Auction Theory, 2nd Edition

16.2 Efficient Allocations 229

16.2 EFFICIENT ALLOCATIONS

Our first concern is with the possibility of achieving efficient allocations via an

incentive compatible mechanism. The Vickrey-Clarke-Groves (VCG) mecha-

nism, a natural extension of the Vickrey multiunit auction and already familiar

from Chapter 5, provides a ready means of achieving efficiency. It is worthwhile

to review its operation in the current context.

An allocation rule

S is efficient if for every x ∈X , the allocation S(x) maxi-

mizes social welfare—that is, the sum of buyers’values—over all allocations, so

S(x) ∈arg max



T

1

,T

2

,...,T

N





i∈N

x

i



T

i



Define

W(x ) =



i∈N

x

i



S

i

(x)



(16.2)

to be the social ...