Report on the 2008 UK 10-40 GHz Spectrum
Auction
Ian Jewitt and Zhiyun Li∗
September 2008.
Abstract
This paper reports on the outcome of the 2008 UK 10-40 GHz Spectrum Auction which was one of the first implementations of (a variant
of) the Clock-Proxy auction format as advocated by Ausubel, Cramton and Milgrom (2006). The auction appeared to run smoothly and
achieve a reasonably efficient outcome. For some bidders their supplementary bids tended to make many of their bids effectively redundant.
The clock phase certainly lead to bidders focussing their attention on
a manageable number of feasible packages as intended. However, the
narrowness of this focussing, together with the redundant bids, reduced
measured opportunity costs and may have lead to low revenues.
1
Introduction
The format of the 2008 UK 10-40 GHz spectrum auction is a significant departure from the simultaneous ascending auctions which have typically been
used for spectrum assignments both within the UK and around the world.
The format can be viewed as a variant of the Clock-Proxy auction proposed
by Ausubel, Cramton and Milgrom (2006). The hoped for advantages of the
format are summarised in the 2006 presentation (Ausubel, Cramton and
Milgrom (2006b)) as follows. The Clock Phase: takes linear prices as far
as they will go, providing simplicity and flexibility for the bidders; expands
substitution possibilities; minimises the scope for collusion; and eliminates
exposure and threshold problems. The Proxy Phase: leads to an outcome
in the core–efficiency with substantial seller revenues.
∗
The views expressed in this note are the authors’ own. This note was funded by
Ofcom.
1
Although this is not the first instance of a Clock-Proxy auction to assign spectrum, differences1 between this auction and the only previous one
we are aware of mean that there is likely to be substantial interest in the
performance of the format in this application.2
The UK 2008 10-40 GHz process departed from the Ausubel, Cramton
and Milgrom (2006) Clock Proxy format by having 3 rather than 2 distinct
bidding elements. The first two bidding elements took place in a primary
stage which is itself effectively a (variant of the) Clock Proxy format. The
purpose of this primary stage was to assign entitlements to quantities of
bandwidth in certain spectrum ranges. The third bidding element, the assignment stage determined how these entitlements were distributed over the
relevant spectrum.
The first bidding element in the primary stage is conducted via an ascending clock auction in which package bidding takes place–bidders commit
to prices for packages rather than their component parts. The second bidding element allows bidders to supplement their bids in the clock auction
with a possibly large number of simultaneous supplementary bids–again
these are on packages of lots. At the end of the primary bid stage the mechanism identifies the value maximising allocation consistent with the bids and
determines the base prices. Base prices are determined according to a modified ‘second-price’ or Vickrey rule which is computationally burdensome and
carried out on propriety Ofcom winner determination and pricing (WDP)
software. A modified, rather than pure Vickrey pricing rule is advocated,
in part, because Vickrey prices can lead to very low revenues for some configuration of reported preferences.3 The following example, adapted from
these references, illustrates. Figure 1 lists some hypothetical bid data in
1
Trinidad and Tobago undertook such an auction on 23 June 2005, Market Design
Incorporated advised. We have not been able to find details of the auction packaging
or bids, but it is clear that there are important differences between the Trinidad and
Tobago auction and the UK one. One difference is however aparent, the Trinidad and
Tobago process fixed in advance the number of possible concession holders: there were
to be two only. The clock phase of the auction determined which of the five qualified
entrants would get the concessions and also determine the minimum price of bandwidth
(See Telecommunications Authority of Trinidad and Tobago and Ausubel Cramton and
Milgrom (2006b)). The fact that an important part of the assignment, determining the
concession holders, is determined at the clock phase means that some of the features of
the UK 10-40 GHz auction which are stressed in our analysis would be masked.
2
Ausubel, Cramton and Milgrom (2005) in response to the FCC’s Public Notice DA 051267 called for a variation in the FCC’s proposed schedule for testing alternative auction
models in favour of the Clock Proxy format.
3
See Ausubel, Cramton and Milgrom (2006), Day and Milgrom (2007) and Day and
Raghavan (2007) for more details.
2
bidderID bidderName units_1 units_2 units_3 units_4 units_5 units_6 units_7 bidAmount
1 Bidder 1
0
0
1
1
0
0
0 1000000
2 Bidder 2
0
0
0
1
0
0
0 1000000
2 Bidder 2
0
0
1
1
0
0
0 1000000
3 Bidder 3
0
0
1
0
0
0
0 1000000
3 Bidder 3
0
0
1
1
0
0
0 1000000
Figure 1: Hypothetical bid data illustrating low Vickrey prices.
TieIDbidderIDbidderName units_1 units_2 units_3 units_4 units_5 units_6 units_7 bidAmountoppCost basePrice
1
2 Bidder 2
0
0
0
1
0
0
0
1000000
0
500000
1
3 Bidder 3
0
0
1
0
0
0
0
1000000
0
500000
Figure 2: WDP software output for the data in figure 1.
which there are 3 bidders; bidder one needs a unit of lots 3 and 4, bidders
2 and 3 only need one unit. The Vickrey prices are zero. It is clearly efficient to assign the lots to bidders 2 and 3 and a single lot is as valuable e.g.
to the coalition of bidder 1 and 2 as two lots would be. The opportunity
cost is zero as confirmed by the WDP software, see figure 2. Figure 2 also
displays the higher base prices which splits equally between bidders 2 and 3
the smallest amount they must pay so that the loser is unable to ‘offer’ the
auctioneer more for the two packages. To summarise, one of the main motivations of the Ausubel, Cramton, Milgrom (2006) Clock-Proxy auction is to
protect against the very low revenues which sometimes arise from charging
opportunity costs as in a Vickrey Auction (zero revenue in the example). In
the above example, the procedure is successful in this regard since the base
prices exceed opportunity costs by a significant amount.
Figure 3 presents the 10-40 GHz auction outcome. Columns 4-10 detail
the assignments of the Lots, column 11 the amount bid for these assignments
by the 10 bidders. Column 12 details the opportunity cost (Vickrey prices)
and column 13 the base prices payable by these bidders. We have added
to the output of the WDP software a final column which simply details the
starting or reserve prices for the lots. There are two striking feature of this
data. First, the bid amounts considerably exceed both the opportunity cost
and base prices. Second, the base price for each package is either equal to
the opportunity cost or it is equal to the reserve price. This means that,
in the event, given the bids4 , as far as revenue is concerned the modified
4
Note however that bidders might have had incentives to behave differently if Vickrey
3
TieID bidderID bidderName units_1 units_2 units_3 units_4 units_5 units_6 units_7 bidAmount oppCost basePrice ReservePrice
2
1 Arqiva
0
2
0
0
0
0
0
1599000 260500
260500
120000
2
2 BT
0
0
0
0
0
1
0
1001000 179000
179000
60000
2
3 Digiweb
2
0
0
0
0
0
0
142000
39000
39000
20000
2
4 Faultbasic
0
0
0
0
1
0
0
750000
0
30000
30000
2
5 MLL
0
0
0
0
0
1
1
250000 179000
179000
90000
2
6 Orange
0
0
0
0
0
2
0
2999999 261000
261000
120000
2
7 RedM
0
0
0
1
0
0
0
34000
1000
10000
10000
2
8 TMobile
8
0
0
0
0
2
1
8500000 319000
319000
230000
2
9 Transfinite
0
0
1
0
0
0
0
97000
0
20000
20000
2
10 UKBB
0
0
0
0
0
0
4
420000
0
120000
120000
Figure 3: Primary Stage Assignment and Base Prices. Note specifically
BP = max{OC, RP }.
second price rule achieved only what Vickrey pricing would have achieved.
Figure 3 details only the outcome of the primary stage of the 10-40
GHz auction. When more than one winning bidders demand the lots in a
band, a new round of assignment stage bid is required to decide the final
lot assignment. It is also a sealed-bid auction and allocations and prices
are again determined on a modified Vickrey basis using the WDP software.
The logic of this relies on the within band differences of valuations being
of second order importance compared to between band differences. In the
event, this was borne out by the bidding behaviour.
The main conclusions of this paper are as follows. The clock phase of
the auction appears to have had a marked impact on the subset of valuations which were effectively reported by bidders throughout the primary bid
phase. This is consistent with what the auction format is designed to achieve:
bidders receive information during the clock stage which enables them to focus their attention on plausible outcomes and this reduces the combinatoric
complexity of the task of reporting "valuations" via bids. This focussing lead
to a successful outcome in the sense that the format elicited consistent bids
which lead to the allocation of all the spectrum. With some reservations5
the allocation was probably reasonably efficient consistent with the stated
objectives of Ofcom. From the point of view of achieving high revenues–
not an objective of Ofcom, but of interest for other potential adopters of the
format, the auction appears to have generated rather low prices. Inspection
of the data shows that bidders focussed heavily on the assignments thrown
up by the clock phase and this lead to low opportunity costs given reported
preferences (low Vickrey prices). The situation was exacerbated by many
pricing had been adopted. See for example Day and Milgrom’s (2007) discussion of bidder
shills.
5
Briefly detailed in section 4.4.
4
bidders making a large number of "redundant" bids leading to there being
far fewer "effective" bids than the number of actual bids made during the
auction. Due to the sparsity of effective bids, the modified second price rule
simply did not have any leverage to protect revenue as discussed above and
displayed in figure 3.
2
The Primary Bid Stage
2.1
Spectrum Packaging and Combinatorics
Spectrum Packaging The process was for spectrum at 10-40 GHz. One
of the design features of the auction was to group the ten 10 GHz sublots,
the two National 28GHz sublots and the six sublots each of National 32
GHz and National 40 GHz. This grouping reduces the number of packages
on which bidders have to deal with in the primary stage of the auction at
the cost of having an extra (assignment stage) stage, see Figure 4.
Number of
lots
Spectrum
Eligibility Points per
lot
Lots 1 - National 10 GHz
10
1
Lots 2 - National 28 GHz
2
6
Lots 3 - First Sub-National 28 GHz
1
2
Lots 4 - Second Sub-National 28 GHz
1
1
Lots 5 - Third Sub-National 28 GHz
1
3
Lots 6 - National 32 GHz
6
6
Lots 7 - National 40 GHz
6
3
Figure 4: The Grouping within Lots and associated Eligibility Points.
Notwithstanding the grouping of sublots, there are potentially a large
number of distinct packages for bidders to consider in the primary bid stage.
Specifically, a bidder with the full amount of eligibility points can choose to
bid on 12, 935 distinct non-null packages6 . This is a large but a distinctly
computable number and is certainly much less than the over 134 million
packages which would have resulted without grouping.
6
This number does not take account of the eligibility cap for all bidders of 42 eligibility
points
5
Eligibility points The purpose of assigning eligibility points for each lot
is to determine the terms of trade with which bidders are allowed to transfer
demand from one package of lots to another during the clock phase and for
subsequent supplementary bids. Bidders lose eligibility7 if they fail to bid
and the loss of eligibility restricts their available choices both within the
clock phase and the supplementary bid phase. This gives bidders incentives
to bid actively during the clock phase. The various lots were assigned eligibility points as detailed in Figure 4. One hopes that the eligibility points
will correspond to some intrinsic value of the lots which is expected to be
reflected in the valuations of bidders. Of course this is a guess at market
valuations which can impact on the efficiency of the auction. There are
other alternatives,8 but the one adopted has the advantage of simplicity. In
the event the final clock prices were (in £000) 69, 707, 97, 37, 130, 594,
151. This series is strongly positively correlated with the eligibility points
per lot 1, 6, 2, 1, 3, 6, 3, having a correlation coefficient of approximately 0.96.
Although this high correlation certainly does not establish the correctness
of the choice of eligibility points, neither does it provide evidence against.
Bidder
Initial Eligibility
Arqiva
BT
Digiweb
Faultbasic
MLL
Orange
RedM
TMobile
Transfinite
UKBB
24
42
7
9
25
18
2
26
12
42
End ClockPhase
Eligibility
13
15
2
6
0
18
0
23
2
3
E: Eligibility of BP: Base Price BP/E
Acquired Lots
(£000's)
12
6
2
3
9
12
1
23
2
12
260.5
179
39
30
179
261
10
319
20
120
21.7
29.8
19.5
10
19.9
21.7
10
13.9
10
10
Figure 5: Base Prices per aquired Eligibility Points by Bidder
Since all bidders began with a legislated maximum of not more than 42
eligibly points, the number of possible bids is much reduced–there are only
7
Specifically, during the clock phase bidders cannot ’spend’ more eligibility than they
spent in the past. During the supplementary bid phase bidders can bid unrestricted
amounts (i.e. no limit on maximum) for lots within their end of clock phase eligibility but
are restricted in how much they can bid on packages which exceed this eligibility.
8
For instance, and specifically, Ausubel, Cramton and Milgrom (2006) propose a ‘revealed preference’ activity rule.
6
6, 928 possible packages. In practice, most bidders began with fewer than
the maximum eligibility points, RedM with only two initial eligibility points
has only five feasible packages. Evidently, given these numbers, it is not
completely beyond the bounds of reason that bidders might enter bids for
each distinct package within their entitlement constraint.
Post clock phase combinatorics At the termination of the clock phase,
the number of eligibility points remaining for the bidders will typically be
reduced and in the 10-40 GHz auction the eligibility of all bidders was indeed
reduced for all bidders except one (Orange). UKBB started with 42 but
ended with only 3; T-Mobile started with 26 and ended with 23. Column
4 of Figure 6 gives details for all bidders. Column 5 of Figure 6 illustrates
that for many bidders the scale of the problem of detailing within eligibility
bids, was perhaps not impossibly large.
Bidder
Initial
Eligibility
Initial number of
possible packages
End clock-phase Number of withinEligibility
eligibility post clock
packages
Arqiva
24
1885
13
334
BT
42
6928
15
499
Digiweb
7
65
2
5
Faultbasic
9
123
6
45
MLL
25
2108
0
0
Orange
18
840
18
840
RedM
2
5
0
0
TMobile
26
2329
23
1672
Transfinite
12
267
2
5
UKBB
42
6928
3
267
Figure 6: Eligibility combinatorics: The number of potential packages on
which bidders may wish to bid: initial and within eligiblity post-clock phase.
Figure 7 displays the actual numbers of bids made by each bidder both
in the clock phase and in the supplementary bid phase of the principal stage
of the auction. Figure 7 also decomposes the supplementary bids into those
which exceeded the terminal eligibility following the clock phase (for which
prices were bounded by clock prices) and those within this eligibility for
which the prices were not so bounded. At the supplementary bid stage the
auction rules distinguish between bids which exceed the bidders terminal
eligibility and those which do not. Bidders are allowed to post unrestricted
bids for packages within their terminal eligibility but are constrained by the
ruling clock prices (when the bidder had sufficient eligibility) for bids on
7
packages which exceed their terminal eligibility. This means that if prices
have risen during the clock phase, there may be little purpose in making lots
of ineffectual bids for initial rather than final eligibility. The clock phase
therefore reduces the size of the combinatoric valuation problem and provides some price information which may be useful in further focussing bids.
The potential importance of the within eligibility distinction is illustrated
by T-Mobile’s bidding: for supplementary bid packages exceeding terminal
eligibility, the average bid was £737, 500, for supplementary bid packages
not exceeding terminal eligibility the average bid was £6, 894, 470.
clock
sealed
sealed exceeding
terminal eligibility
sealed not
exceeding terminal
eligibility
Arqiva
17
22
0
22
BT
17
544
425
119
Digiweb
17
1
0
1
Faultbasic
17
12
6
6
MLL
9
15
9
6
Orange
17
4
0
4
Bidder\Bi
ds
RedM
9
2
1
1
TMobile
17
106
14
92
Transfinite
17
1
0
1
UKBB
17
3
2
1
Figure 7: The number of actual bids by bidder and type of bid
2.2
Redundant and Effective Bids
A very noticeable feature of the bidding is that some bidders made a large
number of redundant (or more accurately almost redundant) bids so that
the effective registration of reported values was much less than the number
of bids entered. We will illustrate with the following selection of the last
few supplementary bids from one of the bidders (BT). Figure 8 displays
the bid amount as the second column and the package bid for in the seven
subsequent columns. Note that the amount of the bid in the first row is at
least as large as any subsequent bid but the package corresponding to this
bid is a subset of all but two of the other packages bid for. Essentially,9 this
9
It is important to note that under the rules of the auction, bids which are "redundant"
in this sense can impact on the outcome of the auction. Both the assignment and revenue
can be changed. The reason is to do with the tie breaking rules of the auction. For
8
means that BT signals to the auction, for example, that it is as content with
one unit of lot 6 as it is with 6 units of lot 6 plus 2 of lot 7 (the last bid).
Hence, the only effective bids in figure 8 are the three highlighted in italics.
Proceeding in a similar way with the whole set of bids, many other bids can
be deleted–including some clock bids.
Bid
BT
BT
BT
BT
BT
BT
BT
BT
BT
BT
BT
BT
BT
1001000
1001000
1000500
1000500
1001000
1001000
1001000
1001000
1001000
1001000
1001000
1001000
1001000
Lot 1
0
0
0
0
0
0
0
0
0
0
0
0
0
Lot 2
0
0
1
1
0
0
0
0
0
0
0
0
0
Lot 3
0
0
1
0
0
0
0
0
0
0
0
0
0
Lot 4
0
0
1
0
0
0
0
0
0
0
0
0
0
Lot 5
0
0
1
1
0
0
0
0
0
0
0
0
0
Lot 6
1
1
0
0
1
1
1
2
2
2
4
5
6
Lot 7
0
2
1
2
3
4
5
3
4
6
2
2
2
Figure 8: Illustration of redundant bids
Many bidders had such redundant bids which markedly reduced the number of effective bids below the number of actual bids detailed in figure 7.
Figure 9 details this effective bid deficit. One sees that the case of BT is
particularly marked–out of 561 bids only 2 were effective in the sense we are
using the word. As bidders added supplementary bids, sometimes the effective number of bids were therefore reduced–bids were made redundant by
subsequent supplementary bids. More bidding generally meant less effective
bids.
This marked ‘reduction’ in the quantity of effective bids may well have
had significant consequences for the outcome of the auction, we discuss this
via some counterfactual alternatives in section 2.3.
The effective bid data are sufficiently reduced that we can get a good
grasp of the mechanisms behind the outcome by listing the effective bids
for the majority of the bidders for whom the number of effective bids were
single digits. Figure 10 displays the list of effective bids made by these 8
bidders. In total there are only 31 bids in contrast to the 700 or so by these
bidders in the actual auction. The highest bids for each of the 8 bidders are
highlighted in italics, for MLL there are two equally high bids (but select the
assignments with equal value of bids, the auction prefers to select the one that assigns
most spectrum (for which the starting prices are charged). Sections 2.3.1 and 2.4 discuss
further.
9
Bidder
Arqiva
BT
Digiweb
Faultbasic
MLL
Orange
RedM
TMobile
Transfinite
UKBB
clock bids sealed bids
17
17
17
17
9
17
9
17
17
17
22
544
1
12
15
4
2
106
1
3
total
effective sealed
effective
bids
bids
22
22
2
2
1
3
1
2
6
6
3
3
2
2
106
106
0
3
3
7
Figure 9: The Effective Bid deficit: numbers of actual and effective bids for
each seller.
bid for unit of lot 2 at £250, 000). Suppose each bidder were assigned the
package on which it bid highest, this is a feasible assignment since there is
a nonnegative excess supply for each Lot. This assignment, at zero price is
in the core and it is evidently also bidder optimal. Hence, the auction rules
applied only to this subset of bidders establishes a zero price–or rather, the
bidders are required to pay the starting (reserve) prices for the individual
lots they receive. This conclusion is confirmed by running the auction WDP
software for the data in figure 10, the results are displayed as figure 11.
In the next section (section 2.3) we also carry out this calculation on the
original bid data but with all the bids of Arqiva and T-Mobile deleted, the
calculations give different results because of the treatment of lots which are
in excess supply. The main point is that bidders listed in figure 10 ended
up expressing rather little demand.
2.3
Discussion of Counterfactual Outcomes
The total number of eligibility points required to purchase all lots is 82
which, at reserve of £10K per eligibility point, would cost £820,000. In the
event, the auction raised a revenue of £1,434,630, i.e. somewhat less than
twice the reserve price. In this section we explore the effect on revenues of
a number of counterfactual bidding scenarios.
10
Lot 1
BT
BT
Digiweb
Digiweb
Digiweb
FaultBasic
FaultBasic
MLL
MLL
MLL
MLL
MLL
MLL
Orange
Orange
Orange
RedM
RedM
RedM
RedM
RedM
Transfinite
Transfinite
Transfinite
UKBB
UKBB
UKBB
UKBB
UKBB
UKBB
UKBB
Total Demand
Supply
XS Supply
Lot 2
0
0
4
3
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
10
6
Lot 3
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
Lot 4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
Lot 5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
Lot 6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
Lot 7
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
6
6
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
2
2
4
3
1
2
1
2
6
4
Bid
1,000,500
1,001,000
200,000
198,000
142,000
535,000
750,000
250,000
50,000
250,000
60,000
110,000
34,000
2,999,999
1,492,957
2,857,887
29,000
34,000
179,000
79,000
97,000
179000
79000
97000
394,000
599,000
420,000
378,000
170,001
302,000
500,001
Figure 10: Complete list of effective bids for bidders other than Arquiva
and TMobile. Note that supply exceeds the value maximising assignment
for these bidders.
Outcome of the Primary Bid Stage run on the data in Figure 10.
TieID
bidderID bidderNa units_1
1
1
1
1
1
1
1
1
2
3
4
5
6
7
8
9
BT
Digiweb
FaultBasic
MLL
Orange
RedM
Transfinite
UKBB
0
4
0
0
0
0
0
0
units_2
0
0
0
1
0
0
0
0
units_3
0
0
0
0
0
0
0
0
units_4
0
0
0
0
0
0
0
0
units_5
0
0
1
0
0
0
0
0
units_6
1
0
0
0
2
1
1
1
units_7
0
0
0
0
0
0
0
2
bidAmou oppCost
1001000
200000
750000
250000
2999999
179000
179000
599000
0
0
0
0
0
0
0
0
basePrice
60000
40000
30000
60000
120000
60000
60000
120000
550000
Figure 11: Calculation of Assignment and Base Prices from data of Figure
10.
11
2.3.1
Impact of deleting two bidders (Arqiva and T-Mobile).
We saw in section 2.2 that many of the bidders had made rather few effective
bids, notwithstanding the much larger number of actual bids made. Here we
evaluate via the auction WDP software the result of the primary bid stage
in the counterfactual situation in which only the bidders listed in figure 10
were present (and in which they made the same bids).
Outcome of the Primary Bid Stage (with Arqiva and T-Mobile not present)
TieID bidderID bidderName units_1 units_2 units_3 units_4 units_5 units_6 units_7 bidAmount oppCost basePrice
1
1
1
1
1
1
1
1
2
3
4
5
6
7
9
10
BT
Digiweb
Faultbasic
MLL
Orange
RedM
Transfinite
UKBB
4
4
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
1
1
2
0
0
1
0
0
0
2
1001000
200000
750000
250000
2999999
34000
179000
599000
0
0
0
0
0
0
0
0
240000
40000
30000
110000
180000
10000
60000
120000
790000
Figure 12: Ofcom software calculation of Primary Stage Assignement and
Base Prices resulting from the deleting 2 bidders (Arquiva and TMobile).
The sparsity of bidding leads to low prices.
Comparing figure 12 with figure 11, there are some discrepancies. Looking at figure 12, we see that MLL is allocated 2 units of Lot 1, 1 unit of Lot
2 and 1 unit of Lot 7 for which MLL bid £250,000, whereas in figure 10 MLL
has no such effective bid. The reason is that because of MLL’s effective bid
of £250,000 for a single unit of Lot 2 we have eliminated, in constructing
figure 10, the bid which determines MLL’s assignment in the figure 12. Essentially, the reason is that there is excess demand for the other lots and
the auction mechanism has a revenue tie-breaking rule which chooses to allocate this spectrum at the starting prices. This illustrates what we pointed
out in section 2.2, that our usage of language in defining "redundant bids"
and "effective bids" is something of an oversimplification. Nevertheless the
language remains useful in analysing the auction outcome.
2.3.2
"Pay as bid" Clock stage
Another counterfactual of interest is what would have happened if the auction had terminated after the clock phase but now with bidders paying their
terminal bids. If bidders did not change their behaviour then the revenue
would have been substantially higher - over £6.7m. Under these counterfactual conditions, the actual auction earned less than a quarter of the (counterfactual) "pay as bid" clock auction.
12
Of course, bidders may well have had incentives to bid very differently.
In particular, the incentive to halt price increases through demand reduction
may have been more acute. Given the feature that bidders cannot, in the
supplementary bid phase, expand their demand at higher prices than those
pertaining in the clock phase10 , there seems no strong reason for this to be
the case. It is difficult to think that bidders believed that they had marked
incentives to bid above their valuations in the clock auction so it does seem
that the revenue only managed to capture a small share of this value11 .
2.3.3
Pseudo Clock Auction: Impact of deleting all supplementary bids
If one takes the view that some of the supplementary bids may have been illconsidered and resulting in a sparsity of effective bids, a natural comparison
involves deleting some of the bids from the supplementary bid stage of the
auction. The second table in Figure 13 provides a natural comparison–what
would have happened if the auction had been terminated after the clock stage
but otherwise under the same rules. If bidders did not change their behaviour
then we see, the revenue increases from approximately £1.4m to £2.7m i.e.
under these conditions revenue would have nearly doubled. The big question
is whether bidders would be likely to change their behaviour. In our view,
there is no strong evidence that behaviour during the clock phase would
have been much different. Unless the supplementary bids are deliberately
misleading12 many have the appearance of something of an afterthought.
Some bidders may have expected the auction to be more or less over after
the clock stage. Second, as we will discuss later, most bidders tended to bid
for their putative clock allocations in the supplementary bid phase.
2.3.4
Impact of deleting BT’s supplementary bids only.
We have seen that although BT made the most bids, only 2 were effective.
The supplementary bids cancelled out the clock bids to the possible detriment to auction revenues. Suppose we delete all the supplementary bids
from BT, in this case the software shows that the assignment is impacted
10
Ausubel Cramton and Milgrom (2006) proposed a relaxed (revealed preference) activity rule in contrast to the unrelaxed activity rule of this auction.
11
It is worth noting in this respect that Ofcom’s stated objectives are efficiency rather
than revenue. However, Ausubel, Cramton Milgrom (2005) emphasise both revenue and
efficiency considerations.
12
Since the data are public, bidders might wish to confuse Ofcom, business rivals and
potential competitors in future auctions with similar formats.
13
Outcome of the Primary Bid Stage
bidderName
units_1
units_2
units_3
units_4
units_5
units_6
units_7
Arqiva
BT
Digiweb
Faultbasic
MLL
Orange
RedM
TMobile
Transfinite
UKBB
0
0
2
0
0
0
0
8
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
1
0
4
bidAmount oppCost basePrice
1,599,000
1,001,000
142,000
750,000
250,000
2,999,999
34,000
8,500,000
97,000
420,000
260,500
179,000
39,000
0
179,000
261,000
1,000
319,000
0
0
260,500
179,000
39,000
30,000
179,000
261,000
10,000
319,000
20,000
120,000
1,417,500
Outcome of the Primary Bid Stage (Clock Bids Only Evaluated)
bidderName
units_1
units_2
units_3
units_4
units_5
units_6
units_7
Arqiva
BT
Digiweb
Faultbasic
MLL
Orange
RedM
TMobile
Transfinite
UKBB
0
0
2
0
0
0
0
8
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
3
0
1
0
0
0
1
0
1
bidAmount oppCost basePrice
1,451,000
918,000
138,000
281,000
0
1,782,000
0
1,891,000
97,000
151,000
747,000
454,000
0
205,000
0
604,000
0
616,000
24,000
6,000
747,000
454,000
20,000
205,000
0
604,000
0
616,000
24,000
30,000
2,700,000
Figure 13: The Primary Bid Stage Outcome compared with the counterfactual calculation on the Clock Phase data only.
mainly by BT now registering a positive value for units of Lot 7 with the
result that BT gains 2 units of 40 GHz at the expense of UKBB. BT pays
and extra £11, 000 for these two lots. UKBB receives one unit of Lot 6 as
a by-product at the expense of MLL. As a result, MLL pays £149, 000 less
than before but all other bidders pay more. The impact on final revenue is
an increase of £86, 500.
2.3.5
Impact of deleting Arqiva’s supplementary bids only.
Arqiva’s supplementary bids were all effective ones, but figure 15 shows that
they had rather little impact on the auction outcome. Arqiva itself would
have won more spectrum (Lot 4) at a cost of £23K. Taking Arqiva’s supplementary bids at face value this additional unit of spectrum was revealed
to be not worth the cost. The auction revenue is about £7K higher.
2.3.6
Impact of deleting T-Mobile’s supplementary bids only.
After BT, T-Mobile exercised the largest number of supplementary bids.
In contrast to BT, but as with Arqiva, (most of) T-Mobile’s supplementary
bids were "effective" in the sense used above–they did not cancel each other
out. It is interesting to note that if T-Mobile’s supplementary bids alone
14
Outcome of the Primary Bid Stage (with BT’s Supplementary Bids Deleted)
TieID bidderID bidderName units_1 units_2 units_3 units_4 units_5 units_6 units_7 bidAmount oppCost basePrice
1
1 Arqiva
0
2
0
0
0
0
0
1599000 212000
267000
1
2 BT
0
0
0
0
0
1
2
896000 190000
190000
1
3 Digiweb
2
0
0
0
0
0
0
142000
50000
50000
1
4 Faultbasic
0
0
0
0
1
0
0
750000
0
55000
1
5 MLL
0
0
0
0
0
0
1
60000
22000
30000
1
6 Orange
0
0
0
0
0
2
0
2999999 294000
294000
1
7 RedM
0
0
0
1
0
0
0
34000
1000
34000
1
8 TMobile
8
0
0
0
0
2
1
8500000 352000
352000
1
9 Transfinite
0
0
1
0
0
0
0
97000
0
20000
1
10 UKBB
0
0
0
0
0
1
2
599000 212000
212000
1504000
Figure 14: The Primary Bid Stage Outcome with the Supplementary Bids
of BT deleted.
Outcome of the Primary Bid Stage (with Arqiva's Supplementary Bids Deleted)
TieID
bidderID bidderNa units_1
units_2
units_3
units_4
units_5
units_6
units_7
bidAmou oppCost basePrice
1
1
1
1
1
1
1
1
1
1
1
2
3
4
5
6
7
8
9
10
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
1
4
1451000
1001000
142000
750000
250000
2999999
29000
8500000
79000
420000
Arqiva
BT
Digiweb
Faultbasic
MLL
Orange
RedM
TMobile
Transfinite
UKBB
0
0
2
0
0
0
0
8
0
0
283500
179000
39000
0
179000
279000
18000
337000
0
0
283500
179000
39000
30000
179000
279000
20000
337000
30000
120000
1496500
Figure 15: The Primary Bid Stage Outcome with the Supplementary Bids
of Arqiva deleted.
15
Outcome of the Primary Bid Stage (with T-Mobile's Supplementary Bids deleted)
bidderName
Arqiva
BT
Digiweb
Faultbasic
MLL
Orange
RedM
TMobile
Transfinite
UKBB
units_1
0
0
2
0
0
0
0
8
0
0
units_2
2
0
0
0
0
0
0
0
0
0
units_3
0
0
0
0
0
0
0
0
1
0
units_4
0
0
0
0
0
0
1
0
0
0
units_5
0
0
0
1
0
0
0
0
0
0
units_6
0
1
0
0
1
2
0
2
0
0
units_7
0
0
0
0
1
0
0
1
0
4
bidAmount oppCost basePrice
1,599,000
1,001,000
142,000
750,000
250,000
2,999,999
34,000
1,891,000
97,000
420,000
260,500
179,000
39,000
0
179,000
261,000
1,000
319,000
0
0
260,500
179,000
39,000
30,000
179,000
261,000
10,000
319,000
20,000
120,000
1,417,500
Figure 16: The Primary Bid Stage Outcome with the Supplementary Bids
of T-Mobile deleted.
are deleted and the primary bid stage outcome recalculated, one finds that
the outcome is unaffected. In other words, even though T-Mobile made a
large number of effective supplementary bids, none of them impacted on the
outcome of the auction. The reason for this rests largely with the sparsity
of effective bids from other bidders.
2.4
Starting versus Reserve Prices: A Strange Feature
We return to the discussion of assignment and pricing when supply exceeds
demand for a particular lot. It seems the following situation can arise.
Bidder 1 bids £1m for a 42 eligibility point package and also bids £1m for a
small subset of that package, say Lot 3. According to our definition of section
2.2, only the second bid is effective. All other bidders only bid on packages
which include Lot 3 in the first round of the clock auction and then bid
for zero lots in the second round, no other bidders enter any supplementary
bids. Hence, since Bidder 1’s bids are revenue maximising and inconsistent
with all other bids, Bidder 1 wins. The auction WDP software assigns 42
eligibility points to Bidder 1–even though according to Bidder 1’s bids, 41
of those eligibility points have no value. The rest of the spectrum is retained
by Ofcom even though the other bidders did bid for the other spectrum (in
combination with Lot 3).
Note that Bidder 1 will not pay the zero opportunity cost, or £10K for
item 3, but £420K for the 42 eligibility points worth of spectrum assigned.
Evidently, Bidder 1 would rather pay £10K for the lesser package according
to the values expressed by his or her bids. Hence, the outcome is not a
bidder optimal core allocation.
An alternative would be to treat the starting prices, i.e. reserve prices
as bids in determining the assignment.
16
3
The Assignment Stage
After the primary stage bid round, when there are more than one winning
bidders demanding the lots in a band, a new round of assignment stage bid is
required to determine the final allocation of lots. Like the supplementary bid
round, the assignment bid round is a sealed-bid auction. Relevant bidders
submit their bids to Ofcom, and the winning bids are those compatible
bids with the largest amount bid. The prices payable by the bidders in
the assignment stage are called Top-Up prices, which are core prices that
generate a bidder-Pareto optimal allocation (Cramton, et al. 2006, Chapter
3 and 5; Day and Raghavan, 2007).
Although the grouping of lots in the primary bid phase reduces the
number of packages for that stage, it potentially does so at the cost of
introducing other complications. For the philosophy behind the grouping
and sequential auction design to be valid, it is important that the tail does
not wag the dog. It is predicated on the assumption that the within group
assignments are of second order importance to the first stage.
3.1
Bidding
The striking aspect of the bids is that Orange appears to have had strong
views on which lots it received and bid significantly higher (£105K) for its
preferred assignment than any other bids. This bid was significantly less
than Orange’s primary stage bid for the two lots of this spectrum which it
was assigned (approximately £3m). The relative magnitudes of these bids
appears to corroborate the view that the within Lot assignment was indeed
of second order importance.
17
Bidder
BT
BT
BT
BT
BT
BT
MLL
MLL
MLL
MLL
MLL
MLL
Orange
Orange
Orange
Orange
Orange
TMobile
TMobile
TMobile
TMobile
TMobile
32GHz Nat band
Frequecy Assignment
Stage Bid
option
Lot 1
0
Lot 2
10000
Lot 3
5000
Lot 4
4000
Lot 5
9000
Lot 6
0
Lot 1
0
Lot 2
3000
Lot 3
5000
Lot 4
5000
Lot 5
3000
Lot 6
0
Lots 1 and 2
105000
Lots 2 and 3
15000
Lots 3 and 4
0
Lots 4 and 5
15000
Lots 5 and 6
15000
Lots 1 and 2
20229
Lots 2 and 3
15151
Lots 3 and 4
10099
Lots 4 and 5
5048
Lots 5 and 6
0
Assignment stage bids for 32 GHz lots.
4
4.1
Evaluation and Conclusions
The auction mechanics and correspondence with the documentation
The auction mechanics seemed to work reasonably smoothly–although we
have not shared in bidder feedback.
4.2
Bidder behaviour
Some bidders appear not to have been prepared. Some of the documentation
may have been obscure. We did not make a systematic search of documentation available to bidders prior to the auction, but found the translation of
essentially mathematical concepts from legal phraseology a challenge.
A recommendation for any future auctions using similar formats is to
invest heavily in helping bidders via a multiplicity of software promptings
and other tools. For instance, we would recommend a device which pointed
18
out to bidders when they bid more for a subset of lots than a superset–or
made them choose ‘more consistent’ different bids.
The suspicion of lack of bidder preparedness makes it hard to gauge the
potential of the format in situations where bidders have spent more resources
in preparing. However, the reservations detailed below about low revenues
might remain a feature even with well-prepared bidders.
4.3
Revenue
The auction seems very likely to have produced low revenue. One wonders
to what extent low revenue is a natural outcome for such auctions. If we
paraphrase the theory behind the auction format, insofar as it can be taken
from13 Ausubel, Cramton and Milgrom (2006). There are two problems14
with Vickrey auctions which the Clock Proxy design is intended to overcome.
1. Combinatoric complexity For even moderate numbers of objects, there
are too many potential combinations of objects on which to make bids.
2. Vickrey outcomes are not necessarily ‘competitive’. Specifically,
outcomes are not in the core when the auctioneer is included as an
agent with preferences increasing in auction revenues. This means
that Vickrey outcomes can yield very low revenues.
The Ausubel, Cramton and Milgrom (2006) Clock Proxy auction and
the UK 2008 10-40GHz Spectrum auction deals with these problems by two
separate devices.
The first is that rather than simply ask bidders to produce an unfeasibly
long list of sealed bid valuations for packages, there is a preceding clock
phase to the auction. The progress of prices and bids during the clock phase
gives guidance to the bidders so that they are better able to gauge which
packages are likely to be of interest to them. In short, the clock phase is
designed to reduce the number of bids and to focus only on relevant ones.
The second is that rather than calculate prices according to the Vickrey
opportunity cost formula, this is modified to guarantee that the assignment
is in the core. Of all core assignments, the bidder optimal one is chosen. This
is supposed to guarantee ‘reasonable’ revenues given reported valuations.
So, the clock phase should help bidders to report most of the valuations
which are likely to be relevant and the Vickrey pricing modification should
13
14
See also, e.g. Day and Milgrom (2007).
Note however that Ofcom’s stated aim is to maximise efficiency rather than revenue.
19
help stop the revenues becoming too low (at some potentially troublesome
constellations of preferences).
There is a real sense in which these two objectives are in conflict. Helping bidders reduce the number of bids they need to make in addition to the
bids corresponding to the eventual assignment reduces the reported opportunity cost of that assignment. The problem–for revenue–arises when the
clock phase does its job too well and bidders jump from the end of the clock
phase to immediately reporting high valuations for packages which together
constitute a feasible assignment. This kills the opportunity cost of the assignment and notwithstanding the modified Vickrey rule can easily lead to
low revenues.
It is very instructive to compare the final clock bids with the highest
supplementary bids for each of the bidders.
Arqiva Arqiva made its highest supplementary bid, £1, 600K, for the same
package as it made its final clock phase bid on (0, 2, 0, 1, 0, 0, 0). Arqiva
also made a very near bid on a subset of this package, it bid £1, 599K
on the package (0, 2, 0, 0, 0, 0, 0) which is the one it was eventually
assigned.
BT BT bid its highest supplementary bid of £1, 001K for the same package as it made its final clock phase bid on (0, 0, 0, 0, 0, 1, 2). BT also
bid £1, 001K of hundreds of other packages including (0, 0, 0, 0, 0, 1, 0)
which it was eventually assigned.
Faultbasic Faultbasic bid £350K in the supplementary round on the package of its final clock phase bid (0, 0, 0, 0, 1, 0, 1). Its highest supplementary bid of £750K was for a subset (0, 0, 0, 0, 1, 0, 0) of this package.
Faultbasic was eventually assigned this subset.
MLL MLL ended the clock phase with zero eligibility but made its highest
supplementary bid of £250K on its final non null clock bid (0, 1, 0, 0, 0, 0, 0).
MLL also bid £250K on 10 other packages, including (0, 0, 0, 0, 0, 1, 1)
which it was eventually assigned.
Orange Orange made its maximum supplementary bid £2, 999, 999 on its
final clock phase package (0, 0, 0, 0, 0, 3, 0) but also bid the same amount
on the subset (0, 0, 0, 0, 0, 2, 0) which it was eventually assigned.
RedM RedM ended the clock phase with zero eligibility but made its
highest supplementary bid of £34K on its final non null clock bid
(0, 0, 0, 1, 0, 0, 0). RedM was eventually assigned this package.
20
T-Mobile T-Mobile made its maximum supplementary bid of £8.5m on
the same package as its final clock phase bid. T-Mobile was eventually
assigned this package.
Transfinite Transfinite only made one supplementary bid. This bid was
on the same package as its final clock phase bid and was in the same
amount–evidently a redundant bid.
UKBB UK Broadband terminated the clock phase with a bid of £151, 000
for the package (0, 0, 0, 0, 0, 0, 1) but made its highest supplementary
bid of £500, 001 for the package (0, 0, 0, 0, 0, 1, 1). Eventually, UK
Broadband was assigned the package (0, 0, 0, 0, 0, 0, 4) on which it had
made the bid £420, 000 during the clock phase15 .
To summarise, all but one of the bidders made their highest supplementary bid either on their final clock phase package, or on a subset of it. In
behaving in this way, bidders are clearly using the clock phase of the auction
to focus their attention on a selection of packages in a way consistent with
the philosophy of the auction design. Arguably, however, from the point of
view of revenue, bidders have ‘gone too far’ in this respect. It seems likely
that this bidding behaviour has lead to lower revenues than might have obtained, for example, in an ascending clock auction with pay as bid pricing.
In the auction this bidding behaviour was a feature both for bidders who
had a large proportion of effective bids (e.g. T-Mobile) and for those which
had a low proportion. In other words, the marked reduction in the number of effective bids displayed in figure 9 is likely to have exacerbated any
‘shortfall’ in revenue, but may not have been its root cause.
4.4
Efficiency
UK Spectrum awards are not designed to achieve maximum revenues, so the
low-revenue feature highlighted above is not necessarily a major issue in this
context.
The assignment seems to have been more stable than the prices in the
sense that the assignment appears to vary less in the various counterfactual
situations we have discussed so far. Compared to the putative assignment at
the end of the Clock Phase, the final assignment gives more spectrum to the
three bidders MLL, RedM and UK Broadband. This spectrum came at the
expense of Arqiva, BT and Orange who all bid the same or very nearly the
15
It is worth observing that Lot 7 finished the clock phase in excess supply.
21
same for subsets of their putative Clock Phase packages as proper subsets
of those packages. It is noticeable that the spectrum flows from bidders
who generally expressed high values to those who generally expressed low
values. One possibility is that the small bidders have found niches between
the expressed valuations of the large bidders which would not have been
present under the fuller expression of valuations which would have been
represented by a larger number of effective bids. However, this interpretation
is speculative. One suspects that the auction worked quite well in allowing
bidders who needed certain lots and valued them highly e.g. T-Mobile and
Orange to acquire the appropriate spectrum.
5
References
Ausubel, Lawrence M., Peter Cramton, and Paul Milgrom (2005) “Comments on Experimental Design for Evaluating FCC Spectrum Auction Alternatives”, 1 June, 2005http://wireless.fcc.gov/auctions/isas/Ausubel_et_al.pdf.
Ausubel, Lawrence M., Peter Cramton and Paul Milgrom, 2006, “The
Clock Proxy Auction: A Practicable Combinatorial Auction Design”, in
Cramton, Yoav, Shoham and Steinberg (Eds.), 2006.
Ausubel, Lawrence M., Peter Cramton and Paul Milgrom, 2006b, “The
Clock Proxy Auction: A Practicable Combinatorial Auction Design”, Presentation National Telecommunications and Information Administration Advanced Technology Forum, http://www.ntia.doc.gov/forums/2006/specman/ntia_cramton.pdf.
Cramton, Peter, Yoav, Shoham and Richard, Steinberg, 2006, Combinatorial Auctions, MIT Press.
Day, Robert W. and Paul Milgrom, 2007, “Core-Selecting Package Auctions”, to appear International Journal of Game Theory.
Day, Robert W. and S. Raghavan, 2007, “Fair Payments for Efficient
Allocations in Public Sector Combinatorial Auctions”, Management Science,
53(9), pp. 1389-1406.
Ofcom, The Wireless Telegraphy (Licence Award) (No.2), Regulations
2007.
Telecommunications Authority of Trinidad and Tobago, First Steps toward a Liberalised Telecommunications Sector, http://www.tatt.org.tt/auction.htm.
22