The next corollary follows immediately from Proposition 1 and from Property 1 of IIVCG

contracts.

Corollary 1. In every IIVCG contract the agent maximizes social welfare.

We now show a uniqueness result for IIVCG: Whenever the agent maximizes declared welfare,

IIVCG contracts are the only contracts that incentivize principals to bid truthfully as a dominant

strategy. This result is reminiscent of the well-known result by Holmstr¨om [17], establishing unique-
ness of VCG auctions for convex domains.13 In fact, our proof makes use of a lemma from [17], in
addition to the convexity of the valuation domains. We give here a sketch of the proof and defer
Incomplete Information VCG Contracts for Common Agency