Auction Theory, 2nd Edition

Chapter | Sixteen

Nonidentical Objects

In considering multiple object auctions we have thus far restricted attention to

situations in which the objects are identical. Furthermore, we supposed that the

marginal value of an additional unit declined with the number of units in hand.

We now turn to the case where the objects, while related, are not identical.

16.1 THE MODEL

Let K =

{

a,b,c,...

}

be a finite set of distinct objects for sale and, as usual, let

N be the set of buyers. Each buyer i ∈N is assumed to assign a value x

i

(

S

)

to

each subset S ⊆K. Subsets of K are called packages or combinations. The set

of possible packages is 2

K

. We can then think of a buyer’s value as a vector

x

i

=



x

i

(

S

)



S⊆K

We will suppose that x

i

(

∅

)

=0 and if S ⊂T , then x

i

(

S

)

≤x

i

(

T

)

.