Auction Theory, 2nd Edition

150 Mechanism Design with Interdependent Values

and so buyer i’s payoff is zero. This means that x

i

< y

i



x

−i



and for him to

win, the single crossing condition ensures that buyer i would have to report a

z

i

≥y

i



x

−i



> x

i

. In that case, he would pay an amount

M

∗

i



z

i

,x

−i



=v

i



y

i



x

−i



,x

−i



> v

i

(

x

)

and so this would not be profitable either.

In the case of private values, the generalized VCG mechanism reduces to

the ordinary second-price auction, and in that case, of course, truth-telling is a

dominant strategy. Also, when there are only two buyers the generalized VCG

mechanism is the direct mechanism that corresponds to the efficient equilibrium

of the English