by Felipe Valencia, José David López, Julián Alberto Patiño, Jairo José Espinosa.

Despite of the efforts dedicated to design methods for distributed model predictive control (DMPC), the cooperation among subsystems still remains as an open research problem. In order to overcome this issue, game theory arises as an alternative to formulate and characterize the DMPC problem. Game theory is a branch of applied mathematics used to capture the behavior of the players (agents or subsystems) involved in strategic situations where the outcome of a player is function not only of his choices but also depends on the choices of others. In this chapter a bargaining game based DMPC scheme is proposed; roughly speaking, a bargaining game is a situation where several players jointly decide which strategy is best with respect to their mutual benefit. This allows to deal with the cooperation issues of the DMPC problem. Additionally, the bargaining game framework allows to formulate solutions where the subsystems do not have to solve more than one optimization at each time step. This also reduces the computational burden of the local optimization problems.