This paper develops a cooperative, distributed form of MPC for linear systems subject to persistent, bounded disturbances. The distributed control agents make decisions locally and communicate plans with each other. Cooperation is promoted by consideration of a greater portion of the system-wide objective by each local agent; specifically, a local agent designs hypothetical plans for other agents, sacrificing local performance for the benefit of system-wide performance. These hypothetical plans are never communicated and no negotiation takes place. The method guarantees robust feasibility by permitting only one agent to optimize per time step, while ‘freezing’ the plans of others, and sufficient conditions are given for robust stability. These properties hold for all structures of cooperation between agents. Thus, a key feature is that coupled constraint satisfaction is compatible with inter-agent cooperation.