In this note we consider a basic property of common agency models: pure strategy equilibria of games where principals compete in direct mechanisms are robust to the possibility that principals might deviate and use more complex indirect mechanisms to design their contracts. We show that this property can be generalized to multi-principal multi-agent models.
Attar, A., Campioni, E., Piaser, G., & Rajan, U. (2004). Pure strategy and no-externalities with multiple agents: A comment (ECON Discussion Papers 2004/76). https://hdl.handle.net/2078.5/29399