Auction Theory, 2nd Edition

6.2 Second-Price Auctions 89

to be the expectation of the value to bidder 1 when the signal he or she receives is

x and the highest signal among the other bidders, Y

1

,isy. Because of symmetry

this function is the same for all bidders and from (6.2), v is a nondecreasing

function of x and y. We will, in fact, assume that v is strictly increasing in x.

Moreover, since u

(

0

)

=0, v

(

0,0

)

=0. The function v plays an important role in

what follows.

For the symmetric model with interdependent values, we proceed in a manner

parallel to the development of Chapter 2 concerning the symmetric independent

private values model. As in Chapter 2, we first derive symmetric ...