Auction Theory, 2nd Edition

204 Some Revenue Considerations

14.1 REVENUE EQUIVALENCE IN MULTIUNIT

AUCTIONS

Our basic setup is the same as in the previous chapter. Specifically, there are K

identical objects for sale and N potential buyers are bidding for these. Bidder i’s

valuation for the objects is given by a K-vector X

i

=



X

i

1

,X

i

2

,..., X

i

K



, where X

i

K

represents the marginal value of obtaining the kth object and these are declining.

We do allow for asymmetries among bidders. Thus, bidders’value vectors, while

drawn independently from

X =



x ∈

[

0,ω

]

K

: ∀k,x

k+1

≥x

k



need not be identically distributed. Let bidder i’s value vector X

i

be distributed

on

X according to the density function