Controlling Versus Enabling — Online Appendix

Section 1 of this online appendix contains the proof of the technical Lemma (Lemma 2) used in the Proof of Lemma 1 in the main paper, which states that Ω* (.) is continuous and differentiable at R*. Section 2 provides the linear example with cost differences between the principal and the agent in choosing the transferable actions, based on the discussion in Section 4.4 of the main paper. We show that it can still be optimal to allocate all transferable decision rights to the same party even when the other party has a cost advantage for some of these decisions. Section 3 contains the proof of the claim in Section 5 of the main paper that if agents can cooperate in P-mode, they can overcome any attempt by the principal to use team payments to eliminate the double-sided moral hazard problem. Section 4 contains the proof that Lemma 1 still applies in the presence of spillovers. Section 5 provides the derivation of the closed form solutions for the linear model with spillovers used in Section 5.1 of the main paper. Section 6 does likewise for the model with pricing and spillovers used in Section 5.2 of the main paper. Section 7 establishes the result stated at the end of Section 5.1 in the main paper, namely that Proposition 5 continues to hold even if prices are endogenous and contractible, and there are production costs. Finally, Section 8 analyzes the hybrid case in a setting with multiple agents, in which some agents can operate in P-mode and others in A-mode.