principal (cid:96)’s expected payment equal to the externality she imposes on the others, as in VCG

auctions with the Clarke pivot rule [7], as well as VCG contracts [22]. We refer to this instantiation

of the IIVCG family as Auction-Inspired contracts. In Section 3.4 we show that while Auction-

Inspired contracts are always IR, the LL property is not necessarily satisﬁed. This is no coincidence

– there is in fact an inherent clash between the two properties:

Theorem (LL-IR tradeoﬀ, see Theorem 3). There are common agency settings for which no IIVCG

contract is both LL and IR.

The above theorem can apply even to settings with a single principal. This impossibility result

highlights how challenging it can be to design contracts under incomplete information, and how

fundamentally diﬀerent this model is from the complete information one.

An algorithmic approach and main results. In light of our impossibility result, we adopt an
Incomplete Information VCG Contracts for Common Agency