DA 03-1065

April 3, 2003

**AUCTION OF REGIONAL NARROWBAND PCS LICENSES**

**SCHEDULED FOR SEPTEMBER 24, 2003**

**COMMENT SOUGHT ON PACKAGE BIDDING PROCEDURES,**

**RESERVE PRICES OR MINIMUM OPENING BIDS, AND OTHER AUCTION PROCEDURES**

Report No. AUC-03‑51-A (Auction No. 51)

By this public notice, the Wireless Telecommunications Bureau ("Bureau")
announces the auction of six regional Personal Communications Service
(PCS) licenses in the 900 MHz band ("narrowband PCS") scheduled to
commence on September 24, 2003 ("Auction No. 51"). These licenses were
previously included as part of the inventory for Auction No. 50.[^1] The
one comment that the Bureau received in response to the *Auction No. 50
Comment Public Notice* stated that the regional licenses are uniquely
complimentary and proposed a combinatorial (package bidding)
auction.[^2] The commenter noted that these regional licenses
effectively constitute a nationwide license and suggested that they
would be more highly valued as a combined package by prospective auction
participants intending to deploy nationwide service.[^3] After
consideration of the issues raised by the comments, the Bureau
determined that it may be appropriate to use package bidding for the
regional licenses. Accordingly, the Bureau removed the six regional
licenses from the Auction No. 50 inventory and announced that they would
be included in Auction No. 51.[^4]

The following table describes the licenses that will be included in
Auction No. 51:

  ------------ ----------- ----------------- --------------------------- -------------
  **Region**   **Channel   **Channel         **Frequency Bands (MHz)**   **Bandwidth
               Number**    Description**                                 (kHz)**

  Northeast    17          12.5 kHz/50 kHz   901.8250--901.8375,         62.5
                           paired            930.70--930.75              

  South        16          12.5 kHz/50 kHz   901.8125--901.8250,         62.5
                           paired            930.65--930.70              

  South        17          12.5 kHz/50 kHz   901.8250--901.8375,         62.5
                           paired            930.70--930.75              

  Midwest      17          12.5 kHz/50 kHz   901.8250--901.8375,         62.5
                           paired            930.70--930.75              

  Central      17          12.5 kHz/50 kHz   901.8250--901.8375,         62.5
                           paired            930.70--930.75              

  West         17          12.5 kHz/50 kHz   901.8250--901.8375,         62.5
                           paired            930.70--930.75              
  ------------ ----------- ----------------- --------------------------- -------------

The Balanced Budget Act of 1997 requires the Commission to "ensure that,
in the scheduling of any competitive bidding under this subsection, an
adequate period is allowed . . . before issuance of bidding rules, to
permit notice and comment on proposed auction procedures . . . ."[^5]
Consistent with the provisions of the Balanced Budget Act and to ensure
that potential bidders have adequate time to familiarize themselves with
the specific rules that will govern the day-to-day conduct of an
auction, the Commission directed the Bureau, under its existing
delegated authority,[^6] to seek comment on a variety of
auction-specific procedures prior to the start of each auction.[^7] We
therefore seek comment on the proposed Auction No. 51 procedures[^8] as
set forth in sections following the "Introduction to Package Bidding,"
below.

# Introduction to Package Bidding

"Package bidding" refers to an auction design in which bidders may place
bids on groups, or *packages*, of licenses. A bid on a package is an
all-or-nothing bid for all of the licenses in that package. This is a
departure from the Bureau's usual simultaneous multiple-round (SMR)
design, in which bidders only have the ability to submit individual bids
for each license. Like our existing SMR design, our current
implementation of package bidding uses a simultaneous multiple-round
design.[^9] In addition to submitting bids on packages, bidders may also
submit bids on individual licenses.

## License Complementarities

Under certain circumstances, package bidding may be desirable for
bidders that wish to aggregate licenses. Bidders have aggregated
licenses under our SMR auction design. However, package bidding may be
appropriate when bidders have strong and divergent *complementarities*
among licenses, and when package bidding rules do not introduce other
undue difficulties.[^10] Complementarities exist when the value of the
whole is greater than the sum of the parts. In the context of spectrum
auctions, complementarities could result in a bidder being willing to
pay more for two licenses together than the sum of the amounts it would
be willing to pay for either license individually. That is, a bidder
willing to pay \$1 million for a license covering Washington, D.C., or
\$1 million for a license covering Baltimore, Maryland, would be willing
to pay more than \$2 million for both licenses together.

Divergent complementarities exist when the patterns of complementarities
are different for different bidders. For example, if one bidder has
complementarities for a geographic aggregation and another bidder has
complementarities for a bandwidth aggregation, then either of these
bidders achieving its desired aggregation would prevent the other bidder
from doing so. That is, if there are two licenses available in each of
two markets, a bidder successfully aggregating both licenses in one
market (bandwidth aggregation) precludes another bidder from aggregating
one license in each market (geographic aggregation).

## Exposure Problem

The *exposure problem* is a financial risk that occurs when a bidder, in
hopes of also winning complementary items, bids more for a single object
than the object alone is worth to that bidder. Package bidding allows
bidders to mitigate the exposure problem by placing all-or-nothing bids
on packages of licenses.[^11]

The following builds upon the previous example of a bidder willing to
pay \$1 million for a license covering Washington, D.C., or \$1 million
for a license covering Baltimore, Maryland, but willing to pay more than
\$2 million for both licenses together. For purposes of this
explanation, assume that the bidder is willing to pay \$3 million for
both licenses together.

In an SMR auction in which bids are submitted on individual licenses,
the bidder would clearly be willing to bid \$1 million for each of the
Washington and Baltimore licenses, for a total of \$2 million. If the
auction price of one of those licenses exceeds \$1 million, the bidder
faces a dilemma. The bidder can stop bidding for a license when the
license price exceeds what the bidder is willing to pay for that license
alone, **or the bidder can keep bidding in hopes of winning both
licenses**. This exposes the bidder to a financial risk. On the one
hand, if the bidder wins both licenses by bidding \$1 million for
Washington and \$1.5 million for Baltimore, it will pay a total of \$2.5
million for both licenses, which is less than the \$3 million it is
willing to pay for both licenses together. Thus, the bidder would be
satisfied with its decision to bid \$1.5 million for the Baltimore
license even though that license alone is only worth \$1 million to the
bidder. On the other hand, if the bidder bids \$1.5 million for the
Baltimore license (again, in hopes of winning both licenses) but wins
only that license and not the Washington license as well, the bidder
would have to pay more for the Baltimore license than the license is
worth to the bidder.

In a package bidding auction, the bidder in the above example could
submit package bids to avoid such a risk. The bidder could create a
package of the Washington and Baltimore licenses and submit a bid for
the package. The bidder would either win the package --- *i.e.*, both
licenses --- at the amount it bid for the package, or it would not win
the package. By placing a bid on a package, the bidder would not have to
worry about the possibility of only winning part of the package. That
is, the bidder could bid up to \$3 million for the package and thereby
express what it is willing to pay not only for the licenses but also for
the complementarity of the licenses.

## Threshold Problem

Allowing package bidding potentially introduces a *threshold problem*
--- the difficulty that multiple bidders for the single licenses (or
smaller packages) that constitute a larger package may have in
outbidding a single bidder on the larger package, even though the
multiple bidders may value the sum of the parts more than the single
bidder values the whole. This may occur because bidders for parts of a
larger package each have an incentive to hold back in the hope that a
bidder for another part will increase its bid sufficiently for the bids
on the pieces collectively to beat the bid on the larger package. The
package bidding procedures that we propose are designed to facilitate
the emergence of bids that will overcome this problem. Specifically, we
propose to allow bids on licenses and packages that individually are not
high enough to enter immediately into the provisionally winning set.
This allowance is meant to facilitate price discovery and diminish the
threshold problem. Effectively, bidders can take "baby steps" toward
getting into the provisionally winning set. Additionally, under these
proposed package bidding procedures, the auction will close after two
consecutive rounds with no new bids. Thus, after a round with no new
bids, bidders will be notified that if no new bids are placed in the
subsequent round, the auction will close.

## Other Package Bidding Highlights

Implementing package bidding requires changes in some of the procedures
used in the Bureau's SMR auctions. Some of the main differences are
introduced in this section in order to highlight the differences between
the Bureau's proposed package bidding procedures for Auction No. 51 and
the Bureau's SMR auction procedures. Later in this public notice, in the
"Auction Structure" and "Bidding Procedures" sections, the Bureau seeks
comment on the package bidding procedures for Auction No. 51.

### Provisionally Winning Bids

In an SMR auction it is a simple matter to determine high bids. At the
end of a bidding round, the high bids are determined based on the
highest gross bid amount received for each license. A high bid from a
previous round is sometimes referred to as a "standing high bid." A
"standing high bid" remains the high bid until there is a higher bid on
the same license at the close of a subsequent round.

In a package bidding auction, *provisionally winning bids* are similar
to standing high bids. Provisionally winning bids are the set of bids
that maximizes revenue at the end of a particular round. The set of
provisionally winning bids cannot include overlapping bids; each license
may be assigned only once. In the event of tied bids or tied sets of
bids, ties are broken randomly. The set of provisionally winning bids
may, of course, include package bids as well as individual license bids.

Unlike in an SMR auction, a provisionally winning bid does not
necessarily remain a provisional winner until there is a higher bid on
the same license or package at the close of a subsequent round. That is,
a bid on a license that is a provisionally winning bid at the end of a
round might not be a provisionally winning bid at the end of a
subsequent round even if no other bids are received for that license.
Determining the provisionally winning bids in a package bidding auction
is more complex than determining the standing high bids in an SMR
auction. In a package bidding auction, whether a bid is a provisional
winner depends on both the amount of the bid and the amount of revenue
generated in the auction when that bid is combined with other bids
submitted in the auction. With package bidding it is possible that,
because of an increase in the bids submitted by one or more other
bidders, a previous round's provisionally winning bid may cease to be a
provisional winner in a subsequent round even though no higher bid has
been placed on that license or package. In a package bidding auction,
competing bids for a license or package consist of not only other bids
for the same license or package, but also bids on packages that include
any of the same licenses. Moreover, because of this, a bid that is not a
provisionally winning bid at the end of a given round could become a
provisionally winning bid at the end of a subsequent round. This is
explained further in the following section.

### All Bids Considered

Under the Bureau's proposed package bidding procedures, all bids placed
in an auction are considered throughout the course of the auction. This
is in contrast with the SMR procedures under which, at the conclusion of
a round, only new bids placed in that round and standing high bids are
considered. Bidders in a package bidding auction must therefore be
mindful that even if a bid did not become a provisional winner when
placed, it could become a provisionally winning bid later in the
auction.

The following table portrays the six licenses available in Auction No.
51.

+-----------+-----------+-----------+-----------+-----------+-----------+
| Channel   | Region    |           |           |           |           |
+-----------+-----------+-----------+-----------+-----------+-----------+
|           | West      | Central   | Midwest   | South     | Northeast |
+-----------+-----------+-----------+-----------+-----------+-----------+
| 16        |           |           |           | CN-       |           |
|           |           |           |           | RPC002-16 |           |
|           |           |           |           |           |           |
|           |           |           |           | (         |           |
|           |           |           |           | South-16) |           |
+-----------+-----------+-----------+-----------+-----------+-----------+
| 17        | CN-       | CN-       | CN-       | CN-       | CN-       |
|           | RPC005-17 | RPC004-17 | RPC003-17 | RPC002-17 | RPC001-17 |
|           |           |           |           |           |           |
|           | (West-17) | (Ce       | (Mi       | (         | (Nort     |
|           |           | ntral-17) | dwest-17) | South-17) | heast-17) |
+-----------+-----------+-----------+-----------+-----------+-----------+

For purposes of this example, assume that bidders place the following
bids in a round: \$50,000 for each of the six licenses and \$200,000 for
the package South-16/South-17/Northeast-17 (the northeast region license
and both licenses in the south region). The resulting provisionally
winning bids following the round would be as follows (the individual
license bids of \$50,000 for each of South-16, South-17 and Northeast-17
are not provisionally winning bids and are not shown):

  ----------- ----------- ----------- ----------- ----------- -----------
  Channel     Region                                          

              West        Central     Midwest     South       Northeast

  16                                                          

  17          \$50,000    \$50,000    \$50,000    \$200,000   
  ----------- ----------- ----------- ----------- ----------- -----------

Total revenue = \$350,000

Next, assume that a bidder places a bid of \$160,000 for the package
South-16/South-17 (both licenses in the south region) in the next round,
and no other new bids are placed.

  ----------- ----------- ----------- ----------- ----------- -----------
  Channel     Region                                          

              West        Central     Midwest     South       Northeast

  16                                              \$160,000   

  17                                                          
  ----------- ----------- ----------- ----------- ----------- -----------

Then, the provisionally winning bids following that round would be as
follows:

  ----------- ----------- ----------- ----------- ----------- --------------
  Channel     Region                                          

              West        Central     Midwest     South       Northeast

  16                                              \$160,000   

  17          \$50,000    \$50,000    \$50,000                **\$50,000**
  ----------- ----------- ----------- ----------- ----------- --------------

Total revenue = \$360,000

Note that in this example the bid of \$50,000 for the northeast region
license was not a provisionally winning bid after the first round but
became a provisionally winning bid after the next round. The new bid of
\$160,000 for package of both licenses in the south region, when
considered with the previous \$50,000 bid for the northeast region
license, was able to beat the previous \$200,000 bid for the package of
the northeast region license and both licenses in the south region.

Considering bids from all rounds allows more potential combinations of
bids, and therefore, potentially greater flexibility for bidders to
submit bids that may become part of the provisionally winning set. As in
the example above, it helps ensure that bids on single licenses or small
packages can combine with other bids to become winners, even when a
different combination of bids has comprised the provisionally winning
set for a number of rounds. Considering bids from all prior rounds also
permits the bids of bidders no longer eligible to participate in the
auction to become part of the provisionally winning set when that is the
most economically efficient outcome. Moreover, considering all bids
throughout the auction encourages sincere bidding.

### Mutually Exclusive Rounds

As explained in the previous section, all bids placed throughout the
course of the auction are considered when determining the winning bids.
However, the proposed procedures restrict **how** the bids are
considered. Bids placed by a bidder in one round are considered mutually
exclusive of that bidder's bids placed in all other rounds. If a bidder
places a bid for one license in one round and for another license in
another round, one bid or the other could be a provisionally winning
bid, but not both at the same time. Likewise, if a bidder places several
bids in one round and several bids in another round, any or all of the
bids from one round or the other could be provisionally winning bids,
but not bids from both rounds at the same time.

Using the example from the previous section, assume that in the first
round of the example the \$50,000 bid for each of the six licenses was
placed by Bidder 1 and the \$200,000 bid for the package of the
northeast region license and both licenses in the south region was
placed by Bidder 2. In the next round of the example, the bid of
\$160,000 for the package of both licenses in the south region was
placed by Bidder 1. Under these assumptions, the provisionally winning
bids at the end of the second round could include Bidder 1's bids from
one round or the other, but not both --- *i.e.*, any or all of Bidder
1's \$50,000 bids for each of the six licenses from the first round, or
Bidder 1's bid of \$160,000 for the package of both licenses in the
south region from the second round. Since the choice of Bidder 1's bids
in the first round achieves greater revenue, the provisionally winning
bids after the second round would remain the same as after the first
round:

  ----------- ----------- ----------- ----------- ----------- -----------
  Channel     Region                                          

              West        Central     Midwest     South       Northeast

  16                                                          

  17          \$50,000    \$50,000    \$50,000    \$200,000   

                                                              

              Bidder 1                            Bidder 2    
  ----------- ----------- ----------- ----------- ----------- -----------

Total revenue = \$350,000

This treatment of bids as mutually exclusive across rounds is done on a
per bidder basis. The provisionally winning bids could include Bidder
1's bids from one round and Bidder 2's bids from a different round.

This mutually exclusive treatment of bids --- for each bidder, allowing
its bids from only one round to become provisionally winning bids ---
allows bidders to mind budget constraints and to pursue backup
strategies. For example, if a bidder wants the license in the west
region or the license in the central region but not both, the bidder
could place a bid for one of the licenses in one round and a bid for the
other license in the next round. Because the bids are considered
mutually exclusive, only one could become a provisionally winning bid.

### Renewing Bids

The proposed procedures include bid renewal to provide a mechanism that
bidders can use so that their bids from different rounds are not
considered mutually exclusive. For example, assume a bidder places a bid
for the west region license in one round. In the following round, the
bidder places a bid for the central region license and renews its bid on
the west region license. Then, after that round, either bid or both
could become a provisionally winning bid.

This concludes the "Introduction to Package Bidding." In the following
"Auction Structure" and "Bidding Procedures," sections, the Bureau seeks
comment on the specific package bidding procedures for Auction No. 51.

# Auction Structure

##  Simultaneous Multiple Round with Package Bidding

The Bureau proposes to award all licenses included in Auction No. 51 in
a simultaneous multiple-round with package bidding (SMR-PB) auction.
This methodology offers every license for bid at the same time with
successive bidding rounds in which bidders may place bids. Bidders will
be able to submit bids on individual licenses, as in our simultaneous
multiple round auction design, but may also submit all-or-nothing bids
on packages of licenses. We seek comment on this proposal.

## Upfront Payments and Initial Maximum Eligibility

The Bureau has delegated authority and discretion to determine an
appropriate upfront payment for each license being auctioned.[^12]
Upfront payments related to the specific spectrum subject to auction
protect against frivolous or insincere bidding and provide the
Commission with a source of funds from which to collect payments owed at
the close of the auction.[^13] The total upfront payment does not affect
the dollar amount a bidder may bid on licenses.

For Auction No. 51 we propose to calculate upfront payments on a
license-by-license basis using the following formula:

> \$.00001 \* kHz \* License Area Population,[^14] rounded.[^15]

We seek comment on this proposal.

The amount of the upfront payment submitted by a bidder will determine
the initial maximum eligibility (as measured in bidding units) for each
bidder. Each license is assigned a specific number of bidding units
equal to the upfront payment, on a bidding unit per dollar basis. This
number does not change during the auction. A bidder's upfront payment is
not attributed to specific licenses or packages. Rather, a bidder may
place bids on licenses and packages as long as the total number of
bidding units associated with those licenses and packages does not
exceed the bidder's eligibility.[^16] For a package, we propose to
calculate the bidding units by adding together the bidding units of the
individual licenses that make up the package. Eligibility cannot be
increased during the auction. Thus, in calculating its upfront payment
amount, an applicant should determine the **maximum** number of bidding
units (either individually or in a package) it may wish to bid on in any
single round and submit an upfront payment covering that number of
bidding units. We seek comment on this proposal.

We list the proposed bidding units and upfront payments for all licenses
in Attachment A.

## Activity and Eligibility Rules

In order to ensure that the auction closes within a reasonable period of
time, an activity rule provides incentives for bidders to participate
throughout the auction. The activity rule requires each bidder to have
active bids in each round that account for a specified fraction of the
bidder's current eligibility, as measured in bidding units. A bidder
that does not satisfy the activity rule will either use an activity rule
waiver (if any remain) or lose bidding eligibility for the next round.
Losing eligibility matters to bidders because a bidder's bidding
activity cannot exceed its current eligibility.

### Measuring Activity

In SMR auctions, a bidder's activity in a round is determined by adding
the bidding units associated with licenses on which the bidder is
active. A bidder is considered active on a license in the current round
of an SMR auction if it is either the high bidder at the end of the
previous bidding round (and did not withdraw the high bid in the current
round), or if it submits a bid in the current round (and does not
subsequently remove the bid). In a package bidding auction, calculating
activity levels in a round is not as simple because a bidder can submit
bids on different packages that contain one or more of the same
licenses. To illustrate this, suppose a bidder submits bids on the
following packages in round *t*:

+---------------------------------------+------------------------------+
| **Package/Licenses**                  | **Bidding Units**            |
+---------------------------------------+------------------------------+
| Package A:                            | 76,000 bu                    |
|                                       |                              |
| South-16 (38,000 bu)                  |                              |
|                                       |                              |
| South-17 (38,000 bu)                  |                              |
+---------------------------------------+------------------------------+
| Package B:                            | 108,000 bu                   |
|                                       |                              |
| Northeast-17 (34,000 bu)              |                              |
|                                       |                              |
| South-17 (38,000 bu)                  |                              |
|                                       |                              |
| Central-17 (36,000 bu)                |                              |
+---------------------------------------+------------------------------+

For Auction No. 51, we propose to measure a bidder's *bidding activity*
in a round as the maximum number of bidding units the bidder can win
considering new bids placed and provisionally winning bids renewed in
that round. Thus, when a bidder submits bids in a round the FCC
Automated Auction System will determine the set of bids, among the
bidder's new bids and renewed provisionally winning bids, that contains
the most bidding units and has no overlap among the licenses. For
instance, in the example above, the two bids contain four distinct
licenses. The sum of the bidding units associated with these four
licenses is 146,000. However, since both packages contain license
South-17, this bidder cannot win both packages at the same time. Under
our proposal the maximum number of bidding units that the bidder can win
is the 108,000 associated with Package B, so the bidder's bidding
activity is 108,000 bidding units. We seek comment on this proposal.

A bidder is also considered to be active if the bidder has provisionally
winning bids from the previous round. A bidder's bids made in different
rounds will be considered mutually exclusive, so the bidding units
associated with provisionally winning bids must be viewed independently
from the bidding units associated with current round bids. We propose to
define a bidder's *eligibility activity* in a round as the greater of
(i) its bidding activity in the round and (ii) the bidding units
associated with the bidder's provisionally winning bids from the prior
round. To illustrate how eligibility activity will be calculated in a
round we continue with our example. Suppose this bidder has
provisionally winning bids on the following licenses from round *t-1:*

  ------------------------------- ---------------------------------------
  **License**                     **Bidding Units**

  South-16                        38,000 bu

  South-17                        38,000 bu
  ------------------------------- ---------------------------------------

The number of bidding units associated with this bidder's provisionally
winning bids is 76,000. Recall that the bidder's bidding activity for
the round is 108,000 bidding units. The eligibility activity for this
bidder in round *t* is therefore 108,000, the greater of its bidding
activity (108,000 bidding units) and the bidding units associated with
its bids in the provisionally winning set (76,000 bidding units).

### Activity Requirement

For Auction No. 51, we propose that, in each round of the auction, a
bidder desiring to maintain its current eligibility would be required to
have eligibility activity equal to sixty percent (three-fifths) of its
current eligibility. For a bidder that failed to meet the activity
requirement in a given round, the Automated Auction System would reduce
the bidder's eligibility for the next round to five-thirds times its
eligibility activity in the current round.[^17] Thus, a bidder's
eligibility in the current round is equal to either its eligibility in
the previous round (bidder met the activity requirement) or five-thirds
of its eligibility activity in the previous round (bidder did not meet
the activity requirement), whichever is less:

Eligibility (t) = Min (Eligibility (t-1), 5/3\*Eligibility Activity
(t-1))

Activity rule waivers provide an exception to this rule and are
discussed in the next section, "Activity Rule Waivers and Reducing
Eligibility."

In addition, we propose to retain the discretion to increase to eighty
percent (four-fifths) the proportion of bidding units on which bidders
must be active to retain their current eligibility. Any such change will
be announced to bidders prior to the beginning of the round in which the
change takes effect. We seek comment on these proposals. Commenters that
believe these activity rules should be modified should explain their
reasoning and comment on the desirability of an alternative approach.
Commenters are advised to support their claims with analyses and
suggested alternative activity rules.

### Activity Rule Waivers and Reducing Eligibility 

For Auction No. 51, we propose that each bidder be provided with five
activity rule waivers that may be used at the bidder's discretion during
the course of the auction as set forth below. Use of an activity rule
waiver preserves the bidder's current bidding eligibility despite the
bidder's eligibility activity in the current round being below the
required minimum level. An activity rule waiver applies to an entire
round of bidding and not to a particular license or package. Activity
rule waivers are principally a mechanism for auction participants to
avoid the loss of auction eligibility in the event that exigent
circumstances prevent them from placing a bid in a particular round.

The Automated Auction System assumes that bidders with insufficient
eligibility activity would prefer to use an activity rule waiver (if
available) rather than lose bidding eligibility. Therefore, the system
will automatically apply a waiver (known as an "automatic waiver") at
the end of any bidding round in which a bidder's eligibility activity is
below the activity requirement unless: (1) the bidder has no activity
rule waivers remaining; or (2) the bidder overrides the automatic
application of a waiver by reducing eligibility, thereby meeting the
minimum requirements. **Note: If a bidder has no waivers remaining and
does not satisfy the activity requirement, its current eligibility will
be permanently reduced, possibly eliminating the bidder from further
bidding in the auction.**

A bidder with insufficient eligibility activity may wish to reduce its
bidding eligibility rather than use an activity rule waiver. If so, the
bidder must affirmatively override the automatic waiver mechanism during
the bidding period by using the "reduce eligibility" function in the
bidding system. In this case, the bidder's eligibility is permanently
reduced to bring the bidder into compliance with the activity rules as
described in the previous section. Once eligibility has been reduced, a
bidder will not be permitted to regain its lost bidding eligibility.

The activity rule waivers described above are automatic waivers. Under
the Bureau's SMR auction design, bidders can submit automatic or
proactive waivers. Unlike automatic waivers, proactive waivers keep the
auction open absent other bidding activity. We propose not to allow
bidders to submit proactive waivers in the context of package bidding
for Auction No. 51. As part of the package bidding design for Auction
No. 51 we are proposing a two-round simultaneous stopping rule, in which
the bidding on all licenses remains open until the second consecutive
round in which no new bids are placed. After the second consecutive such
round, bidding closes simultaneously on all licenses.[^18] The two-round
stopping rule affords bidders some additional time to consider their
current status, and eliminates the need for bidders to use a proactive
activity rule waiver to prevent the auction from closing in the current
round. We seek comment on this proposal.

## Information Relating to Auction Delay, Suspension, or Cancellation

For Auction No. 51, we propose that, by public notice or by announcement
during the auction, the Bureau may delay, suspend, or cancel the auction
in the event of natural disaster, technical obstacle, evidence of an
auction security breach, unlawful bidding activity, administrative or
weather necessity, or for any other reason that affects the fair and
efficient conduct of competitive bidding.[^19] In such cases, the
Bureau, in its sole discretion, may elect to resume the auction starting
from the beginning of the current round, resume the auction starting
from some previous round, or cancel the auction in its entirety. Network
interruption may cause the Bureau to delay or suspend the auction. We
emphasize that exercise of this authority is solely within the
discretion of the Bureau, and its use is not intended to be a substitute
for situations in which bidders may wish to apply their activity rule
waivers. We seek comment on this proposal.

# Bidding Procedures

## Round Structure

The Commission will conduct this auction over the Internet. Telephonic
Bidding will also be available, and the FCC Wide Area Network will be
available as well.

The initial bidding schedule will be announced in a public notice
listing the qualified bidders, which is released approximately 10 days
before the start of the auction. The package bidding format will consist
of sequential bidding rounds, each followed by the release of round
results. Details regarding the location and format of round results will
also be included in a subsequent public notice.

The Bureau has discretion to change the bidding schedule in order to
foster an auction pace that reasonably balances speed with the bidders'
need to study round results and adjust their bidding strategies. The
Bureau may increase or decrease the amount of time for the bidding
rounds and review periods, or the number of rounds per day, depending
upon the bidding activity level and other factors. We seek comment on
this proposal.

## Reserve Price or Minimum Opening Bid 

The Balanced Budget Act calls upon the Commission to prescribe methods
for establishing a reasonable reserve price or a minimum opening bid
when FCC licenses are subject to auction, unless the Commission
determines that a reserve price or minimum opening bid is not in the
public interest.[^20] Consistent with this mandate, the Commission has
directed the Bureau to seek comment on the use of a minimum opening bid
and/or reserve price prior to the start of each auction.[^21]

Normally, a reserve price is an absolute minimum price below which an
item will not be sold in a given auction. Reserve prices can be either
published or unpublished. A minimum opening bid, on the other hand, is
the minimum bid price set at the beginning of the auction below which no
bids are accepted. It is generally used to accelerate the competitive
bidding process. Also, the auctioneer often has the discretion to lower
the minimum opening bid amount later in the auction. It is also possible
for the minimum opening bid and the reserve price to be the same amount.

In light of the Balanced Budget Act's requirements, the Bureau proposes
to establish minimum opening bids for Auction No. 51. The Bureau
believes a minimum opening bid, which has been used in other auctions,
is an effective bidding tool.[^22]

Specifically, for Auction No. 51, the Commission proposes the following
license-by-license formula for calculating minimum opening bids:

> \$.00001 \* kHz \* License Area Population,[^23] rounded.[^24]

For a package, we propose to calculate the minimum opening bid by adding
together the minimum opening bids of the individual licenses that make
up the package. We list the proposed minimum opening bids for all
licenses in Attachment A. We seek comment on this proposal.

## Packages

The Bureau proposes that, in addition to bidding on individual licenses,
bidders be permitted to create and bid on up to twelve different
packages of their own choosing during the course of the auction. Bidders
will not be required to identify or create their packages before the
start of the auction, but may create their packages as the auction
progresses.[^25] A bidder may modify or delete a package it has created
up until the point where it has bid on the package and the round has
closed. If the bidder submits a bid on a package and subsequently
removes the bid during the same round, the bidder has the option of also
deleting or modifying the package. However, once a bidder bids on a
package and the round closes, the package may not be modified or deleted
and counts as one of the bidder's twelve allowable packages. A bid on an
individual license does not count as a bid on a package; packages
consist of two or more licenses. We seek comment on this proposal.

## Winning and Provisionally Winning Bids 

*Winning bids* in a package bidding auction are the set of "consistent"
bids (non-overlapping, and for each winning bidder, only bids made or
renewed in the same round) on individual licenses and packages that
maximizes total revenue when the auction closes.[^26] *Provisionally
winning bids* are the set of consistent bids that maximizes total
revenue in a particular round (they would win if the auction were to
close in that round), assigning each license to either a bidder or the
FCC. When determining winning and provisionally winning bids, all bids
made in every round throughout the course of the auction (except for
bids that are placed and subsequently removed during the same round)
will be considered. In addition, each license is treated as having a bid
placed by the FCC at \$1000 less than the minimum opening bid. This
procedure will ensure that a bid on a license or package at the minimum
opening bid always beats the FCC bid.[^27]

Since there can be more than one set of consistent bids that produces
the maximum revenue, we propose to use a procedure that randomly selects
among these tied sets when determining the provisionally winning bids.
This tie breaking procedure involves two steps: (1) the assignment of a
*selection number* to each bid,[^28] and (2) the determination of, among
all tied bid sets, the set that produces the *maximum sum of selection
numbers*. We seek comment on this proposal.

A bid's *selection number* is the sum of *n* pseudo-random numbers where
*n* is the number of licenses comprising the bid's package. A bid's
selection number will be included in the publicly-available round
results released after each round.

Once the selection numbers have been generated for each bid, the second
step of the tie breaking procedure will decide the provisionally winning
bids. Computer software is used to determine, among all tied bid sets,
the set that produces the maximum sum of selection numbers.[^29] Thus,
the set of provisionally winning bids is the set of consistent bids that
maximizes revenue and maximizes the sum of selection numbers. Each bid
will be assigned a new selection number in every round. Consequently, if
there are ties, the set of provisionally winning bids may change even
after a round in which there are no new bids. The solver will not be run
after the last round of the auction, so that the winning set is the same
as the set of provisional winners generated after the next-to-the-last
round (*i.e.*, there won't be any surprise winners).

Please note that it is possible that a provisionally winning bid might
not be the highest bid on the particular license or package. This
possibility is primarily due to each bidder's bids being considered
mutually exclusive across rounds. For example, if one bidder has placed
the highest bid on each of two different licenses in two different
rounds (and did not renew the earlier of the two bids), then those two
bids are considered as mutually exclusive and only one of them can be a
provisionally-winning bid.

## Minimum Acceptable Bids and Bid Increments

The Bureau proposes that in each round, eligible bidders will be able to
place bids on a given license or package in any of nine different
amounts.[^30] The Automated Auction System interface will list the nine
acceptable bid amounts for each license and package. In the first round
of the auction, the minimum acceptable bid for a license or package will
be equal to its minimum opening bid. The Bureau proposes that in all
subsequent rounds, the minimum acceptable bid for a license or package
will be the greatest of: (i) the minimum opening bid; (ii) the bidder's
own previous high bid on a license or package plus *x%*, where the
Bureau will specify the value of *x* in each round; and (iii) the
*current price estimate* of the license plus *z%*, or for a package, the
sum of the current price estimates for the licenses in the package plus
*z%*, where the Bureau will specify the value of *z* in each round.

Current price estimates are estimates of the prices of the individual
licenses being auctioned. The estimates take into account the minimum
opening bids for the licenses as well as all the bids placed in the
auction and, therefore, reflect all available information that has been
revealed in the auction about the relative demands for the licenses.
Current price estimates for the component licenses of a package that is
provisionally winning are constrained to sum to the provisionally
winning bid for the package. These estimates are generated during round
results following every round of the auction as part of the mathematical
optimization process used by the Bureau to determine the provisionally
winning bids. The precise methodology used to calculate current price
estimates is described in Attachment B. Until a bid is placed on a
license or on a package containing that license, by any bidder in any
round, the current price estimate is the FCC bid amount.

The Bureau proposes to retain an exception to part (iii) for calculating
the minimum acceptable bid for a "global" package --- a package
consisting of all six of the licenses available in the auction. After
the first round of the auction, part (iii) of the minimum acceptable bid
rule for a global package will always be the revenue generated by the
provisionally winning bid set in the previous round plus *w%*. The
Bureau makes this distinction in order to retain the ability to ensure
that bids for the global package will continue to increase even if we
employ a percentage *z* that does not guarantee that outcome.

The result of the minimum acceptable bid calculation will be rounded
using our standard rounding procedure.[^31] Initially, the Bureau
proposes to set *x* at ten, *z* at five and *w* at five, but retains the
discretion to adjust these variables during the course of the auction.

For bids higher than the minimum acceptable bid --- *i.e.*,
multi-increment bids --- we propose to define the amount of the
additional bid increments as *v%* of the minimum acceptable bid, where
the minimum acceptable bid is determined as discussed above. Initially,
the Bureau proposed to set *v* at ten, but proposes to retain the
discretion to adjust the amount during the course of the auction. Thus,
when *v* equals ten, a bidder will be able to place multi-increment bids
of the minimum acceptable bid plus approximately 10%, 20%, etc. with the
maximum bid being approximately equal to the minimum acceptable bid plus
80%.

The Bureau retains the discretion to change minimum acceptable bids, and
to do so on a license-by-license and package-by-package basis, if
circumstances so dictate. The Bureau will do so by announcement in the
Automated Auction System.[^32] We seek comment on these proposals.

## Last and Best Bids

We propose to allow bidders that wish to drop out of the auction or that
believe they are about to lose their bidding eligibility to have an
opportunity before they drop out to place up to two mutually exclusive
sets of "last and best" bids on any licenses or packages for which they
remain eligible. This is a limited exception to minimum acceptable bids
and to click-box bidding. Such bids may be of any amount (in thousand
dollar increments) between the bidder's previous high bid on the license
or package and the amount of the highest acceptable bid for the license
or package in the current round (the eighth increment above the minimum
acceptable bid).[^33] If a bidder chooses this option, it will not be
permitted to make any further bids during the auction. We seek comment
on this proposal.

## Renewed Bids

Without regard to the minimum acceptable bid requirement, we propose to
allow a bidder to "renew" in the current round the highest previous bid
it made on any license or package; that is, it may resubmit the bid
without increasing the amount bid. No eligibility activity or bidding
activity is conferred for renewing a non-provisionally winning bid.
Renewed provisionally winning bids confer bidding activity (non-renewed
provisionally winning bids count toward eligibility activity). Renewed
bids will be treated as being made in the current round.

Renewals provide bidders a means to ensure that bids from previous
rounds are considered *in addition to* the bids placed in the current
round. Otherwise, bids made in different rounds are treated as mutually
exclusive, so that the bidder may win some or all of the bids from the
current round, or a previous round, but not both. We seek comment on
this proposal.

## Information Regarding Bid Removal and Bid Withdrawal

For Auction No. 51, the Bureau proposes the following bid removal
procedures. Before the close of a bidding period, a bidder has the
option of removing any bid placed in that round. By removing selected
bids in the bidding system, a bidder may effectively "unsubmit" any bid
placed within that round. A bidder removing a bid placed in the same
round is not subject to a withdrawal payment. Once a round closes, a
bidder may no longer remove a bid.

The Bureau proposes for Auction No. 51 that bidders not be permitted, in
any round, to withdraw bids made in previous rounds. With the
implementation of package bidding, bidders should not face exposure
risks as they might in a simultaneous multiple round auction design. Bid
withdrawal was designed to allow bidders to back out of failed
aggregations --- to avoid winning some licenses that are worth little to
them without the others they need to implement their business plan.
Therefore, to the extent that bids are allowed on all packages of
licenses with significant complementarities, the use of withdrawals to
mitigate such risk is no longer necessary. We seek comment on this
proposal.

## Stopping Rule

The Bureau has discretion "to establish stopping rules before or during
multiple round auctions in order to terminate the auction within a
reasonable time."[^34] For Auction No. 51 the Bureau proposes to employ
a two-round simultaneous stopping rule. A two-round simultaneous
stopping rule means that all licenses remain open until two consecutive
rounds have occurred in which no new bids are received. After the second
consecutive such round, bidding closes simultaneously on all licenses.
Thus, unless circumstances dictate otherwise, bidding would remain open
on all licenses until bidding stops on every license. Renewed bids are
not considered new bids for purposes of the stopping rule; in other
words, a round in which the only bids that are placed are renewed bids
is considered a round with no new bids for purposes of the stopping
rule. Last and best bids are considered new bids for purposes of the
stopping rule. We seek comment on this proposal.

The Bureau proposes to reserve the right to declare that the auction
will end after a specified number of additional rounds ("special
stopping rule"). The Bureau proposes to exercise this option only in
certain circumstances, such as, for example, where the auction is
proceeding very slowly, there is minimal overall bidding activity, or it
appears likely that the auction will not close within a reasonable
period of time. Before exercising this option, the Bureau is likely to
attempt to increase the pace of the auction by, for example, increasing
the number of bidding rounds per day, and/or increasing the minimum
acceptable bids. We seek comment on these proposals.

# Conclusion

Comments are due on or before April 17, 2003, and reply comments are due
on or before April 24, 2003. Because of the disruption of regular mail
and other deliveries in Washington, DC, the Bureau requires that all
comments and reply comments be filed electronically. Comments and reply
comments must be sent by electronic mail to the following address:
[auction51@fcc.gov]{.underline}.[^35] The electronic mail containing the
comments or reply comments must include a subject or caption referring
to Auction No. 51 Comments. The Bureaus request that parties format any
attachments to electronic mail as Adobe^®^ Acrobat^®^ (pdf) or
Microsoft^®^ Word documents. Copies of comments and reply comments will
be available for public inspection during regular business hours in the
FCC Public Reference Room, Room CY-A257, 445 12th Street, SW,
Washington, DC 20554. Copies of comments and reply comments will also be
available from the Commission's copy contractor: Qualex International,
445 12^th^ Street, SW, Room CY-B402, Washington, DC 20554; phone (202)
863-2893; fax (202) 863-2898; e-mail <qualexint@aol.com>.

**In addition, the Bureaus request that commenters fax a courtesy copy
of their comments and reply comments to the attention of Kathryn Garland
at (717) 338-2850.**

This proceeding has been designated as a "permit‑but‑disclose"
proceeding in accordance with the Commission's *ex parte* rules.[^36]
Persons making oral *ex parte* presentations are reminded that memoranda
summarizing the presentations must contain summaries of the substance of
the presentations and not merely a listing of the subjects discussed.
More than a one or two sentence description of the views and arguments
presented is generally required.[^37] Other rules pertaining to oral and
written *ex parte* presentations in permit-but-disclose proceedings are
set forth in Section 1.1206(b) of the Commission's rules.[^38]

For further information concerning this proceeding, contact:

**Auctions and Industry Analysis Division, WTB**

For legal questions: Christopher Shields at (202) 418-0660

For general auction questions: Lisa Stover at (717) 338-2888

For questions about package bidding: Martha Stancill at (202) 418-0660

> Craig Bomberger at (202) 418-0660

**Commercial Wireless Division, WTB**

For service rule questions: Amal Abdallah at (202) 418-7307

> Evan Baranoff at (202) 418-7142
>
> JoAnn Epps at (202) 418-0620
>
> Dwain Livingston at (202) 418-0620

-- FCC --

# Attachment A {#attachment-a .unnumbered}

Placeholder for Attachment A

# Attachment B {#attachment-b .unnumbered}

##  {#section .unnumbered}

## Using the Smoothed Anchoring Method to Obtain Current Price Estimates {#using-the-smoothed-anchoring-method-to-obtain-current-price-estimates .unnumbered}

This appendix describes the method by which bid information on packages
and licenses is used to approximate a "price" associated with each
license at the close of every round. These "current price estimates," as
they are called, are then used in the next round when calculating part
(iii) of the proposed minimum acceptable bid formula.[^39] Specifically,
for a license, this value is the current price estimate of the license
plus z%. For a package, the value is the sum of the current price
estimates of the licenses that make up the package plus z% of the sum.

The current price estimates of the licenses are based on the concept
that every linear optimization problem has a dual problem that provides
pricing information. We begin by discussing a simplified representation
of the FCC winner determination problem and then discuss its linear
programming relaxation before explaining the dual problem of interest.
The winner determination problem is shown in (P1):

(P1): ![](media/image2.wmf){width="2.879861111111111in" height="1.2in"}

where *B^t^* is the set of considered bids in round *t,*

*b~j~* is the bid amount of bid *j,*

*L* is the set of licenses being auctioned,

![](media/image3.wmf){width="2.2222222222222223in" height="0.5in"} and,

![](media/image4.wmf){width="2.611111111111111in" height="0.5in"}

In this formulation, *x~j~* is an indicator variable that equals one if
bid *j* is in the provisionally winning set and zero otherwise. Thus,
the sum of the bid amounts of all provisionally winning bids produces
the maximum obtainable revenue for round *t*. Constraints (1) ensure
that each license is awarded exactly once. The constraints that ensure
that a bidder's bids between rounds are mutually exclusive are not
represented in (P1) since they will be ignored in the linear
representation of the problem.[^40]

The linear program of (P1) relaxes the restriction on the variables
*x~j~*, for all *jB^t^*, allowing these variables to take on any value
between zero and one. The linear programming representation of (P1) is
shown in (P2):

(P2): ![](media/image5.wmf){width="2.7895833333333333in" height="1.2in"}

The dual formulation of (P2) can be used to identify a price, *~i~*, for
each license *i*, and is shown in the following linear program (P3):

(P3): ![](media/image6.wmf){width="5.438888888888889in"
height="1.3666666666666667in"}

where *F* *B^t^* is the set of FCC bids on each license[^41] and,

![](media/image7.wmf){width="2.5833333333333335in" height="0.5in"}.

The optimal value of each variable, *~i~*, in (P3) corresponds to a dual
price[^42] -- often called a "shadow price" -- for each constraint,
i.e., each license, in (P2). The dual price of each license measures the
monetary cost of not awarding the license to whom it has been
provisionally assigned under the solution to (P2). Thus, this monetary
cost has a clear and natural use in estimating the current price of a
license given the bids considered in the current round.

Constraints (2) in (P3) ensure that the dual price of a license must be
at least as large as the greatest bid made on that license. For a
package, these constraints ensure that the sum of the dual prices of the
licenses that make up a particular package must be at least as large as
the greatest bid made on that package. Constraints (3) in (P3) ensure
that if a license has not been bid on, the dual price of that license is
at least as large as the FCC bid amount.

Ideally, the solution to (P2) is identical to the solution of (P1). When
this occurs, the sum of the dual prices of the licenses comprising any
provisionally winning bid equals the winning bid amount. However, (P2)
is only an approximation to the integer problem[^43] and often
*overestimates* the maximum revenue of (P1). When this occurs, the sum
of the dual prices of the licenses in at least one provisionally winning
bid will be greater than the respective bid amount. Thus, using the dual
prices of (P3) can result in minimum acceptable bid amounts that are too
high.

We propose to resolve this issue by using *pseudo-dual prices,*[^44]
rather than the dual prices of (P3)*.* These pseudo-dual prices are
obtained by forcing the sum of the dual prices of the licenses
comprising a provisionally winning bid to equal its respective bid
amount. For example, suppose there are two bids in the provisionally
winning set in round *t*: a bid on license A for \$10 and a bid on
package BC for \$25. The pseudo-dual price of A would exactly equal \$10
and the sum of the pseudo-dual prices of B and C would exactly equal
\$25. These restrictions ensure that the sum of the pseudo-dual prices
equals the maximum revenue for the round (e.g. \$35) and that minimum
acceptable bid amounts reflect the bid amounts of bids in the
provisionally winning set.

Pseudo-dual prices for each license *i*, denoted *~i~*, satisfy the
following constraints:

![](media/image8.wmf){width="5.399305555555555in"
height="1.7236111111111112in"}

where *W^t^ B^t^* is the provisionally winning bid set in round *t*
and*,*

~*j*~ is a slack variable that represents the difference between the bid
amount of

non-winning bid *j* and the sum of pseudo-dual prices of the licenses
contained

in non-winning bid *j*

Constraints (5) ensure that for each provisionally winning bid, the sum
of the dual prices of the licenses comprising that bid equal its
respective bid amount. This new restriction requires that we ease
restriction (2) in (P3) for non-winning bids in order to ensure that a
feasible solution exists. Constraints (4) provide this needed slack.
Constraints (6) are equivalent to constraints (3) in (P3) and
constraints (7) force the slack variables to be non-negative.

Satisfying constraints (5) implies that the sum of the pseudo-dual
prices always yields the maximum revenue for the round. There are likely
to be many sets of pseudo-dual prices that satisfy this constraint set.
For instance, in the example provided earlier, the pseudo-dual prices of
B and C might be any two numbers that together sum to \$25.

By keeping constraints (4)-(7), we have the flexibility to choose an
objective function that will help in selecting among multiple solutions
while still ensuring that the sum of the pseudo-dual prices yields the
maximum revenue of the round. We would like an objective function that
minimizes the values of the slack variables *~j~,* for all *j B^t^ \\
(W^t^ F)* in order to obtain pseudo-dual prices that are close to the
dual prices of (P3). We have tested a number of alternative objective
functions:

1.  Minimization of the maximum *~j~* for all *jB^t^ \\ (W^t^ F)*
    followed by maximization of the minimum ~*i*~ for all *i* in license
    set *L*, in an iterative manner. (DeMartini, Kwasnica, Ledyard and
    Porter, 1999)

2.  Minimization of the sum of the squares of *~j~* for all *jB^t^ \\
    (W^t^ F)*. (also DeMartini, Kwasnica, Ledyard and Porter, 1999)

3.  Minimization of the sum of the *~j~* for all *jB^t^ \\ (W^t^ F)*
    using a "centering" algorithm[^45] to solve, essentially finding an
    average among all sets of optimal pseudo-dual prices.

In testing the above alternatives, we frequently observed instances
where the pseudo-dual price of a license significantly changed from
round to round. We acknowledge that prices of licenses should be allowed
to reflect real changes, both increases and decreases, in the way
bidders value the licenses over time. However, we believe that large
oscillations in minimum acceptable bid amounts for the same bid that are
due to irrelevant factors such as multiple optimal solutions, can be
confusing to bidders. We have therefore chosen a method that attempts to
balance minimizing the slack variables and reducing the fluctuations in
pseudo-dual prices from round to round. This method requires solving two
optimization problems, the first of which is alternative 3 above, which
we present as (P4):

(P4):![](media/image9.wmf){width="5.218055555555556in"
height="2.189583333333333in"}

Since multiple optimal solutions can exist to (P4) we solve a second
optimization problem that chooses a solution in a way that reduces the
magnitude of price fluctuations between rounds. Specifically, we use an
objective function that applies the concepts of exponential
smoothing[^46] to choose among alternative pseudo-dual prices with the
additional constraint on the problem that the sum of the slack variables
equals ^\*^ (the optimal value of (P4)). This objective function
minimizes the sum of the squared deviations of the resulting pseudo-dual
prices in round *t,* from their respective smoothed prices in round
*t-1.*[^47] At the start of the auction, we use the minimum opening bid
prices as the prior smoothed prices. Since these opening prices are
based on bandwidth and population, the pricing algorithm begins with *a
priori* information about the differences among licenses.

Let ![](media/image10.wmf){width="0.20833333333333334in"
height="0.2638888888888889in"} be the pseudo-dual price of license *i*
in round *t.* The smoothed price for license *i* in round *t* is
calculated using the following exponential smoothing formula:

![](media/image11.wmf){width="1.5138888888888888in"
height="0.2638888888888889in"}

where ![](media/image12.wmf){width="0.3055555555555556in"
height="0.2638888888888889in"}is the smoothed price in round *t*-1,

0 1, and

![](media/image13.wmf){width="0.2222222222222222in"
height="0.2638888888888889in"} = the minimum opening bid amount for
license *i.*

Consistent with prior practice of the Commission, a weighting factor of
![](media/image14.wmf){width="0.5416666666666666in" height="0.19375in"}
has been chosen but can change, as the Commission requires*.*

The following quadratic program (QP) will find the pseudo-dual price,
![](media/image15.wmf){width="0.20833333333333334in"
height="0.2638888888888889in"}, for each license *i* in round *t* that
minimizes the sum of the squared deviations from the respective smoothed
prices in round *t-1* while ensuring that the pseudo-dual prices sum up
to the provisionally winning bid amounts and that the sum of the slack
variables is minimized.

(QP):![](media/image16.wmf){width="5.445138888888889in"
height="2.625in"}

where ![](media/image17.wmf){width="0.2916666666666667in"
height="0.2638888888888889in"} is known and treated as a constant within
the optimization.[^48]

Among alternative prices that satisfy all constraints, the objective
function of this optimization problem chooses one that forces the
pseudo-dual prices to be as close as possible to the previous round's
smoothed price. Thus, we call this the *Smoothed Anchoring Method* since
we "anchor" on the smoothed prices when solving for the pseudo-dual
prices. We define the "current price estimate" for license *i* in round
*t* as the pseudo-dual price,
![](media/image18.wmf){width="0.20833333333333334in"
height="0.2638888888888889in"}, obtained by solving (QP).

The minimum acceptable bid amount for a license in round *t+1* under
part (iii) will be the current price estimate of the license, as
calculated above, plus z%. For a package, the value will be the sum of
the current price estimates of the licenses that make up the package
plus z% of the sum. This part (iii) amount is then compared to the
amounts of parts (i) and (ii), and the greatest is the minimum
acceptable bid for the next round.

[^1]: Narrowband PCS Spectrum Auction Scheduled for March 26, 2003;
    Comment Sought on Reserve Prices or Minimum Opening Bids and Other
    Auction Procedures, DA 02-3234, *Public Notice*, 67 Fed. Reg. 72,417
    (rel. November 26, 2002) ("*Auction No. 50 Comment Public Notice*").

[^2]: Narrowband PCS Spectrum Auction Revised Inventory and Start Date
    for Auction No. 50; Notice and Filing Requirements, Minimum Opening
    Bids, Upfront Payments and Other Auction Procedures, DA 03-372,
    *Public Notice*,  68 Fed. Reg. 15,174 (rel. February 7, 2003)
    ("*Auction No. 50 Procedures Public Notice*").

[^3]: Space Data Comments in response to *Auction No. 50 Comment Public
    Notice* at 2-3.

[^4]: *Auction No. 50 Procedures Public Notice*, 68 Fed. Reg. 15,174.

[^5]: 47 U.S.C. § 309(j) (as amended by Section 3002(a)(E)(i), Balanced
    Budget Act of 1997, Pub. L. 105-33, 111 Stat. 251 (1997) ("Balanced
    Budget Act")).

[^6]: *See* Amendment of Part 1 of the Commission's Rules ---
    Competitive Bidding Proceeding, WT Docket No. 97-82, *Order,
    Memorandum Opinion and Order, and Notice of Proposed Rule Making*,
    12 FCC Rcd 5686, 5697, ¶ 16 (1997) ("*Part 1 Order*") (clarifying
    that pursuant to Section 0.131 of the Commission's rules, the Chief,
    Wireless Telecommunications Bureau, has delegated authority to
    implement all of the Commission's rules pertaining to auctions
    procedures).

[^7]: *See* Amendment of Part 1 of the Commission's Rules ---
    Competitive Bidding Procedures, Allocation of Spectrum Below 5 GHz
    Transferred from Federal Government Use, 4660-4685 MHz, WT Docket
    No. 97-82, ET Docket No. 94-32, *Third Report and Order and Second
    Further Notice of Proposed Rule Making*, 13 FCC Rcd 374, 448, ¶ 124
    (1998) ("*Part 1 Third Report and Order*"). The Commission directed
    the Bureau to seek comment on specific mechanisms related to
    day-to-day auction conduct including, for example, the structure of
    bidding rounds and stages, establishment of minimum opening bids or
    reserve prices, minimum acceptable bids, initial maximum eligibility
    for each bidder, activity requirements for each stage of the
    auction, activity rule waivers, criteria for determining reductions
    in eligibility, information regarding bid withdrawal and bid
    removal, stopping rules, and information relating to auction delay,
    suspension or cancellation. *Id.* at ¶ 125.

[^8]: The proposed design is essentially the same as that developed for
    Auction No. 31. *See* *generally* Auction of Licenses in the 747-762
    and 777-792 MHz Bands Scheduled for June 19, 2002; Further
    Modification of Package Bidding Procedures and Other Procedures for
    Auction No. 31, *Public Notice*, 17 FCC Rcd 5140 (2002), *Erratum*,
    17 FCC Rcd 7049 (2002).

[^9]: Unless otherwise specified, "SMR" will refer to SMR *without*
    package bidding. SMR *with* package bidding will be specified as
    such. Unless otherwise specified, a "package bidding auction" means
    an SMR auction with package bidding.

[^10]: *See generally* C, "Threshold Problem," below.

[^11]: In SMR auctions, the Commission generally has allowed bidders to
    mitigate the exposure problem by withdrawing standing high bids to
    the extent allowed by auction-specific procedures.

[^12]: *Part 1 Order,* 12 FCC Rcd at 5697-98, ¶ 16; *see also Part 1
    Third Report and Order*, 13 FCC Rcd at 425, ¶ 86.

[^13]: *See* Implementation of Section 309(j) of the Communications
    Act - Competitive Bidding, PP Docket No. 93-253, *Second Report and
    Order*, 9 FCC Rcd 2348, 2378-79, ¶¶ 171-176 (1994).

[^14]: All population figures are from the 2000 U.S. Census, U.S.
    Department of Commerce, Bureau of the Census. *See* Census 2000
    Summary File 1 (SF1) and July 3, 2001, News Releases covering the
    U.S. Virgin Islands, Guam, the Northern Mariana Islands, and
    American Samoa.

[^15]: Results are rounded using our standard rounding procedure:
    results above \$10,000 are rounded to the nearest \$1,000; results
    below \$10,000 but above \$1,000 are rounded to the nearest \$100;
    and results below \$1,000 are rounded to the nearest \$10.

[^16]: Bidders are permitted to bid on and create packages from only
    those licenses they selected on FCC Form 175.

[^17]: The bidder's new eligibility would be its eligibility activity in
    the current round multiplied by the reciprocal of the activity
    requirement (1/activity requirement) --- in this case, (1/(3/5)), or
    5/3.

[^18]: The stopping rule is described more fully in below, "Stopping
    Rule," below.

[^19]: 47 C.F.R. § 1.2104(i).

[^20]: 47 U.S.C. § 309(j) (as amended by Balanced Budget Act, Section
    3002(a)). The Commission's authority to establish a reserve price or
    minimum opening bid is set forth in 47 C.F.R. § 1.2104(c) and (d).

[^21]: *Part 1 Third Report and Order,* 13 FCC Rcd at 454-455, ¶ 141.

[^22]: *S*e*e*, *e.g.*, Auction of 800 MHz SMR Upper 10 MHz Band,
    Minimum Opening Bids or Reserve Prices, *Order*, 12 FCC Rcd 16,354
    (1997); Auction of the Phase II 220 MHz Service Licenses, Auction
    Notice and Filing Requirements for 908 Licenses Consisting of
    Economic Area (EA), Economic Area Grouping (EAG), and Nationwide
    Licenses, Scheduled for September 15, 1998, Minimum Opening Bids and
    Other Procedural Issues, *Public Notice*, 13 FCC Rcd 16,445 (1998).

[^23]: All population figures are from the 2000 U.S. Census, U.S.
    Department of Commerce, Bureau of the Census. *See* Census 2000
    Summary File 1 (SF1) and July 3, 2001, News Releases covering the
    U.S. Virgin Islands, Guam, the Northern Mariana Islands, and
    American Samoa.

[^24]: Results are rounded using our standard rounding procedure:
    results above \$10,000 are rounded to the nearest \$1,000; results
    below \$10,000 but above \$1,000 are rounded to the nearest \$100;
    and results below \$1,000 are rounded to the nearest \$10.

[^25]: Bidders are limited to bidding on, and hence creating packages
    from, those licenses which they selected on their FCC Form 175 and
    for which they have eligibility. *See generally* B, "Upfront
    Payments and Initial Maximum Eligibility," and C, "Activity and
    Eligibility Rules."

[^26]: If the auction closes with any license(s) unsold, the unsold
    license(s) will remain held by the FCC.

[^27]: For example, suppose Bidder 1 bids \$13,000 for License A; there
    are no bids for License B, which has a minimum opening bid of
    \$10,000; and Bidder 2 bids \$20,000 for Package AB. In determining
    the provisional winners, we will consider License B to have been bid
    on by the FCC at \$1000 less than the minimum opening bid, i.e.,
    \$9,000. The provisional winning set will therefore consist of
    Bidder 1 holding License A and the FCC holding License B because the
    sum of their bids (\$13,000+ \$9,000 = \$22,000) exceeds Bidder 2's
    bid for Package AB (\$20,000).

[^28]: A pseudo-random number generator based on the L'Ecuyer algorithms
    will be used to assign a selection number to each bid. A description
    of the L'Ecuyer algorithms can be found in L'Ecuyer, P. (1999) "Good
    Parameters and Implementations for Combined Multiple Recursive
    Random Number Generators" *Operations Research* 47 (1), pp.159-164.
    A longer version of this paper and the C code for the algorithms can
    be found on the author's website at
    http://www.iro.umontreal.ca/\~lecuyer/papers.html.

[^29]: There is a rare chance that more than one set of bids can satisfy
    these conditions. If such a case exists, all such sets will be
    generated and assigned a random number. The set with the largest
    associated random number will be the set of provisionally winning
    bids.

[^30]: Bidders must have selected the licenses on FCC Form 175 and must
    have sufficient eligibility to place a bid on the particular
    licenses or packages. *See* B, "Upfront Payments and Initial Maximum
    Eligibility," *supra*.

[^31]: Results above \$10,000 are rounded to the nearest \$1,000;
    results below \$10,000 but above \$1,000 are rounded to the nearest
    \$100; and results below \$1,000 are rounded to the nearest \$10.

[^32]: As described further in the "Renewed Bids" and "Last and Best
    Bids" sections, there are two exceptions to the minimum acceptable
    bid requirement. First, bidders who choose to place no further bids
    in the auction may place "last and best bids" at any amount between
    the bidder's previous high bid --- or, if the bidder has not placed
    a bid on the license or package, the minimum opening bid --- and the
    eighth increment above the minimum acceptable bid. Second, at any
    time bidders may "renew" their highest previous bid on a license or
    package without increasing the bid: however, a bidder is not
    conferred activity of any kind for renewing a non-provisionally
    winning bid. Because bids in each round are considered mutually
    exclusive, renewing a provisionally winning bid does not double
    count that bid towards a bidder's total eligibility activity credit.

[^33]: If the bidder has never placed a bid on the license or package,
    the lower bound on the last and best bid amount will be equal to the
    minimum opening bid.

[^34]: 47 C.F.R. § 1.2104(e).

[^35]: Comments and reply comments in response to this Public Notice may
    not be filed using the Commission's Electronic Comment Filing
    System, which is used for the Commission's docketed rule making
    proceedings.

[^36]: 47 C.F.R. §§ 1.1200(a), 1.1206.

[^37]: 47 C.F.R. § 1.1206(b).

[^38]: *Id*.

[^39]: In addition to the part (iii) formula derived here, the minimum
    acceptable bid also considers part (i) and (ii) amounts, where (i)
    is the minimum opening bid and (ii) is the bidder's own previous
    high bid plus x%, where x is specified by the Bureau. The minimum
    acceptable bid is the *greatest* of the three amounts.

[^40]: These constraints will be ignored in the linear program
    representation since they are rarely binding in the relaxation of
    the integer-programming problem and because adding such constraints
    to the dual problem creates "degeneracy" in the solution thereby
    causing multiple alternative solutions.

[^41]: The bid amount for a FCC bid is some small amount less than the
    minimum-opening bid for that license. *See* Auction Of Licenses in
    the 747-762 and 777-792 MHz Bands Scheduled for March 6, 2001;
    Modifications to the Calculation for Determining Minimum Acceptable
    Bids and the Provisions Concerning "Last and Best Bids" and Other
    Procedural Issues, DA 01-12, *Public Notice*, 16 FCC Rcd 217 (2001)
    (Section III discusses the reasons for this approach).

[^42]: We note that for non-linear problems, these dual prices are also
    known as *Lagrange multipliers.*

[^43]: When the problem is a convex optimization problem, the primal and
    dual problems yield the same objective function values. This is
    called strong-duality. These conditions do not hold for integer
    programming problems, often resulting in a gap between the linear
    programming and integer programming solution values.

[^44]: In our research we found this term first applied to auction
    pricing in the paper by Rassenti, Smith and Bulfin (1982), "A
    Combinatorial Auction Mechanism for Airport Slot Allocation," *Bell
    Journal of Economics*, vol. 13, pp. 402-417.

[^45]: The centering algorithm used in this testing was the barrier
    method available in CPLEX, a commercial optimization package.

[^46]: Exponential smoothing often is used in determining minimum
    acceptable bids in FCC auctions. *See, e.g.,* Auction of Licenses in
    the 698-746 MHz Band Scheduled for June 19, 2002; Notice and Filing
    Requirements, Minimum Opening Bids, Upfront Payments and Other
    Auction Procedures, DA 02-563, *Public Notice*, 17 FCC Rcd 4935,
    4971-4972, 5003-5005 (rel. March 20, 2002) ("*Auction No. 44
    Procedures Public Notice*").

[^47]: This objective function is a convex, quadratic function. This
    quadratic optimization problem is solved using the barrier method.

[^48]: Once the pseudo-dual prices, $\pi_{i}^{t}$, have been determined,
    the smoothed prices, $p_{i}^{t}$, can be calculated and used for
    solving (QP) in round *t+1*.