3.3 A Characterization of the Outcome-Speciﬁc Payment Scheme

The deﬁnition of IIVCG contracts in the previous section includes a characterization of expected
payments for action a∗(b). In this section we complete the picture by characterizing the outcome-
13Holstr¨om’s result is a generalization of the one by Green and Laﬀont [13], and in fact applies more generally to

smoothly connected domains.

12

speciﬁc payments for all actions (Lemma 1). The characterization relies on Property 1 of IIVCG

contracts – that the agent always maximizes the declared social welfare. Since the agent acts in

his own self-interest, the payments must incentivize the agent to choose the welfare-maximizing

action. We use this fact to deduce the format of the payments.

The characterization makes use of the following deﬁnition. For every action a deﬁne

(cid:26)

(cid:12)(cid:12) a ∈ arg max

La =

w ∈ Rm≥0

a(cid:48) {Eo∼F|a(cid:48) [w(o)] − ψ(a(cid:48))}

(cid:27)

,
Incomplete Information VCG Contracts for Common Agency