utilities of each player associated with that player's own performance and constraints are not sufficient to model a constrained game and to define equilibria; for the latter, one also needs to model how a player values the fact that other players meet their constraints. We study three different approaches to other players' constraints, and show that they exhibit completely different equilibrium behaviors. Further, we study a general class of stochastic games with partial information, and focus on the case where the players are indifferent to whether the constraints of other players hold.