valuation according to other principals using the concept of a correlation graph, and use this to

set the payments. Correlation graphs and G-correlated settings are deﬁned in Section 5.1, and in

Section 5.2 we use these to deﬁne Weighted IIVCG.

5.1 Correlation Graphs and G-Correlated Settings

A correlation graph (Deﬁnition 5) describes how principals’ valuations are correlated.

(As one

interpretation, principals’ valuations can be intuitively thought of as reﬂecting their socioeconomic

status, and the correlation graph as a natural way to describe it.)

on edges d : [n]2 → [0, 1] such that(cid:80)

Deﬁnition 5. A correlation graph G is a weighted directed graph with vertex set [n] and weights

k∈[n] d(k, (cid:96)) = 1, and d((cid:96), (cid:96)) = 0 ∀(cid:96) ∈ [n].

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We introduce the following “running example” for this section to demonstrate our deﬁnitions.
Incomplete Information VCG Contracts for Common Agency