In multiple-principal multiple-agent models of moral hazard, we provide sufficient conditions for the outcomes of pure-strategy equilibria in direct mechanisms to be preserved when principals can offer indirect communication schemes. The conditions include strong robustness in the direct mechanism game, as developed in the literature on competing mechanisms by Peters (2001) and Han (2007a), and a no-correlation property we define. We provide a rationale for restricting attention to take-it or leave-it offers, as is typically done in applications. We show via examples that it is necessary to allow direct mechanisms to be stochastic and to include private recommendations from principals to agents to preserve the corresponding equilibrium outcomes, and that the no-correlation condition is tight
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