Multiple autonomous robots are expected to interact in Industry 4.0 scenarios, which makes it key to identify distributed techniques for their control and coordination. Game theory has a strong potential to be an excellent representation methodology for the establishment of cooperation among distributed robotic agents. In this paper, we consider a model of two industrial robots within a production line and we show how to describe their interaction, with their different objectives and control being kept into account. We also formalize a Bayesian game that takes into account imperfections in the system, such as the possibility that the robots make a wrong evaluation on a specific item in production. For both the standard static game and its Bayesian version, we compute the Nash equilibrium and we argue how it ultimately represents a point of convergence of the distributed control of the robots.