Auction Theory, 2nd Edition

130 Efficiency and the English Auction

We examine circumstances under which in the general model with

interdependent and possibly asymmetric values, the English auction, neverthe-

less, allocates efficiently. We retain all the assumptions made in Chapter 6.

In particular, it is assumed that the valuations v

i

(x) are continuously differ-

entiable functions of all the signals and that v

i

(

0

)

=0. Furthermore, we have

assumed that for all i and j,

∂v

i

∂x

j

≥0

with a strict inequality when i =j. In this chapter, the joint distribution of bidders’

signals, f , will play no further role, since we will be concerned with ex post

equilibria, and these depend only on