In multiple-principal multiple-agent models of moral hazard, we provide sufficient conditions for the outcomes of pure-strategy equilibria in simple mechanisms to be preserved when principals can offer indirect communication schemes. The conditions include strong robustness in the simple mechanism game, as developed in the literature on competing mechanisms by Peters (2001) and Han (2007), and a no-correlation property we define. We show via an example that the no-correlation condition is tight in moral hazard models. Finally, we provide a rationale for restricting attention to take-it or leave-it offers, as is typically done in applications.
Andrea Attar, Eloisa Campioni, Gwenaël Piaser, and Uday Rajan, “Competing mechanism games of moral hazard: communication and robustness”, Review of Economic Design, vol. 16, n. 4, December 2012, pp. 283–296.