Constrained Games: The Impact of the Attitude to Adversary´s Constraints

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.