Auction Theory, 2nd Edition

14.2 Revenue Equivalence with Multiunit Demand: An Example 211

and the ex ante expected payment of a bidder is

m

D

=



1

0

m

D

(x) dx

2

=

1

10

Since there are two bidders, the expected revenue of the seller in a discriminatory

auction is twice the ex ante payment of each bidder and equals, as it must,

1

5

. 

CHAPTER NOTES

The multidimensional revenue equivalence principle in Proposition 14.1 is due

to Krishna and Perry (1998). It calculates the payoff U

i



x

i



by integrating the

function q

i

along the ray from 0 to x

i

(as in (14.5)). It turns out, however,

that the calculation does not depend on the particular path along which the

integral is evaluated—it is path independent ...