Our deﬁnition of the IIVCG family (Deﬁnition 2) speciﬁes only the expected payments to the

agent for every action, where the expectation is over the action’s stochastic outcome. This is not

enough – a contract must determine the payments for every possible outcome realization. We

4One could also consider relaxing the LL constraint by requiring not that every contractual payment is non-negative
but rather that only the aggregate payment from the principals to the agent is non-negative for every outcome; this
does not change our results (see Remark 7).

5The concept of “revenue” in a multi-principal settings may require new deﬁnitions.

5

address this by characterizing the outcome-speciﬁc payments that incentivize welfare maximization

on behalf of the agent:

of the other principals’ reports b−(cid:96), and (cid:80)
Incomplete Information VCG Contracts for Common Agency