Auction Theory, 2nd Edition

12.2 Some Open Auctions 179

units, then the amount he pays is

k

i



k=1

c

−i

K−k

i

+k

Continuing with the example, bidder 1’s payment is

c

−1

6

+c

−1

5

+c

−1

4

=b

2

3

+b

3

3

+b

2

2

The Vickrey pricing rule is illustrated in the last panel of Figure 12.3. The

shaded area is the total amount, b

2

3

+b

3

3

+b

2

2

=20 +24+28 =72, paid by bidder

1; as depicted, this is the area lying under the residual supply function facing

bidder 1.

The basic principle underlying the Vickrey auction is the same as the one

underlying the Vickrey-Clarke-Groves mechanism discussed in Chapter 5: Each

bidder is asked to pay an amount equal to the externality he exerts on other

competing bidders. In the example, had bidder 1 been absent, the three units

allocated to him would have gone to the other bidders: two ...