Auction Theory, 2nd Edition

12 Private Value Auctions: A First Look

willing to pay for the object. Each X

i

is independently and identically distributed

on some interval [0, ω] according to the increasing distribution function F.

It is assumed that F admits a continuous density f ≡F



and has full support.

We allow for the possibility that the support of F is the nonnegative real line

[0,∞) and if that is so, with a slight abuse of notation, write ω =∞. In any case,

it is assumed that E

[

X

i

]

< ∞.

Bidder i knows the realization x

i

of X

i

and only that other bidders’ values

are independently distributed according to F. Bidders are risk neutral; they seek

to maximize their expected profits. All components of the model other than the

realized values are assumed to be commonly known to all