This paper examines the role of the revelation principle in common agency games. We show how the introduction of a separability condition on the preferences of the agent is sufficient for the revelation principle to hold. Therefore, it is still possible to restrict attention to direct mechanisms without any loss of generality even when competition over contracts is considered.
Attar, A., Majumdar, D., Piaser, G., & Porteiro, N. (2003). Common agency games with separable preferences (ECON Discussion Papers 2003/101). https://hdl.handle.net/2078.5/33602