(cid:88)

(cid:96)∈[n]

Wela(v) =

Eo∼F|a[v(cid:96)(o)] − ψ(a); a∗(v) ∈ arg max

a∈A Wela(v).

We seek contracts such that for every bid proﬁle b, the agent’s action choice x∗(b) is “declared
welfare maximizing”; we denote this by x∗(b) = a∗(b).9 Since we focus on truthful contracts, when
playing according to their dominant strategies the principals report b = v, and the agent’s choice
a∗(v) is indeed socially eﬃcient.

The last design objective is computational complexity: given a bid proﬁle b and an outcome o,
the payments t(cid:96)(b, o) should be computable in polynomial time for every (cid:96) ∈ [n]. To summarize our
desiderata, we seek truthful, IR and LL contracts, which incentivize the agent to maximize welfare

and whose payments are computable in polynomial time.
Incomplete Information VCG Contracts for Common Agency