On multiple-principal multiple-agent models of moral hazard

We provide two examples in a pure moral hazard setting with two principals and two agents. Example 1 shows that a strongly robust equilibrium in simple (direct) mechanisms can no longer be sustained as an equilibrium when a principal can deviate to an indirect communication scheme. Conversely, an equilibrium with one principal offering an indirect mechanism cannot be replicated as an equilibrium in simple mechanisms. Example 2 shows more directly that a payoff profile that can be achieved in equilibrium when one principal offers an indirect mechanism cannot be achieved as an equilibrium profile in simple mechanisms.