September 2009
Intermediate to advanced
336 pages
9h 37m
English
Content preview from Auction Theory, 2nd Edition
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120 Asymmetries and Other Complications
0
b
1
X
2
X
1
b
2
z
9
z
0
z
9
z
0
1
2
v
2
(·,
z
0
)
v
1
(
z
9
, ·)
FIGURE 8.2 A discontinuous equilibrium in the second-price auction.
and pays β
2
(y) =v
1
(z
,y) ≤ v
1
(x,y), the ex post value to bidder 1, so he does
not regret winning. Moreover, in order to win, bidder 2 would have to pay
β
1
(x) =v
2
(x,z
) ≥v
2
(x,y), the ex post value to bidder 2, so bidder 2 does not
regret losing. Third, suppose that x ∈[z
,z
]and y < z
. In that case, bidder 1 wins
the auction and pays β
II
(y)<v
1
(z
,y) ≤v
1
(x,y), so he does not regret winning.
To win, bidder 2 would have to pay β
1
(x) =v
2
(x,z
)>v
2
(x,y), so he does not
regret losing, either. The remaining cases ...
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