September 2009
Intermediate to advanced
336 pages
9h 37m
English
Content preview from Auction Theory, 2nd Edition
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16.5 Some Computational Issues 233
Example 16.1. With three or more buyers, bundling may not be optimal.
Suppose that there are two objects, a and b, and three buyers with values
given in the following table.
abab
x
1
8414
x
2
4712
x
3
7110
Notice that a and b are complements since for each buyer x
i
(
ab
)
> x
i
(a) +x
i
(
b
)
.
3
Without bundling, the efficient allocation is to give a to buyer 1 and b to
buyer 2. The welfare from this allocation is 15 and this exceeds the welfare from
any other allocation. If buyer 1 were not present, or equivalently if he reported
x
i
=0, then it would be efficient to give a to buyer 3 and b to buyer 2 for a
total welfare W
−1
(0,x
−1
) =14,
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