G) and w(cid:96) = ˆb(cid:96)

G)(b−(cid:96), ˆb(cid:96)

(cid:88)

(cid:88)

(cid:88)

(cid:88)

(cid:96)∈[n]

w(cid:96) (1)
=

d((cid:96), k)ˆbk (2)
=

d((cid:96), k)ˆbk (3)
=

ˆbk.

(cid:96)∈[n]

(cid:96)∈[n]

k∈[n]

k∈[n]

(cid:96)∈[n]

k∈[n]

Equality (1) follows from the choice of w(cid:96)s above, and the deﬁnition of ˆb(cid:96)
Incomplete Information VCG Contracts for Common Agency