all zero. The LL requirement that the agent is never paid a negative amount then means that he

cannot be paid a positive amount either. When all payments are zero, the agent will not take any

action with nonzero cost, in contradiction to the requirement that the agent maximizes welfare.

14

A speciﬁc setting that illustrates Proposition 2 appears in the next section (proof of Theorem 3).

3.5 The LL-IR Tradeoﬀ

As we have seen, a natural IIVCG instantiation (namely Auction-Inspired IIVCG) is IR, but does

not guarantee LL. In Section 5 we show a diﬀerent instantiation that guarantees LL but not IR. We

now show that the clash between LL and IR is unavoidable (see Appendix B.3 for the full proof):

Theorem 3. There exist common agency settings for which no IIVCG contract satisﬁes both LL

and IR, even with a single principal.
Incomplete Information VCG Contracts for Common Agency