Consultation on a Licensing Framework for Broadband Radio Service (BRS) — 2500 MHz Band

Annex E — Example of the Proposed Activity Rules

1. For the purposes of this example, only two products will be considered: product X and product Y. Suppose that product X contains two generic licences in it, X1 and X2, each with an eligibility of 50 points, and that product Y contains two generic licences, Y1 and Y2, each with an eligibility of 25 points.

2. A single bidder, Bidder A, would like to obtain two licences of X1/X2. This package will be denoted as (2, 0). However, if the price of the package with two licences of X1/X2 exceeds the price of a package with one X1/X2 licence and one Y1/Y2 licence by more than $500,000, then Bidder A would prefer a package with one X1/X2 licence and one Y1/Y2 licence, denoted as package (1, 1).

3. Eventually, if the prices become too high, Bidder A will be unable to afford two licences and will need to reduce its demand to one licence. In this case, Bidder A again prefers one licence from X1/X2, but will switch to one Y1/Y2 licence if the price of one X1/X2 licence, denoted as package (1, 0), exceeds the price of one Y1/Y2 licence, denoted as package (0, 1) by more than $500,000.

4. Bidder A’s total budget is $2,800,000. If the price of obtaining two licences becomes greater than this, Bidder A must reduce its demand to one licence.

Round 1

5. In Round 1, the opening bid prices are announced; the opening bid price for X1/X2 is $1,000,000 per licence, and for Y1/Y2, it is $600,000 per licence. The price of a package with two X1/X2 licences is $2,000,000, whereas the price of a package with one X1/X2 licence and one Y1/Y2 licence is $1,600,000 (a price difference of $400,000). As Bidder A prefers two X1/X2 licences unless the price difference is greater than $500,000, Bidder A will bid for two X1/X2 licences, package (2, 0):

Annex E - Round 1
Product Price Bid Eligibility Points
X1/X2 $1,000,000 2 100
Y1/Y2 $600,000 0 0
Total Package $2,000,000 (2, 0) 100

Round 2

6. In Round 1, several other bidders shared Bidder A’s preference for X1/X2, whereas few bidders bid on Y1/Y2. As a result, the prices in Round 2 are $1,200,000 for X1/X2 and $650,000 for Y1/Y2. The price for a package with two X1/X2 licences is $2,400,000, whereas the price for a package with one X1/X2 licence and one Y1/Y2 licence is $1,850,000 (a price difference of $550,000). As Bidder A prefers one X1/X2 licence and one Y1/Y2 licence when the price difference is greater than $500,000, Bidder A now bids on one licence of each category, package (1, 1), thereby reducing eligibility from 100 to 75 points.


Annex E - Round 2
Product Price Bid Eligibility Points
X1/X2 $1,200,000 1 50
Y1/Y2 $650,000 1 25
Total Package $1,850,000 (1, 1) 75

Round 3

7. In Round 2, the low price of Y1/Y2 caused many bidders to switch demand to that category. As a result, the price of Y1/Y2 increased at a faster rate than the price of X1/X2. The Round 3 prices are $1,250,000 for X1/X2 and $800,000 for Y1/Y2. The price for a package with two X1/X2 licences is $2,500,000, whereas the price for a package with one X1/X2 licence and one Y1/Y2 licence is $2,050,000. This price difference is only $450,000, so Bidder A would prefer to switch back to bidding on two X1/X2 licences, package (2, 0).

8. Using only an eligibility point activity rule, switching back at this point would be impossible because Bidder A would no longer have enough eligibility to bid for a package worth 100 points. This limitation could have the effect of creating a disincentive for Bidder A to bid on its most favourable package in Round 2. Bidder A would have needed to bid on a less profitable package in order to maintain its eligibility for as many rounds of the auction as possible.

9. With a revealed preference/eligibility point hybrid activity rule, however, Bidder A is free to switch back as long as the package satisfies revealed preference with respect to each prior eligibility point reducing round:

Annex E - Round 3
Product Price Bid Eligibility Points
X1/X2 $1,250,000 2 100
Y1/Y2 $800,000 0 0
Total Package $2,500,000 (2, 0) 100 (Eligibility is 75)

10. In order to place a bid with eligibility points greater than its current eligibility (75 points), Bidder A must meet the revealed preference constraint with respect to each prior eligibility-reducing round. In this case, the only eligibility-reducing round is Round 2, where Bidder A decreased its eligibility from 100 points to 75 points. In other words, in order for Bidder A to be able to switch its bid from (1, 1) to (2, 0), the (2, 0) package had to become relatively cheaper than the (1, 1) package. Mathematically, the revealed preference constraint is stated as follows, where R refers to the round:

(Price of (2, 0) in R3) – (Price of (2, 0) in R2) ≤ (Price of (1, 1) in R3) – (Price of (1, 1) in R2)
($2,500,000 – $2,400,000) ≤ ($2,050,000 – $1,850,000)
$100,000 ≤ $200,000

11. The price of package (2, 0) increased by $100,000 from Round 2 to Round 3, whereas the price of package (1, 1) increased by $200,000. Therefore, the constraint is satisfied and Bidder A is permitted to place the bid for the package (2, 0).

Round 4

12. In Round 4, the price of X1/X2 increases to $1,400,000, whereas the price of Y1/Y2 increases to $1,000,000. The price for a package with two X1/X2 licences is $2,800,000, whereas the price for a package with one X1/X2 licence and one Y1/Y2 licence is $2,400,000. This price difference is only $400,000 so Bidder A prefers the same package as in Round 3:

Annex E - Round 4
Product Price Bid Eligibility Points
X1/X2 $1,400,000 2 100
Y1/Y2 $1,000,000 0 0
Total Package $2,800,000 (2, 0) 100 (Eligibility is 75)

13. Bidder A’s eligibility is still only equal to 75, so it must meet the revealed preference constraint in order to place this bid. As before, the requirement is that the (2, 0) package needs to be relatively cheaper than the (1, 1) package (as compared to Round 2):

(Price of (2, 0) in R4) – (Price of (2, 0) in R2) ≤ (Price of (1, 1) in R4) – (Price of (1, 1) in R2)
($2,800,000 – $2,400,000) ≤ ($2,400,000 – $1,850,000)
$400,000 ≤ $550,000

14. This constraint continues to be satisfied, that is, the price of the package (2, 0) increased by $400,000 which is no more than the increase in the price of the package (1, 1) from Round 2 to the current round, Round 4, which is $550,000. Bidder A is permitted to place this bid for the package (2, 0).

Round 5

15. In Round 5, the price continues to increase on both products, with X1/X2 at $1,650,000 and Y1/Y2 at $1,200,000. As a result, both two-licence combinations, (2, 0) and (1,1) now exceed Bidder A’s budget of $2,800,000. Bidder A must decrease its demand to one licence. As the price of X1/X2 ($1,650,000) is $450,000 greater than the price of Y1/Y2 ($1,200,000), Bidder A places a bid for one X1/X2 licence, package (1, 0), given that Bidder A prefers one X1/X2 licence when the price of one X1/X2 licence exceeds the price of one Y1/Y2 licence by less than $500,000.

16. This bid further reduces Bidder A’s eligibility to 50 points. Bidder A is within its eligibility of 75 points, so there are no revealed preference constraints on this bid.

Annex E - Round 5
Product Price Bid Eligibility Points
X1/X2 $1,650,000 1 50
Y1/Y2 $1,200,000 0 0
Total Package $1,650,000 (1, 0) 50

Round 6

17. In Round 6, the price on X1/X2 increases at a faster rate, increasing the price difference to $550,000, which is greater than the $500,000 threshold. Bidder A thus switches its bid to one Y1/Y2 licence, package (0, 1) as Bidder A prefers one Y1/Y2 licence when the price of one X1/X2 licence exceeds the price of one Y1/Y2 licence by more than $500,000. This bid further reduces Bidder A’s eligibility to 25 points:

Annex E - Round 6
Product Price Bid Eligibility Points
X1/X2 $1,800,000 0 0
Y1/Y2 $1,250,000 1 25
Total Package $1,250,000 (0, 1) 25

Round 7

18. In Round 7, the price on Y1/Y2 increases at a faster rate than X1/X2. At Round 7 prices, Bidder A prefers one X1/X2 licence, as the price of one X1/X2 licence exceeds the price of one Y1/Y2 licence by less than $500,000, causing Bidder A to again desire to switch:

Annex E - Round 7
Product Price Bid Eligibility Points
X1/X2 $1,850,000 1 50
Y1/Y2 $1,400,000 0 0
Total Package $1,850,000 (1, 0) 50 (Eligibility is 25)

19. In order to place this bid, Bidder A must satisfy revealed preference with respect to every round in which it has reduced its eligibility. Bidder A reduced its eligibility in Round 2, Round 5 and Round 6. It is helpful to summarize the prices and bids placed up to this point:

Annex E - Round 7
Product Price
Round 1 Round 2 Round 3 Round 4 Round 5 Round 6 Round 7
X1/X2 $1,000,000 $1,200,000 $1,250,000 $1,400,000 $1,650,000 $1,800,000 $1,850,000
Y1/Y2 $600,000 $650,000 $800,000 $1,000,000 $1,200,000 $1,250,000 $1,400,000
Bid (2, 0) (1, 1) (2, 0) (2, 0) (1, 0) (0, 1)  

20. The constraints are as follows:

Constraint with respect to Round 2

(Price of (1, 0) in R7) – (Price of (1, 0) in R2) ≤ (Price of (1, 1) in R7) – (Price of (1, 1) in R2)
($1,850,000 – $1,200,000) ≤ ($3,250,000 – $1,850,000)
$650,000 ≤ $1,400,000

21. The price of the package (1, 0) increased by $650,000 from Round 2 to the current round, Round 7, which is no more than the increase in the price of package (1, 1), $1,400,000, where package (1, 1) is the package that Bidder A bid on in Round 2.

Constraint with respect to Round 5

(Price of (1, 0) in R7) – (Price of (1, 0) in R5) ≤ (Price of (1, 0) in R7) – (Price of (1, 0) in R5)
($1,850,000 – $1,650,000) ≤ ($1,850,000 – $1,650,000)
$200,000 ≤ $200,000

22. The price of the package (1, 0) increased by $200,000 from Round 5 to the current round, Round 7, which is no more than the increase in the price of the package (1, 0), where the package (1, 0) is the package that Bidder A bid on in Round 5.

Constraint with respect to Round 6

(Price of (1, 0) in R7) – (Price of (1, 0) in R6) ≤ (Price of (0, 1) in R7) – (Price of (0, 1) in R6)
($1,850,000 – $1,800,000) ≤ ($1,400,000 – $1,250,000)
$50,000 ≤ $150,000

23. The price of the package (1, 0) increased by $50,000 from Round 6 to the current round, Round 7, which is no more than the increase in the price of the package (0, 1), where the package (0, 1) is the package that Bidder A bid on in Round 6.

24. All three revealed preference constraints are satisfied, so Bidder A is permitted to place this bid.

Supplementary Round

25. In the bidding of Round 7, the aggregate demand drops sufficiently that the clock rounds conclude, making Round 7 the final clock round. Bidder A is in the position of having a final clock package of one X1/X2 licence. Note that if there had only been an eligibility point activity rule in the clock stage, Bidder A would likely have, instead, a final clock package of one Y1/Y2 licence, a less desirable package.

26. With the revealed preference limit, Bidder A is now guaranteed to win its final clock package if all licences are sold in the clock rounds of the auction. If there are some unallocated licences in the final clock round, Bidder A can still guarantee winning its final clock package by submitting a bid, increasing the dollar amount by at least the final clock price of those unallocated licences minus the opening bid prices of the unallocated licences. This guarantee may be compromised if all other supplementary bids do not include at a minimum, all licences contained in the bidder’s final clock package.

27. Now, suppose that Bidder A wishes to increase its bid on the package (1, 1) (i.e. one X1/X2 licence and one Y1/Y2 licence) to its maximum budget of $2,800,000. This package is larger than Bidder A’s final clock package in terms of eligibility points. Therefore, Bidder A must satisfy revealed preference with respect to its final clock package, as well as with respect to each eligibility-reducing round beginning with the last round in which Bidder A had sufficient eligibility to bid on the package (1, 1), i.e. beginning with Round 5. Therefore, Bidder A’s supplementary bid for the package (1, 1) must meet the revealed preference conditions with respect to Round 5, Round 6 and Round 7.

28. The revealed preference constraints are as follows, starting with the final clock package constraint:

Revealed preference with respect to the final clock package

(Sup Bid on (1, 1)) – (Price of (1, 1) in R7) ≤ (Highest Bid on (1, 0)) – (Price of (1, 0) in R7)
(Sup Bid on (1, 1)) ≤ (Highest Bid on (1, 0)) + (Price of (1, 1) in R7) – (Price of (1, 0) in R7)
(Sup Bid on (1, 1)) ≤ $1,850,000 + $3,250,000 – $1,850,000
(Sup Bid on (1, 1)) ≤ $3,250,000

Revealed preference with respect to Round 6

(Sup Bid on (1, 1)) – (Price of (1, 1) in R6) ≤ (Highest Bid on (0, 1)) – (Price of (0, 1) in R6)
(Sup Bid on (1, 1)) ≤ (Highest Bid on (0, 1)) + (Price of (1, 1) in R6) – (Price of (0, 1) in R6)
(Sup Bid on (1, 1)) ≤ $1,250,000 + $3,050,000 – $1,250,000
(Sup Bid on (1, 1)) ≤ $3,050,000

Revealed preference with respect to Round 5

(Sup Bid on (1, 1)) – (Price of (1, 1) in R5) ≤ (Highest Bid on (1, 0)) – (Price of (1, 0) in R5)
(Sup Bid on (1, 1)) ≤ (Highest Bid on (1, 0)) + (Price of (1, 1) in R5) – (Price of (1, 0) in R5)
(Sup Bid on (1, 1)) ≤ $1,850,000 + $2,850,000 – $1,650,000
(Sup Bid on (1, 1)) ≤ $3,050,000

29. Thus, Bidder A’s supplementary bid on the (1, 1) package is most constrained by the revealed preference constraints relative to rounds 5 and 6. In this case, the constraining amount is $3,050,000, allowing Bidder A to place the $2,800,000 bid.

Revealed Preference Constraints for the (0, 1) Package

30. The (0, 1) package is also subject to revealed preference constraints. These are based on the packages in each eligibility-reducing round beginning with the last round in which Bidder A had sufficient eligibility to bid on the (0, 1) package, as well as in the final clock round. In this example, the last round in which Bidder A had sufficient eligibility to bid on the (0, 1) package was Round 7, which is also the final clock round. So, the only constraint on the bid for the (0, 1) package is:

(Sup Bid on (0, 1)) – (Price of (0, 1) in R7) ≤ (Highest Bid on (1, 0)) – (Price of (1, 0) in R7)
(Sup Bid on (0, 1)) ≤ (Highest Bid on (1, 0)) + (Price of (0, 1) in R7) – (Price of (1, 0) in R7)
(Sup Bid on (0, 1)) ≤ $1,850,000 + ($1,400,000 – $1,850,000)
(Sup Bid on (0, 1)) ≤ $1,400,000

31. So, without any supplementary bids placed on the final clock package, the highest supplementary bid that Bidder A can place on the (0, 1) package is $1,400,000 because Bidder A bid $1,850,000 for (1, 0) in the final clock round. However, if for example Bidder A places a supplementary bid on its final clock package of $2,300,000, then Bidder A may also place a supplementary bid on the (0, 1) package of up to $1,850,000.


Annex F — Algebraic Description of Proposed Revealed Preference Activity Rules in the Clock Rounds and the Supplementary Round

Revealed Preference in the Clock Rounds

1. The activity rule in the clock rounds allows for a bidder to always be able to place a bid on any package that is within the bidder’s current eligibility. As well, in any round, the bidder can bid on a larger package than would be permitted by the bidder’s current eligibility provided that the package satisfies revealed preference with respect to each prior eligibility-reducing round. However, bidding on a larger package does not increase the bidder’s eligibility in subsequent rounds. A bidder will never be allowed to place a bid on a package that exceeds its initial eligibility.

2. A product refers to a particular category in a given service area. Industry Canada is proposing two categories of licences, paired and unpaired, with two categories in Region A (43 service areas), one category in Region B (16 service areas) and two categories in Region C (two service areas). In total 106 products will be available in the 2500 MHz auction.

Region A — 86 products

  • blocks C/C’ to G/G’ (five generic licences of 10 + 10 MHz);
  • block I (one licence of 25 MHz);

Region B — 16 products

  • blocks E/E’ to G/G’(three generic licences of 10 + 10 MHz);

Region C — 4 products

  • blocks A/A’ to B/B’ and E/E’ to G/G’ (five generic licences of 10 + 10 MHz); and
  • block H (one licence of 25 MHz).

3. A package in clock round t satisfies revealed preference with respect to an earlier clock round s for a given bidder if the bidder’s package Qt has become relatively less expensive than the package on which the bidder bid in clock round s, Qs, as the clock prices have progressed from the clock prices in clock round s to the clock prices in clock round t. Algebraically, the revealed preference constraint is the condition that:

\[ \sum_{i=1}^m (Q_{t,i}× (P_{t,i} − P_{s,i})) \le \sum_{i=1}^m (Q_{s,i}× (P_{t,i} − P_{s,i})) \]

where:

i” indexes the products;

m” is the number of products, where the maximum number of products proposed for the 2500 MHz auction is 106;

Qt,i is the quantity of the ith product bid in clock round t;

Qs,i is the quantity of the ith product bid in clock round s;

Pt,i is the clock price of the ith product bid in clock round t; and

Ps,i is the clock price of the ith product bid in clock round s.

4. A bidder’s package, Qt, of clock round t is consistent with revealed preference in the clock rounds if it satisfies the revealed preference constraint with respect to all eligibility-reducing rounds prior to clock round t for the given bidder.

Revealed Preference in the Supplementary Round

5. There is no limit on the supplementary bid amount for the final clock package. The activity rule in the supplementary round states that all supplementary bids must satisfy the revealed preference limit with respect to the final clock round regardless of whether the supplementary bid package is larger or smaller than the final clock package.

6. In addition, supplementary bids on packages that are larger than the final clock package must satisfy the revealed preference limit with respect to each eligibility-reducing round, beginning with the last round in which the bidder had sufficient eligibility to bid on the package, unless the increase in package size is due to placing bids on unallocated licences, where unallocated licences are those licences where supply is greater than aggregate demand in the final clock round.

7. Let Q denote the package on which the bidder wishes to place a supplementary bid. Let Qs denote the package on which the bidder bid in clock round s and let Bs denote the bidder’s highest dollar amount bid in the auction for package Qs, whether the highest dollar amount was placed in a clock round or a supplementary round.

8. A supplementary bid, B, for the package Q satisfies the revealed preference limit with respect to a clock round s, if B is less than or equal to the highest dollar amount bid on the package bid in clock rounds, that is, Bs plus the price difference in the respective packages, Q and Qs, using the clock prices of clock round s. Algebraically, the revealed preference limit is the condition that:

\[B \le B_s + \sum_{i=1}^m (P_{s,i} × (Q_{i} − Q_{s,i}))\]

where:

i” indexes the products;

m” is the number of products;

Qi is the quantity of the ith product in the package Q;

Qs,i is the quantity of the ith product in the package Qs of clock round s;

Ps,i is the clock price of the ith product in clock round s;

B is the dollar amount of the supplementary bid for the package Q; and

Bs is the highest dollar amount bid on package Qs either in a clock round or in the supplementary round.

9. In addition, for supplementary bid package Q, let T(Q) denote the last clock round in which the bidder’s eligibility was at least the number of eligibility points associated with the package Q.

10. A given bidder’s collection of supplementary bids is consistent with the revealed preference limit if the supplementary bid for the package Q, with a dollar amount, B, for the given bidder satisfies the following conditions:

  • (a) for a package Q, comprising the entire final clock package plus any or all licences that are provisionally unallocated to any bidder in the final clock round, the dollar amount, B, must satisfy the revealed preference limit, as specified in paragraph 8, with respect to the final clock round only; note that this places no constraint on the dollar amount of a supplementary bid for the final clock package;
  • (b) for any package Q, comprising other than the entire final clock package plus any or all licences that are provisionally unallocated to any bidder in the final clock round, the dollar amount B must satisfy the revealed preference limit, as specified in paragraph 8 with respect to the final clock round and with respect to every eligibility-reducing round equal to T(Q) or later.

11. Note that, in the application of paragraph 8, the package Qs may itself be subject to a revealed preference limit with respect to another package. Thus, the rule may have the effect of creating a chain of constraints on the dollar amount of a supplementary bid for a package Q relative to the dollar amounts of other clock bids or supplementary bids.

12. See Annex E for an example of the revealed preference activity rules.


Annex G — Proposed Pricing Rule

1. Prices are determined at two points in the auction: first at the end of the allocation stage to determine the base prices, which are the minimum that winning bidders will pay for their winning packages; and second, at the end of the assignment stage to determine the incremental payments for specific licences, known as assignment prices. Industry Canada is proposing to use a second-price rule to determine the prices to be paid by winning bidders. More specifically, Industry Canada proposes to apply bidder-optimal core prices and to use the "nearest Vickrey" approach in determining both the base prices and the assignment prices. The final price paid by a winning bidder is the sum of the base price and the assignment price(s).

Base Prices

2. Each winning allocation stage bid has an associated price for the package of licences contained within the bid, known as the base price. A separate base price is determined for each winning bidder.

3. Industry Canada is proposing the use of a second-price rule to calculate base prices such that the base price for a winning bidder will be at least the opening bid price, but no higher than the actual amount bid. Second prices are often referred to as Vickrey prices and represent the opportunity cost of the bidder winning the package.

4. The Vickrey price for each winning Bidder J is calculated as follows. First, from the value of the winning combination of packages (see paragraph 57, Annex D), subtract Bidder J’s winning bid (value A). Next, recalculate the winning combination of packages in the hypothetical situation where all Bidder J’s bids are excluded, as if Bidder J had not participated in the auction (value B). The Vickrey price for Bidder J is defined as the value of the winning combination of packages with all Bidder J’s bids excluded (value B) minus the sum of the winning allocation stage bids for all bidders other than Bidder J (value A), that is, B – A.

5. An extra payment beyond the Vickrey prices is sometimes required as a result of complementarities. In the event that an extra payment is required, the payment to be made will be adjusted proportionate to the size of the bidder’s package as measured by the bidder’s winning package evaluated at the opening bid prices.

6. The set of base prices for the winning allocation stage bids must satisfy the following conditions:

  • (a) First condition: The base price for a winning allocation stage bid must be greater than or equal to the opening bid prices for the licences included in the package associated with the winning bid, but not more than the dollar amount of the winning bids.
  • (b) Second condition: The set of base prices must be sufficiently high that there is no alternative bidder, or group of bidders prepared to pay more than any winning bidder or group of winning bidders. If there is only one set of base prices that meet the first and second conditions, this determines the base prices for the allocation stage.
  • (c) Third condition: If there are many sets of base prices that fulfil the first and second condition, the set(s) of base prices that minimize(s) the sum of base prices across winning bidders is selected. If there is only one set of base prices satisfying these three conditions, this determines the base prices for the allocation stage.
  • (d) Fourth condition: If there is more than one set of base prices that satisfy the first three conditions, the set of base prices that minimize the weighted sum of squares of differences between the base prices and the Vickrey prices will be selected. The weighting is relative to the price of the bidder’s package evaluated at the opening prices. This approach for selecting among sets of base prices that minimize the sum of base prices across winning bidders is referred to as the “nearest Vickrey” approach.

7. These conditions characterize a unique set of base prices such that each winning bidder pays no more than the dollar amount of its winning bid and pays at least the aggregate value of the opening bid prices for the package of licences.

8. A software algorithm will be used to determine the set of base prices that meets the conditions outlined above.

9. The following is an example of how base prices are calculated. This example is based on the 2012 Spectrum Auction Design paper by P. Cramton (http://www.cramton.umd.edu/papers2005-2009/cramton-spectrum-auction-design.pdf).

10. Suppose that there are five bidders, 1, 2, 3, 4, 5, bidding for two licences, A and B. The following bids are submitted (“b” designates the bidder):

b1{A} = $28

b2{B} = $20

b3{AB} = $32

b4{A} = $14

b5{B} = $12

11. The bids of the five bidders are represented in Figure G1.

12. In this example, the highest value combination of bids would assign licence A to Bidder 1 and licence B to Bidder 2, generating $48 in value. There is no other assignment of the licences that yields a higher value.

13. To calculate the Vickrey price for Bidder 1, Bidder 1’s bid is removed. The best assignment without Bidder 1 assigns licence A to Bidder 4 at $14 and licence B to Bidder 2 at $20, resulting in $34. The sum of the winning bids for all bidders other than Bidder 1 is $20 ($48 – $28). Thus, the Vickrey price for Bidder 1 is $14 ($34 – $20). Similarly, if Bidder 2’s bid is removed, then the best assignment is to assign licence A to Bidder 1 and licence B to Bidder 5, resulting in a value of $40. The sum of the winning bids for all bidders other than Bidder 2 is $28 ($48 – $20). Thus, the Vickrey price for Bidder 2 winning B is $12 ($40 – $28).

14. Hence, the Vickrey outcome is for Bidder 1 to pay $14 for licence A and for Bidder 2 to pay $12 for licence B. Total revenues with these payments are $14 + $12 = $26. As shown in Figure G1, this means that Bidder 1 can reduce its bid to $14 before being displaced by Bidder 4. Similarly, Bidder 2 can reduce its bid to $12 before being displaced by Bidder 5.

15. The problem is that these payments sum to $26, which less than Bidder 3’s bid of $32 for both licences A and B. Therefore, Bidder 1 and Bidder 2 must split an additional payment of $6 ($32 – $26), to ensure that their combined payment is greater than that of Bidder 3, satisfying the condition that no other bidder or group of bidders were prepared to pay more for the licences in question. That is, Bidder 1 and Bidder 2 must pay, collectively, at least $32.

Figure G1 — Example of Calculating Base Prices

Example of Calculating Base Prices (the long description is located below the image)
Description of Figure 1

This figure is a graph illustrating the example in paragraph 9 of Annex G, which demonstrates how to calculate base prices using a second-price rule and why an additional payment beyond second prices is sometimes required.

16. If the opening bid prices for licence A and licence B are the same amount, the additional payment of $6 is split equally between the two bidders. Each bidder is therefore paying an additional $3 above its Vickrey price, with Bidder 1 paying $17 ($14 + $3) and Bidder 2 paying $15 ($12 + $3), as shown in Figure G1. However, if the opening bid prices for the two licences are different amounts, the two bidders must split the extra payment proportionately, in reference to the opening bid amounts (the fourth condition). For example, if the opening bid price for licence A is $8 and the opening bid price for licence B is $4, then the opening bid price of Bidder 1’s package is twice as large as that of Bidder 2. Therefore, Bidder 1 would pay twice as much as Bidder 2 of the extra payment, with Bidder 1 paying an additional $4, for a total payment of $18 and Bidder 2 paying an additional $2, for a final payment of $14.

Assignment Prices

17. The assignment stage will consist of a sequence of assignment rounds. Industry Canada proposes to run product-by-product assignment rounds, in descending order of the populations of the associated service areas, conducting a separate assignment round for each product, where necessary. This process would enable bidders to know which specific frequencies they have won in the most populated service areas before they participate in the assignment rounds for the adjacent, less populated service areas. However, two or more products would be aggregated into a single assignment round if all of the following criteria are met: the products are in the same region (i.e. Region A, Region B or Region C); their service areas form a contiguous geographic area; and the winners, and the number of generic licences they have won are sufficiently similar across service areas, according to predefined criteria.

18. The assignment bid is a package bid for the specific frequency locations of all licences being assigned within the round. The assignment prices will be determined from the set of assignment stage bids for the products being assigned in that round.

19. Industry Canada is proposing to use a second-price rule to calculate assignment prices. The assignment price is attributable to the entire collection of licences assigned in a given assignment round and not to individual licences that comprise the package.

20. For the purpose of calculating assignment prices, the Vickrey price for each winning Bidder J is calculated as follows. First, from the value of the winning combination of assignment bids (see paragraph 71, Annex D), subtract Bidder J’s winning bid (value A). Next, recalculate the winning combination of assignment bids in the hypothetical situation where all Bidder J’s assignment bids are equal to zero, as if Bidder J did not have a preference for any of the assignment options it was presented in the round (value B). The Vickrey price for Bidder J is defined as the value of the winning combination of assignment bids with all Bidder J’s bids set to equal zero (value B) minus the sum of the winning assignment bids for all bidders other than Bidder J (value A), that is, B - A.

21. The assignment stage prices for each winning assignment bid in a given assignment round must satisfy the following conditions:

  • (a) First condition: The assignment prices must be positive or zero and not more than the dollar amount of the winning assignment stage bid.
  • (b) Second condition: The set of assignment prices must be sufficiently high that there is no alternative combination of valid assignment bids that sum to more than the winning assignment bids. If there is only one set of assignment prices that satisfies the first two conditions, this determines the assignment prices.
  • (c) Third condition: If there are many sets of assignment prices that fulfil the first and second conditions, the set(s) of assignment prices that minimize(s) the sum of assignment prices across winning assignment stage bids is selected. If there is only one set of assignment prices that satisfies these three conditions, this determines the assignment prices.
  • (d) Fourth condition: If there are many sets of assignment prices that satisfy the first three conditions, the set of assignment prices that minimizes the weighted sum of squares of differences between the assignment prices and the Vickrey prices will be selected. The weighting is relative to the price of the bidder’s package evaluated at the opening prices. This approach for selecting among sets of assignment prices that minimize the sum of assignment prices across winning assignment bids is referred to as the “nearest Vickrey” approach.

22. A software algorithm will be used to determine the set of assignment prices that meet the conditions outlined above.


Annex H — Glossary

Glossary
Term Definition
Activity rule A rule that limits what bids a bidder can make in subsequent rounds of a multiple round auction. The activity rules are intended to avoid bid sniping and to encourage truthful bidding.
Aggregate demand The total number of bids for a product.
Allocation stage A stage of the auction in which the number of spectrum licences that a bidder wins in each service area, as well as the base price for these licences is determined.
Assignment price The price for specific licences that a winning bidder has won in the assignment stage.
Assignment stage A stage of the auction in which bidders that have won generic licences are assigned specific licences.
Base price The price for a package of licences that a winning bidder has won in the allocation stage. The base price is calculated at the end of the allocation stage. It does not include the assignment price.
Bid amount The price that a bidder bids for a particular licence or package of licences.
Bid shading The strategy of bidding below one’s valuation, typically as a way to improve profits in first-price auctions.
Bid sniping The tendency for a bidder to wait until the last possible opportunity to place a serious bid. Auctions often have activity rules in place to prevent bid sniping.
Category A spectrum block or group of spectrum blocks with similar properties. A category can include a single licence for each service area or a group of generic licences for each service area.
Clock price A price for a product in a clock round.
Clock round A round in the allocation stage of the auction in which bidders can submit a bid for a single package of licences in response to prices announced by Industry Canada.
Complementary goods X and Y are complementary goods if the demand for X decreases when the price of Y increases. Complementary goods are typically purchased together and are more valuable together than they are apart (the sum is greater than the parts). The complementarity may be strong or weak. The level of complementarity between goods is important in designing an auction.
Demand reduction A situation where a bidder reduces its demand to keep prices low.
Efficient assignment/outcome The assignment of the licences to the bidders that value them the most.
Eligibility-based activity rule An activity rule based on eligibility points where a bidder cannot bid for a package of licences for which the sum of the eligibility points for these licences exceeds the bidder’s current eligibility points. A bidder’s initial level of eligibility is based on its pre-auction financial deposit. In subsequent rounds, its number of eligibility points is set by the bids placed in the previous round (and the activity percentage for that round).
Eligibility points Each licence is assigned a certain number of eligibility points that are related to its population, bandwidth and estimated value. They are first used in the determination of the pre-auction deposit, and then for the eligibility-based activity rule. A bidder’s initial eligibility points define the upper limit of licences for which the bidder can bid (based on the sum of bidding points associated with the licences in its bid).
Eligibility-reducing round A clock round in which the number of eligibility points associated with a bid is less than the bidder’s eligibility. In subsequent rounds, the bidder’s eligibility is reduced.
Excess demand The extent to which the aggregate demand exceeds the number of licences available.
Exposure risk The risk of winning only some licences in a collection of licences that a bidder wants. This may occur when bids are treated individually instead of being treated as a package.
Final clock package The package that the bidder bid on in the final clock round.
First-price rule A pricing rule which requires winning bidders to pay the full amount of their winning bid.
Gaming or game playing Bidding in an auction in a way that does not truthfully represent the bidder’s true valuation of the spectrum, but may increase the bidder’s chances of a favourable outcome. Examples of gaming include demand reduction, parking and tacit collusion.
Generic licences Licences that are similar enough and of comparable value such that they can be offered together in a single category. Bidders may then express a demand for a number of generic licences at a particular price.
Lost licence As part of a tie resolution mechanism in the allocation stage, a licence that was included in a bidder’s final clock package, but that is not included in an alternate package that could be assigned to the bidder.
Opening bid prices Opening bid prices are the starting prices for the spectrum licences in the auction, and the minimum that Industry Canada will accept for each licence.
Package bid A package bid is a bid on a set of licences.
Parking A strategy in which bidders bid on licences that they do not expect to win simply to maintain greater eligibility for later in the auction.
Pre-auction financial deposit A pre-auction financial deposit that Industry Canada requires all bidders to submit with their application to participate in the auction. The deposits are based on the licences on which the applicant wishes to be eligible to bid.
Price discovery A feature of multiple-round auctions in which information about bidder demands and prices is reported to bidders, giving them the opportunity to adjust subsequent bids based on the information.
Pricing rule The rule that determines the price paid by the bidder.
Product A category in a given service area.
Revealed preference activity rule An activity rule based on prices and bidding activity in previous rounds. The rule allows a bidder to shift toward larger packages, in terms of associated eligibility points that have become relatively less expensive.
Second-price rule A pricing rule that requires winning bidders to pay an amount that is sufficient to ensure that no other bidder, or group of bidders, was prepared to pay more than the winning bidders for the licence(s) in question.
Service area

Industry Canada has established four tiers of service areas, which it uses for competitive licensing. These areas cover the entire geography of Canada and are based on Statistics Canada’s Census Divisions and Subdivisions. The definition of the service areas within these tiers and accompanying maps and data tables are available on Industry Canada’s website. See Service Areas for Competitive Licensing at http://www.ic.gc.ca/eic/site/smt-gst.nsf/eng/h_sf01627.html.

For the 2500 MHz auction, licences will be auctioned using Tier 3 service areas (58 service areas), except in the Northwest Territories, Yukon and Nunavut, where three Tier 4 service areas will be used.

Specific licence Licences that are treated individually, each with its own characteristics. Specific licences are appropriate when each licence has unique characteristics that determine its value.
Substitute goods X and Y are substitute goods if the demand for X increases when the price of Y increases. Consequently, a bidder may wish to switch its bid from the more expensive good (Y) to the less expensive good (X) when the price of Y increases, as the two goods are deemed similar enough.
Substitution The act of shifting demands across products or packages in response to price changes, increasing the demand of the product that has become relatively more attractive as a result of the price change.
Supplementary bid A bid placed for a single package in the supplementary round.
Supplementary round A single round that occurs after the clock rounds end in a combinatorial clock auction (CCA). Bidders are able to bid on multiple packages in the supplementary round, either submitting bids for new packages or improving their bids for packages that they bid for in the clock rounds.
Tacit collusion Cooperative behaviour among bidders whereby they do not engage in any explicit communication and do not enter into any explicit agreement, but in some manner attempt to coordinate on a better joint outcome than would be attained by purely competitive bidders.
Valid bid A bid that is accepted by the auction system.
Winner determination The process of determining winning bids and prices to be paid using an algorithm.

Annex I — Summary of the Proposals for Consideration

Proposals presented on a licensing framework for Broadband Radio Service (BRS) in the 2500 MHz band.

Proposals related to the service area for Lloydminster (Alberta/Saskatchewan)

3-1 Industry Canada is seeking comments on whether or not the service area boundary for licences in the 2500 MHz band should deviate from the provincial boundary around the City of Lloydminster, (Alberta/Saskatchewan).

Proposals related to the auction format and rules

4-1 Industry Canada is seeking comments on its proposal to use the CCA format, as well as the general attributes outlined above, including:

  • (a) the products available for auction, including the categorization of generic licences;
  • (b) the use of product-specific stages in the assignment round, ordered by population;
  • (c) the combined eligibility point and revealed preference activity rule in the clock rounds, and the revealed preference limit in the supplementary round;
  • (d) the use of a second-price rule;
  • (e) the information to be disclosed during, and post-auction;
  • (f) the guarantee of contiguity for generic licences won within a product; and
  • (g) the contiguity of blocks retained by Industry Canada.

Proposals related to bidder participation

5-1 Industry Canada is seeking comments on its proposed changes to the definition and rules related to associated entities. Specifically, comments are sought on:

  • (a) the types of agreements that should be captured under the definition of associated entities;
  • (b) the level of information to be disclosed to the public prior to the auction;
  • (c) the provision that typical roaming and tower sharing be specifically excluded from the revised definition of associated entities and whether other types of agreements such as the purchase of backhaul capacity should be deemed excluded;
  • (d) the proposal that entities that are deemed associated entities may apply to be treated as separate entities for participation in the auction;
  • (e) the proposal that associated entities may request to have the spectrum aggregation limit apply to them separately, based on an analysis of their association and of whether they intend to compete in the same licence service area;
  • (f) the criteria to be considered in determining whether the entities are competing; and
  • (g) the proposal that no changes be made to the affiliated entities rule.

5-2 Industry Canada is seeking comments on the rules prohibiting collusion that would apply to bidders in the 2500 MHz auction.

Proposals related to the conditions of licence for spectrum licences to be auctioned in the 2500 MHz band

6-1 Industry Canada is seeking comments on its proposal to issue spectrum licences in the 2500 MHz band with a 20-year licence term.

6-2 Industry Canada is seeking comments on the proposed wording of the condition of licence related to the spectrum aggregation limit.

6-3 Industry Canada is seeking comments on the proposed wording of the condition of licence related to transferability and divisibility.

6-4 Industry Canada is seeking comments on the proposed wording of the condition of licence related to eligibility criteria.

6-5 Industry Canada is seeking comments on the proposed wording of the condition of licence related to the treatment of existing spectrum users.

6-6 Industry Canada is seeking comments on the proposed wording of the condition of licence related to radio station installations.

6-7 Industry Canada is seeking comments on the proposed wording of the condition of licence related to the provision of technical information.

6-8 Industry Canada is seeking comments on the proposed wording of the condition of licence related to compliance with legislation, regulation and other obligations.

6-9 Industry Canada is seeking comments on the proposed wording of the condition of licence related to technical considerations, and international and domestic coordination.

6-10 Industry Canada is seeking comments on the proposed wording of the condition of licence related to lawful intercept requirements.

6-11 Industry Canada is seeking comments on the proposed condition of licence related to the research and development requirement.

6-12 Industry Canada is seeking comments on the application of the general deployment condition of licence as stated above. Specifically, comments are sought on:

  • (a) the population coverage, as specified in Table 4, for each licence service area; and
  • (b) the time frame proposed.

6-13 Industry Canada is seeking comments only on the proposed wording of the condition of licence related to mandatory antenna tower and site sharing.

6-14 Industry Canada is seeking comments only on the proposed wording of the condition of licence related to mandatory roaming.

6-15 Industry Canada is seeking comments on the proposed condition of licence related to the requirement for annual reporting.

Proposals related to the conditions of licence for existing BRS licensees in the 2500 MHz band

7-1 Industry Canada is seeking comments on the proposed wording of the condition of licence related to the treatment of existing spectrum users for the existing BRS licensees.

7-2 Industry Canada is seeking comments on the proposed wording of the condition of licence related to the spectrum aggregation limit for existing BRS licensees.

7-3 Industry Canada is seeking comments on the proposed wording of the condition of licence related to transferability and divisibility for existing BRS licensees.

7-4 Industry Canada is seeking comments on the proposed wording of the condition of licence related to eligibility criteria for existing BRS licensees.

7-5 Industry Canada is seeking comments on the proposed condition of licence related to technical considerations, and international and domestic coordination for existing BRS licensees.

7-6 Industry Canada is seeking comments on the proposed wording of the condition of licence related to lawful intercept requirements for existing BRS licensees.

Proposals related to the auction process

8-1 Industry Canada is seeking comments on the proposed opening bids as presented in Table 5.

8-2 Industry Canada is seeking comments on the proposed eligibility points for spectrum licences in the 2500 MHz band, as outlined in Table 6.

8-3 Industry Canada is seeking comments on the proposed pre-auction deposits as outlined above.

Proposals related to the licence renewal process

11-1 Industry Canada is seeking comments on the proposed renewal process for spectrum licences in the 2500 MHz band.

Date modified: