Auction Theory, 2nd Edition

196 Equilibrium and Efficiency with Private Values

13.4.2 Single-Unit Demand

The inefficiency of the uniform-price auction does not result from the fact that

multiple units are sold per se but rather from the fact that multiple units are

demanded. Consider a situation in which K > 1 units are up for sale but each

bidder has use for at most one unit—the case of single-unit demand. This is

equivalent to supposing that the value vectors are drawn from the set

X

(

1

)

={x ∈

[

0,ω

]

K

: ∀k > 1, x

k

=0}

Thus, f no longer has full support on

X . We already know that in a uniform-price

auction it is weakly dominant to bid b

1

=x

1

, and since the value of all additional

units ...