In this work we propose a distributed model predictive control scheme based on a cooperative game in which two different agents communicate in order to find a solution to the problem of controlling two constrained linear systems coupled through the inputs. We assume that each agent only has partial information of the model and the state of the system. In the proposed scheme, the agents communicate twice each sampling time in order to share enough information to take a cooperative decision. We provide sufficient conditions that guarantee practical stability of the closed-loop system as well as an optimization-based procedure to design the controller so that these conditions are satisfied. The theoretical results and the design procedure are illustrated using two different examples. Copyright © 2010 John Wiley & Sons, Ltd.