1. The Exposure Problem in
Static and Dynamic Auctions
Wong Weng Yew, Joshua

2. Introductions

3. Economics is fun
and motivating…

4. nal number of licenses), the fifth the number of incumbents, the sixth the reve-
nue per population unit, and the last the revenue divided by the population units
per license, which is a more meaningful performance measure.
and serious business… Table 1
UMTS Auctions in Europe in the Year 2000
Where When # Bidders # Licenses # Incumb !/Pop !/(Pop/Lic)
UK 03/04 13 5 4 630 3150
Netherlands 07 9/6 5 5 170 850
Germany* 07/08 12/7 4-6* 4 615 3690
Italy 10 8/6 5 4 210 1050
Austria* 10 6 4-6* 3 103 618
Switzerland 11/12 10/4 4 3 19 76
UMTS Auctions in Europe in the Year 2000
Source: Grimm et al. (2003)

5. Figure 1: European 2000-2001 3G Mobile Spectrum Auctions
Per-Capita Revenues, by Country (right-hand scale)
some interesting figures
(auctions are shown on the dates at which they finished)
Dow Jones European Telecom Stock Price Index (left-hand scale)
1700 700
1500 600
Revenue per Capita (Euros)
1300 500
Market Index (Euros)
1100 400
900 300
700 200
500 100
300 0
Netherlands
Belgium
Italy
Germany
Switzerland
Austria
Greece
Denmark
UK
Jan-00 Jul-00 Jan-01 Jul-01
source: Klemperer

6. beauty
contests?

7. Countries using auctions:
Austria, Belgium, Denmark, Germany,
Greece, Italy, Netherlands, Switzerland, UK
Countries using beauty contests:
Finland, France, Ireland, Norway, Portugal,
Spain, Sweden
beauty
contests?

8. Suppose you’re the Minister
que ferais-tu?

9. The Exposure Problem in
Static and Dynamic Auctions
2 concerns – 2 problems – 2 auctions – 3 results

10. Two concerns
(in all auctions)
Efficiency & revenue

11. Why auctions?
Efficiency:
Auctions tend to put scarce resources in the hands of
those who value them most
Revenue:
Higher revenues can displace distortionary tax revenues,
and avoid giving firms big windfall gains for nothing

12. Selling multiple objects
Sellers are often interested in selling off a number of
different objects:
T-bills
Mobile telephone licenses for different regions
Procurement auctions (electric power generation)
Collections (stamps, comic series)
Logging rights on multiple parcels of land

13. Two problems
(in multi-unit auctions)
Demand reduction & the exposure problem

14. mpact the quantity demanded too. This reduces incentives to keep
h.
Demand reduction
eme 1: Fixed demand
Uniform price auction of carbon
dioxide emissions reductions.
bidding You are the big polluter, and
you are bidding for promises to
reduce emissions in return for
true MC cash (supplying emission
reductions).
Say the price is now p, and
there is excess supply. You can
close the auction out by the
amount of the excess supply
Q and get the demanded units at
the high price.

15. Demand reduction
Key take-away:
Uniform pricing creates incentives for
bidders to bid below their marginal
values, creating inefficiencies.

16. Demand reduction
Key take-away:
Uniform pricing creates incentives for
bidders to bid below their marginal
values, creating inefficiencies.
Possible solutions:
1) reduce supply anti-competitively
2) create some elasticity
3) charge different prices for different units

17. Exposure problem
Complements
+ =
Item A Item B AB
Bidder 1 a b a+b+c
Bidder 2 a + αc b + αc a+b

18. Exposure problem
Items may be complements, suggesting that
prices of these items should be able to
respond to each other.
Selling two items, X and Y, sequentially:
In bidding for X, bidders need to guess
whether they can win Y. They might be too
over-optimistic and only win one item.
Alternatively, pessimistic bidders may fail
to win when it is efficient for them to do so.
Sell them in the same auction?

19. Exposure problem Package bidding
Bid withdrawals
The FCC has been using an auction called the
simultaneous ascending auction. Price discovery in
the early rounds of the auction help bidders
determine if winning their packages is feasible, which
mitigates the exposure problem.
However, Milgrom (2000)* shows that no competitive
equilibrium exists nonetheless in the SAA when items
are complements.

20. Exposure problem Package bidding
Bid withdrawals
The FCC has been using an auction called the
simultaneous ascending auction. Price discovery in
the early rounds of the auction help bidders
determine if winning their packages is feasible, which
mitigates the exposure problem.
However, Milgrom (2000)* shows that no competitive
equilibrium exists nonetheless in the SAA when items
are complements.
Key takeaway:
Bidders have to bid higher than their values for certain
items in the package they want to win in order to have a
chance of winning all items. They risk not winning all the
items and thus overpaying for the items they won.

21. There are some solutions
Dasgupta and Maskin (2000) have
proposed a “super” auction which is fully
efficient, even with complementarity and
I study two auctions which
multiple units for sale.
1) are simple
2) have no demand reduction problem
Unfortunately, the auction is too
complicated to conduct in real life.
I specifically analyze them in terms of
their efficiency and revenue, and
Combinatorial auctions can mitigate the
bidder behaviour in response to the
exposure problem. You bid only on
exposure problem.
packages you want. But this has its own
problems (poor transparency,
computational limits).

22. Two auctions
Vickrey & Ausubel

23. Vickrey auction
Recall: the uniform price auction is not efficient when
multiple items are sold.
Bidders submit price bids for each of the items.
The auctioneer ranks the bids and the highest n bids win.
However, bidders only pay the highest losing nth bids that they displace.
It is a dominant strategy to just bid your values in this auction.
Item A Item B Item C
Bidder 1 12 11 10
Bidder 2 7 0 0
Bidder 3 9 7 6
Table 2: Bidder valuations
Example: If all bidders bid according to the dominant
strategy, then bidder 1 wins all three items and pays
3.2 Ausubel auction
9+7+7. This outcome is efficient.
Analogous to the Vickrey auction is the auction proposed by Ausubel (2004). In this auction,
the auctioneer, via the use of of an ascending clock, gradually increase prices, starting from

24. Ausubel auction
In this auction, the auctioneer names a price, and bidders make
quantity bids at that price. Items, if any are won, are allocated at
that price, and the auctioneer increases the price, prompting
another bout of bidding. Bidders are not allowed to increase their
quantity bids as the price increases, which allows for the
following “clinching rule”:
For each bidder, whenever the total bid of the other bidders is
less than the supply, the bidder is deemed to have “clinched” the
difference.
It is an equilibrium strategy for bidders to bid for any item as long
as their value for that item is more than the current price.

25. Ausubel auction
Brief Article
Example:
WongItem A Yew, Joshua C
Weng Item B Item
Bidder 1 12 11 10
Bidder 2 7 0
April 7, 2010 0
Bidder 3 9 7 6
Table 2: Bidder valuations
Price Bidder 1 Bidder 2 Bidder 3
2 Ausubel auction 0 3 1 3
6 3 1 2
7 3 0 1
alogous to the Vickrey auction is the auction proposed by Ausubel (2004). In this auctio
9 3 0 0
auctioneer, via the use of of an ascending clock, gradually increase prices, starting fro
ow price. At each posted price point, bidders make known the quantities that they wou
e to be allocated. Allocation at each posted price is done by a simple procedure. For ea
der, the residual supply, calculated by subtracting out from the total supply the sum of t

26. Budget constraints
• You are bidder 1 and
you have $29
Item A Item B Item C
• You donʼt know the Bidder 1
Bidder 2
12
7
11
0
10
0
values of the rest Bidder 3 9 7 6
• How do you bid? Table 2: Bidder valuations
3.2 Ausubel auction
Analogous to the Vickrey auction is the auction proposed by Ausubel
the auctioneer, via the use of of an ascending clock, gradually increa

27. Experimental literature
• Manelli et al. (2006) find similar
efficiency in both auctions.
• Engelmann and Grimm (2009) find
overbidding in the Vickrey auction, less
so in the Ausubel auction.

28. Results
On revenue, efficiency, and overbidding

29. Experiments
• Vickrey and Ausubel auctions
• Items can be complements, or not
• 3 items
• 3 bidders

30. Additive vs Complementary
Environments
• Additive environment: #!"
• You simply add up the '#"
values of the items you '!"
won &#"
• Complementary &!"
environment: %#"
• If you win one item, %!"
thatʼs it. $#"
• If you win two items, $!"
add up the values, and
#"
multiply the sum by 1.5.
• If you win three items, !"
$"()*+" %"()*+," &"()*+,"
add up the values, and -..(/0*"
multiply the sum by 2. 12+34*+*5)-67"

31. would imply lower bidder surpluses in these auctions. In the complementary environm
surpluses were similar in both auctions.
Results
The results seem to suggest that the Ausubel auction dominates the Vickrey auct
of efficiency when items sold are complements. A discussion of the implications of
is given in Section 6 on page 30.
VAA (n = 7) AAA (n = 6) t-statistic (p-value) ranksu
Efficiency 0.870 (0.181) 0.859 (0.184) 0.2362 (0.8176)
Revenue 19.406 (4.876) 25.150 (4.969) −3.5289 (0.0047)
Bidder surplus 5.737 (4.965) −0.267 (5.807) 3.0835 (0.0104)
Conditional overbid 12.606 (10.994) 12.200 (11.325) 0.0964 (0.925)
Conditional underbid 4.346 (4.688) 7.550 (7.714) −1.2669 (0.2314)
Consistency 0.088 (0.107) 0.224 (0.188) −5.4236 (0.0002)
VAC (n = 7) AAC (n = 6) t-statistic (p-value) ranksu
Efficiency 0.488 (0.315) 0.772 (0.294) −4.8397 (0.0005)
Revenue 27.477 (8.259) 32.492 (7.634) −1.5495 (0.1495)
Bidder surplus 6.951 (10.416) 7.842 (9.798) −0.2456 (0.8105)
Conditional overbid 35.776 (27.135) 33.158 (15.834) 0.2564 (0.8023)
Conditional underbid 1.471 (2.332) 1.767 (3.196) −0.2771 (0.7868)
Consistency 0.078 (0.131) 0.087 (0.132) −0.1959 (0.8483)
Table 4: Summary of results. Means, standard deviationsstatistical methodology
note on in parentheses, as well

32. Revenue, additive
• Revenue is higher in the Ausubel
auction 30
beta = 0
Vickrey
28 Ausubel
• Bidders bid higher than they
should on their first few items 26
and lower on the rest 24
22
revenue
20
18
16
14
12
10
1 2 3 4 5 6 7 8 9 10
round

33. Revenue, additive
• Revenue is higher in the Ausubel
auction 30
beta = 0
Vickrey
28 Ausubel
• Bidders bid higher than they
should on their first few items 26
and lower on the rest 24
22
• Bidder surplus is lower in
revenue
20
Ausubel auction than Vickrey
auction 18
16
14
12
10
1 2 3 4 5 6 7 8 9 10
round

34. Revenue, additive
• Revenue is higher in the Ausubel
auction 30
beta = 0
Vickrey
28 Ausubel
• Bidders bid higher than they
should on their first few items 26
and lower on the rest 24
22
• Bidder surplus is lower in
revenue
20
Ausubel auction than Vickrey
auction 18
16
• Bidder surpluses are low in the 14
Ausubel auction
12
10
1 2 3 4 5 6 7 8 9 10
round

35. Revenue, additive
• Revenue is higher in the Ausubel
auction 30
beta = 0
Vickrey
28 Ausubel
• Bidders bid higher than they
should on their first few items 26
and lower on the rest 24
22
• Bidder surplus is lower in
revenue
20
Ausubel auction than Vickrey
auction 18
16
• Bidder surpluses are low in the 14
Ausubel auction
12
• Learning? Revenues improve in 10
1 2 3 4 5 6 7 8 9 10
over 10 rounds in Vickrey. round
Ausubel revenues are stable

36. Revenue, complementary
beta = 0.5
45
• Revenue is similar in
both auctions 40
(statistically speaking).
The graph suggests 35
revenue
otherwise though:
30
• Learning? Revenues 25
improve in both Vickrey
Ausubel
auctions 20
1 2 3 4 5 6 7 8 9 10
round

37. The index for consistency ranges from zero to one, the lower the in
bidders (as defined on page 25).
Efficiency, additive
5.2 Efficiency
• Similar efficiencies
In each round, the valuation of the allocation is given by adding
1
beta = 0
3
packages won by the individual bidders: V = j=1 vj . Given th
• bidders in each round, it is possible to compute, using simple li
0.9
Rationality loss? 0.8
the 0.7
• Results possible
the smallest similar to valued allocation and the optimal / highes
0.6
efficiency
Vmin Manelli et ,al. (2006) three items are sold. In both auction m
and Vmax where all 0.5
that this is precisely the case. Table 5 on the following page gives t
0.4
• Efficiency improved
achievable in each round and for each bidding environment. We not
0.3
in the β =10 rounds in
over 0.5 environment involve one person winning all three it
0.2
Vickrey
Ausubel auction, not so 0.1
Ausubel
in Vickrey auction 0
The index of efficiency in each round is given by 1 2 3 4 5
round
6 7 8 9 10
(dynamic learning?)
V − Vmin
Vmax − Vmin

38. Efficiency,
complementary
• The Ausubel auction is 1
beta = 0.5
more efficient than the 0.9
Vickrey auction 0.8
0.7
• Exposure problem! 0.6
efficiency
0.5
•
0.4
Efficiency improved 0.3
over 10 rounds in 0.2
Ausubel auction, not 0.1
Vickrey
Ausubel
so in Vickrey auction 0
1 2 3 4 5 6 7 8 9 10
round
(dynamic learning?)

39. Exposure problem
• In Ausubel auction, it is
possible bid high with a low
chance of making a loss Conversion of Ausubel quantity bids to
(due to the price bids:
complementarity condition) Same bids for all 3 items
• In Vickrey auction, this is
Vickrey Ausubel
not possible
Additive 3% 9%
• Bidders feel more confident
Complementary 8% 48%
in bidding above their
values if they have a lower
chance of losing money
• Bid data suggest this is the
case

40. Overbidding, additive
beta = 0
50
• Overbidding does not 45
make sense in the 40
both auctions 35
Overbidding
•
30
There is non-trivial 25
overbidding, similar in Vickrey
20 Ausubel
both auctions
15
•
10
Overbidding is stable 1 2 3 4 5 6 7 8 9 10
round

41. Overbidding,
complementary
•
beta = 0.5
Difficulties in saying 50
what exactly is an 45
“overbid” due to the 40
complementarity 35
Overbidding
condition 30
25
Vickrey
•
Ausubel
Just a form of 20
comparison 15
10
• Not very useful 1 2 3 4 5
round
6 7 8 9 10

42. Bidder surplus, additive
beta = 0
18
16 Vickrey
Ausubel
14
• Ausubel bidders earn 12
10
zero surplus
biddersurplus
8
6
• Vickrey auction 4
2
favours bidders 0
−2
−4
1 2 3 4 5 6 7 8 9 10
round

43. Bidder surplus,
complementary
beta = 0.5
18
Vickrey
16 Ausubel
14
• Similar bidder 12
surpluses 10
biddersurplus
8
•
6
But the Ausubel 4
auction is more 2
efficient 0
−2
−4
1 2 3 4 5 6 7 8 9 10
round

44. Discussion
For further research, thoughts

45. Exposure problem
revisited
• Result is sensitive to
• value distributions
• number of bidders (more competitive)
• “unequal” bidders
• number of items
• for sale
• that bidders want
• Intuitively, we should expect the exposure problem to be
somewhat mitigated in the Ausubel auction, since the
dynamic nature of the auction helps bidders form
expectations of the final price they pay

46. Overbidding
• Are bidders rational?
• Studies find overbidding in second-price sealed-bid single
unit auctions
• Not so for English (open ascending price) auctions
• Dynamic nature helps bidders learn faster
• BUT we find overbidding in both their multi-unit counterparts
• Need more rounds for learning
• Maybe bidders just like to win items?
• An experiment with real monetary compensation could
test for this (punishment for losing)

47. Choice of auctions
• Demand problem is not an issue in these auctions.
Overbidding seems more prevalent than
underbidding.
• Simple to understand? Price discovery vs simplicity
• These auctions can only sell very “similar” items
• Other factors not considered in this auction are also
very important:
• Collusion (possible low revenues)
• Perception of fairness and transparency

48. Other topics of interest

49. Problems encountered
• Long duration
• Logistical nightmare
• Data consolidation
• Participants uncertain about rules
• Getting volunteers

50. Experimental procedures

51. Valuations
• Valuations are drawn randomly for each
item from the integers 0 to 10 inclusive.
• The set of valuations for each session
is exactly the same.

52. Rules
• Ausubel
• The auction starts at price 5 and rises
in increments of 0.5
• Vickrey
• Bidders can bid prices anywhere from
zero onwards, in multiples of 0.2
• All ties are randomly allocated

53. Participants
• Each participant played in total 20
rounds, in either the Vickrey or Ausubel
auction.
• Ten rounds in the additive
environment
• Ten rounds in the complementary
environment

54. Procedures
• Instructional phase
• Auction phase
• Participants can ask questions at any
time

55. Miscellany

56. vary demand according to
Scheme 2: Variable demand
price
bidding
true MC
Q
This is seldom seen in real life though. WHY?
negative impact on Q
back

57. note on statistical
methods
• sample sizes are admittedly small
• however, McCabe and Moore 1998 assert that
the two-sample t-test is quite accurate for a
broad range of distributions when the sample
sizes are as small as 5
• the test is robust to small sample sizes (Posten
1978)
• a similar study (Manelli et al. 2006) used
sample sizes of 5 and 4.
back

58. Package bidding
• More efficient as complementarity
increases
• Longer to complete
• Lower revenues
back

59. Bid withdrawals
• Porter (1999)
• Efficiency and revenue do increase,
but at expense of bidder surpluses
back