# Licensing Framework for Mobile Broadband Services (MBS) — 700 MHz Band

## Annex A — Glossary of Auction Related Terms

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 on a product.

Allocation stage
A stage of the combinatorial clock 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.

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 complementarities may be strong or weak. The level of complementarities 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 on 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 bidder demands and prices are reported to bidders, giving them the opportunity to adjust subsequent bids based on the information.

Pricing rule
The rule that determines the price to be 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 700 MHz auction, licences will be auctioned using Tier 2 service areas for all frequency blocks.

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.

top of page

## Annex B — The Combinatorial Clock Auction (CCA) Format

1. Industry Canada will use a combinatorial clock auction (CCA) format for the 700 MHz licensing process. A CCA involves a bidding process that includes a price discovery stage, which is similar to the simultaneous multiple round ascending (SMRA) auction format. However, the CCA format also has attributes which remove or reduce some design concerns associated with the SMRA auction format. In particular, in a CCA, bidders are able to bid on packages of licences instead of individual ones, eliminating the risk that bidders may win some but not all of the licences that they desire. This is particularly important given the regional nature of the licences to be auctioned and the complementarities that exist between these licences.

2. Generic licences and anonymous bidding are other features that will be used in the 700 MHz auction. Generic licences are blocks of spectrum that are similar in terms of frequency location in the band, block size, technology and interference constraints and are of comparable value, such that they can be grouped together in a "single category" for bidding purposes in the auction. The use of generic licences will decrease bidding complexity by reducing the number of categories available to bid on in the auction, and will enhance substitution among licences. The use of anonymous bidding will reduce the potential for gaming. Pricing rules and activity rules that encourage truthful bidding throughout the auction process, i.e. bidding in a manner that is consistent with how a bidder truly values the package, will further improve the process.

### 1. Overview of the CCA

3. A CCA is comprised of two stages, the allocation stage and the assignment stage (Figure 1) . In the allocation stage, the number of spectrum licences that a bidder will win in each service area and the base price to be paid by each winning bidder are determined. Where generic licences are offered, an additional stage is needed to determine the specific frequencies that will be assigned to each winning bidder. This stage is referred to as the assignment stage.

### Figure 1 — CCA Process

Description of Figure 1

Figure 1 is a flowchart representing a visual description of the combinatorial clock auction (CCA) process and portraying the sequence of steps included in the process. The CCA is comprised of two stages, the allocation stage and the assignment stage.

The allocation stage includes two steps, the first of which is called the clock rounds and the second is called the supplementary round. The clock rounds are a series of rounds in which bidders submit bids on categories of licences. In any round, if there is excess demand in any category of licences, the price of those licences will increase and the clock rounds will continue until such a time as there is no excess demand in any category of licences. When there is no longer excess demand in any category of licences, the process will move to the supplementary round. The supplementary round is a single round where bidders have the opportunity to make additional bids.

At the end of the allocation stage, the winning bidders and the base prices are determined.

If there were no generic licences offered or won in the allocation stage, an assignment stage is not necessary and the auction ends at the conclusion of the allocation stage.

If there were any generic licences offered and won in the allocation stage, the process then moves to the assignment stage. At the end of the assignment stage, winning assignments and final prices are determined. This signifies the end of the auction.

### 2. The Allocation Stage

4. The allocation stage of the auction determines the winning bidders and the number of licence blocks that they have won. The allocation stage is divided into two phases: the clock rounds and the supplementary round. All valid bids submitted during both phases of the allocation stage are used to determine the winning packages and base prices.

5. The clock rounds allow for price discovery, helping to reduce a bidder’s uncertainty regarding the value of the licences. Bidders are able to respond to the changes in prices accordingly, shifting their bids to licences that continue to be consistent with their business objectives.

6. During each clock round, bidders are only able to bid on one package of licences; however, there may be other packages that they would be interested in winning. The supplementary round provides bidders with an opportunity to improve bids that they placed in the clock rounds and/or to submit bids for packages that they were eligible to bid on but unable to submit in the clock rounds.

7. There is a spectrum cap of two blocks of paired spectrum in each service area. Therefore, bidders will be unable to bid on more than two licences of paired spectrum in each service area. Large wireless service providers are further limited in that they can only bid on one paired licence in each service area among blocks B, C, C1 and C2. This cap on large wireless service providers does not, however, include block A. (It should be noted that large wireless service providers are defined as companies with 10% or more of the national wireless subscriber market share, or 20% or more of the wireless subscriber market share in the province of the relevant licence area. The subscriber market share for Ontario will apply for the licence area 2-06, Eastern Ontario and Outaouais. For the Tier 2-14 licence area (Yukon, Northwest Territories and Nunavut), only the national market share criteria will apply.)

### 3. Clock Rounds

8. The allocation stage begins with the clock rounds. Licences or sets of generic licences (substitutable licences of comparable value) are defined prior to the auction, and are separate categories in each service area in the auction.

9. For the 700 MHz auction, there will be four categories of licences in each of the 14 service areas:

• block A in the lower 700 MHz band (one licence of 6+6 MHz)
• blocks B and C in the lower 700 MHz band (two generic licences of 6+6 MHz)
• blocks D and E in the lower 700 MHz band (two generic licences of 6 MHz)
• blocks C1 and C2 in the upper 700 MHz band (two generic licences of 5+5 MHz)

Table 1 — Clock Rounds
A B C D E C1 C2
Paired   Paired
(Generic)
Unpaired
(Generic)
Paired
(Generic)

10. A category in a given service area is referred to as a product. Given that there will be four categories of licences in each of the 14 service areas, there will be 56 products (4 x 14) in the 700 MHz auction.

11. The licences are auctioned simultaneously over multiple clock rounds. In each round and for each product, bidders indicate the number of licences in each product on which they would like to bid given the prevailing prices. For a product in any of the categories containing two generic licences, the bid is "0," "1" or "2." For a product in the block A category, which contains only one licence, the bid is "0" or "1." All of the individual bids placed by a bidder in a given round are considered to be a single package bid, creating an all-or-nothing bid. The price of the package bid is equal to the sum of the bids for individual products, evaluated at the prevailing clock prices.

12. When there is excess demand for a product, its price increases in the next round. There is excess demand for a product when the number of licences that are bid for exceeds the number of licences available.

13. To remain in the auction, a bidder must submit a valid bid with a value greater than zero for at least one licence in the first clock round. This bid cannot be withdrawn and will be part of the bids considered in determining the assignment of licences at the end of the allocation stage. The last valid bid submitted during each clock round is binding and will be considered in determining both winning packages and base prices after the supplementary round ends.

14. Bidding remains open in the clock rounds on all products until there is no excess demand for any of the products.

### 4. Conclusion of Bidding in the Clock Rounds

15. The clock rounds end when there is a round in which there is no excess demand for any of the products. This round is referred to as the final clock round. The package on which a bidder placed a bid in the final clock round is referred to as its final clock package. At this point, Industry Canada will announce that the clock rounds have ended and that the auction will proceed to the supplementary round (see Section 9 of this annex).

### 5. Information in the Clock Rounds

16. Before the start of each clock round, each bidder will receive information regarding its own bids from the previous round and the number of eligibility points that it will have in the next round. In addition, all bidders will be informed of the aggregate demand for each product from the previous round and the prices for each product in the next round. Bidders will not be informed about the individual bids submitted by other bidders or the remaining eligibility of other bidders. In addition, information about the aggregate demand from the final clock round will be withheld until the end of the auction.

### 6. Bid Increments

17. In the first clock round, the price of each licence will be equal to the opening bid price listed in Table 3 in Section 4.2 of the Framework.

18. During subsequent clock rounds, if there is excess demand for a given product, the price of the given product will increase in the next round. Industry Canada will use activity‑based increments where the increment for each product is based on the level of excess demand for the product during the previous clock round. Products that generate greater excess demand are subject to a larger bid increment than products that generate less excess demand. Prices will increase more quickly for products with higher demand, potentially shortening the length of the auction. If there is no excess demand, the price of the product will not increase in the next clock round.

19. The bid increments for the 700 MHz auction will be in the range of 1-20% of prices in the previous clock round (rounded to the nearest thousand). Further information on the calculation of bid increments will be published in the information package provided to qualified bidders.

### 7. Eligibility Points

20. Each of the 98 licences has been assigned a specific number of eligibility points (points) that are related to the population covered by the licence, its bandwidth and the estimated value of the spectrum. Generally, one point has been assigned per 5 MHz of spectrum per 100,000 in population count. The five service areas of Southern Quebec, Eastern Ontario and Outaouais, Southern Ontario, Alberta and British Columbia are the exception. For these five service areas, the eligibility points per paired spectrum block have been adjusted in proportion to the opening bid prices. Section 4.3 of the Framework lists the eligibility points associated with the paired and unpaired blocks of spectrum being auctioned, as well as the population of their respective service areas.

21. Eligibility points are used in the determination of the pre‑auction financial deposits and in the activity rules during the auction, influencing the bids that bidders can submit. In their application, each potential bidder must indicate the total number of "points" worth of licences on which they wish to bid. This number defines a bidder’s initial level of eligibility points and, hence, the maximum number of licences that a bidder is eligible to bid on at the start of the auction.

22. Bidder eligibility points cannot be increased once the auction has started.

### 8. Activity Rule in the Clock Rounds

23. An activity rule has been established to encourage truthful bidding throughout the clock rounds. This facilitates the price discovery process, allowing bidders to make changes to their bidding strategies dynamically throughout the auction, in response to increasing prices. The activity rules discourage a bidder from misrepresenting its true demand, as doing so will limit the bidder’s ability to bid on what it really wants later in the auction.

24. A revealed preference/eligibility point hybrid activity rule will be used for each clock round. It comprises both an eligibility‑based activity rule and a revealed preference activity rule.

25. The eligibility‑based activity rule is similar to the rule that has been used in previous SMRA auctions. Bidders begin each clock round with a set number of eligibility points and these determine the maximum activity level for that clock round. For example, a bidder with 100 eligibility points can bid on licences whose total sum of associated points is 100 or less.

26. The eligibility point activity requirement for the 700 MHz auction is 100%. Specifically, in each round, a bidder is required to bid on licences whose total sum of associated points is equal to 100% of its eligibility points if it wishes to maintain that eligibility level in the subsequent round.

27. The eligibility‑based activity rule considers the size of the package that the bidder is bidding on, where size is the sum of the eligibility points for each licence in the package. The eligibility‑based activity rule requires bidders to bid on packages of the same size or smaller as prices rise. When a bidder switches to a package that is smaller than the package that it has previously bid on, (that is, has fewer eligibility points worth of licences), the bidder’s eligibility is reduced. A clock round in which a bidder’s eligibility is reduced is called an eligibility‑reducing round. These rounds play a special role in the activity rules of the 700 MHz auction.

28. Bidders are required to have eligibility points to bid during the clock rounds. If a bidder’s eligibility drops to zero during the clock rounds, the bidder will no longer be able to bid in the clock rounds, but will be able to bid in the supplementary round provided that it placed at least one valid bid with a value greater than zero during the clock rounds.

29. However, there are some shortcomings with using only the eligibility‑based activity rule. Price discovery might be lessened, as there is an incentive for bidders to choose only larger packages when prices are low, rather than a package that may work better for them, so that they maintain a higher number of eligibility points for later in the auction. Furthermore, an eligibility‑based activity rule may prevent a bidder from making a desirable substitution to a package that is larger in terms of associated eligibility points, but which has become relatively less expensive. In such a case, the eligibility‑based activity rule would prevent the bidder from bidding on its most preferred package.

30. A revealed preference activity rule will lessen these problems, as it allows bidders to exceed their eligibility points in order to bid on packages that have become comparatively less expensive. Revealed preference refers to the information that a bidder discloses regarding its inclination toward one package versus another. In particular, if a bidder chooses one package over another given a certain price differential between the two packages, then the bidder should always choose the same package given the same price differential.

31. For example, suppose that a bidder desires either a smaller package, X, or a larger package, Y, but not both. At the current prices, X is preferred, but in subsequent rounds, the prices for the licences in X increase much faster than the prices for the licences in Y. As a result, the bidder prefers Y to X at the new prices. The revealed preference activity rule allows the bidder to switch from X to Y because Y is now the better value. In contrast, the eligibility point rule would not allow the switch because Y is larger than X. This example illustrates the problem with using the eligibility‑based activity rule exclusively and the advantage of using the eligibility‑based activity rule in combination with the revealed preference activity rule.

32. However, bidding on a larger package will not increase the bidder’s eligibility in subsequent rounds. Furthermore, a bidder will never be able to bid on a package with associated eligibility points exceeding the bidder’s initial eligibility. For an algebraic description of the revealed preference activity rule in the clock rounds, see Annex D. For an example of the revealed preference activity rule in the clock rounds, refer to Annex C.

33. Using both an eligibility‑based activity rule and a revealed preference activity rule will provide extra flexibility to the bidder. A bidder can continue to bid just as it would under the eligibility‑based activity rule. In addition, the bidder is given some extra flexibility to bid on a larger package provided that the larger package has become relatively less expensive, providing more opportunity for bidders to adjust their bids in response to information received in the clock rounds.

### 9. Supplementary Round

34. The second phase of the allocation stage is the supplementary round. The supplementary round is a single round process in which bidders have the opportunity to place additional bids on packages, subject to constraints that are based on the bids that they placed in the clock rounds (see Section 10 of Annex B). These additional bids could be used to improve bids on packages previously submitted in the clock rounds and/or to submit bids for which they were eligible to bid on, but unable to submit in the clock rounds.

35. In the clock rounds, a bidder is allowed to bid on only one package of licences per round. As there may be other packages that a bidder would be interested in winning, the supplementary round provides bidders with an opportunity to place their best and final bids on packages that they were willing and eligible to bid on in the clock rounds, but did not necessarily bid on. These supplementary bids are critical in ensuring that the licences are allocated to the bidders who value them the most and that winning bidders pay an amount that is sufficient to ensure that no other bidder or group or bidders was willing to pay more for the licences.

### 10. Activity Rule in the Supplementary Round

36. The activity rule in the supplementary round encourages truthful bidding throughout the allocation stage of the auction and ensures that supplementary bids are consistent with preferences expressed in the clock rounds.

37. Any bidder that placed at least one valid bid with a value greater than zero in the clock rounds may submit bids in the supplementary round. However, a bidder is not required to submit bids in the supplementary round.

38. All licences are available for bidding in the supplementary round, so that bidders can improve on bids submitted during the clock rounds or submit bids for packages of licences that they did not bid on in the clock rounds.

39. A bidder can only make one supplementary bid for a given package of licences. The limit on the number of different supplementary round packages that a bidder will be allowed to place will be announced after the bidder qualification has occurred, but will be no less than 500 different packages. A bidder will not be permitted to make a supplementary bid on a package comprising no licences.

40. The bid amount for a supplementary bid must be at least the sum of the opening bid prices for all the licences included in the package. Furthermore, if a bidder submitted a bid on a certain package in the clock rounds, the supplementary bid amount must be greater than the bidder’s highest bid for that package.

41. Each bid in the supplementary round must satisfy the following revealed preference activity rule.

42. Revealed Preference Limit: There is no limit on the supplementary bid amount for the final clock package, which is the package that the bidder bid on in the final clock round. All other supplementary bids must satisfy revealed preference with respect to the final clock round, regardless of whether the supplementary bid package is worth more or less eligibility points than the bidder’s eligibility in the final clock round.

43. In addition, supplementary bids for packages that exceed the bidder’s eligibility in the final clock round must satisfy revealed preference with respect to each eligibility‑reducing round, beginning with the last round in which the bidder had sufficient eligibility to bid on the package. The application of the revealed preference limit could have the effect of creating a chain of constraints on the dollar amount of a supplementary bid relative to the dollar amount of other supplementary bids.

44. The revealed preference limit with respect to the final clock package provides the bidder with an incentive to bid on the most preferred package throughout the clock rounds. This is because supplementary bids are limited by bids submitted in the clock rounds. Given that the bidder does not know which round will be the final clock round, the bidder will be motivated to always bid truthfully to improve its chance of winning its most preferred package; otherwise, the bidder will be constrained in the supplementary round.

45. Non‑disclosure of aggregate demand: At the end of the final clock round, the aggregate demand from the final clock round will not be provided to bidders.

46. This activity rule provides the strongest incentive for truthful bidding during the supplementary round, encouraging bidders to bid based on their valuations rather than on any expected guarantee of winning their final clock package. The structure of the supplementary round bidding constraints guarantees that the final clock allocation will not change if there are no unallocated licences. If there are unallocated licences, each bidder will be allocated its final clock package if it has submitted a supplementary bid that increases the dollar amount of its final clock package by at least the value of the unallocated licences as evaluated at the final clock prices less the opening bid prices of the unallocated licences. However, as the aggregate demand in the final clock round will not be available to bidders as they go into the supplementary round, bidders will not know the exact amount that they need to bid to ensure that they win their final clock package, encouraging bidders to bid truthfully on the packages that are of interest to them. Furthermore, the ability to ensure this allocation may be compromised if any other supplementary bid does not include, at a minimum, all of the licences contained in the bidder’s final clock package.

47. Further information on the process for submitting supplementary bids will be available in the information package provided to qualified bidders.

### 11. Determining the Winning Packages in the Allocation Stage

48. All valid bids received from bidders in the clock rounds and in the supplementary round are considered for the determination of winning packages. In addition, a reserve bid for every licence, at the opening bid price, will be included in the determination of winning bidders at the end of the allocation stage. In this process, it is as if Industry Canada is a bidder in the auction, placing a bid on every licence at the opening bid price. The purpose of including a reserve bid for every licence is to ensure that the incremental value that a bidder would be prepared to pay for an additional licence is at least the opening bid price of that licence. The reserve bids will not be treated as a package, but rather as having been placed by different bidders so that any number of reserve bids can be selected in the winning combination.

49. A solver will be used to identify the highest value combination of valid bids subject to the requirements that each bidder wins no more than one of its packages and that each licence is allocated no more than once. If there is only one combination of bids that meets the criteria, this will be the winning outcome that determines the winning packages and winning bidders. For details, see Mathematical Formulations for Winner and Price Determination in the Combinatorial Clock Auction for Mobile Broadband Services (MBS) — 700 MHz Band (http://www.ic.gc.ca/eic/site/smt- gst.nsf/eng/sf08697.html).

50. If there is more than one combination of valid bids having the same highest value, the tie will be resolved first, by minimizing the number of "lost licences," where a lost licence is a licence that was included in the bidder’s final clock package, but is not included in an alternate package that could be assigned to the bidder. The rationale for selecting the combination of valid bids that minimizes the number of lost licences as the first tie‑breaking rule is to select an assignment that is the most similar to the final clock allocation.

51. If there is still a tie, the second tie‑breaking rule is to select the combination of valid bids that includes the greatest number of associated eligibility points. Note: If reserve bids are part of the winning combination, the eligibility points associated with the reserve bids will not count towards the eligibility points of the winning combination. This is to maximize the quantity of spectrum that is allocated. If, subsequently, there is still a tied outcome, the tie will be broken by a pseudo‑random number generator built into the auction software.

### 12. Determining the Base Price in the Allocation Stage

52. The base price is the minimum amount that the winning bidders will pay for their generic winning packages; it does not include the additional, incremental amount that winning bidders may pay for specific licences as determined in the assignment stage should there be generic licences included in the winning allocation stage package. The base price is determined using all valid bids submitted by all bidders during the allocation stage.

53. Industry Canada will use a second-price rule to calculate the base prices such that winning bidders, individually and collectively, will pay an amount that is sufficient to ensure that there is no other bidder or group of bidders prepared to pay more for the licences. This amount is typically less than the actual winning bid submitted in the allocation stage, either in the clock rounds or the supplementary round, and must be greater than or equal to the total sum of the opening bid prices for the combination of licences included in their winning package. The benefit of using a second-price rule is that it encourages bidders to bid truthfully, potentially leading to a more efficient outcome.

54. Industry Canada will apply bidder-optimal core prices and use the “nearest Vickrey” approach to determine the base prices. In some cases, the second price (Vickrey price) may not be high enough to ensure that there is no alternative bidder or group of bidders prepared to pay more for the licences in question, and so an additional payment above Vickrey prices is required. In the event that such a payment is required, the portion of the additional payment to be paid by each winning bidder will be weighted based on the winning package sizes evaluated at the opening bid prices. Further information on the determination of base prices can be found in Annex E.

### 13. Information at the end of the Allocation Stage

55. At the end of the allocation stage, after the results have been verified, each bidder will be informed of its own winning packages, along with the base price to be paid for its package.

56. At this point, bidders will know with certainty the number of licences in each product that they have won; however, where there are generic licences, they will not necessarily know the specific licences that they have won.

### 14. The Assignment Stage

57. As there are generic licences, the auction will then advance to the assignment stage, where the specific assignment of the generic licences will be determined. Only bidders that have won one or more generic licences during the allocation stage will have the option to participate in the assignment stage.

58. Industry Canada will run three sequential assignment rounds (i.e. one for each category of generic licences): blocks B and C; blocks D and E; and blocks C1 and C2. This is to allow bidders that have won licences in the same category of generic licences across multiple service areas to express their preference for particular licences.

59. In each assignment round, winning bidders are allowed to submit multiple top-up bids for the specific licence(s) that they most prefer in each service area, using a single round process for each category. Each bid reflects the incremental value that the bidders place on winning these particular frequency blocks.

60. Winning bidders do not have to place bids in the assignment stage if they do not have an assignment preference, as they are guaranteed the number of generic licences that they have already won. However, a bidder is not guaranteed to win the same block across all service areas and risks winning different specific licences in different service areas if it does not submit any assignment bids, as each winning bidder has both a right and an obligation to purchase one of the licences in each product presented to it in the assignment round(s).

61. For example, in the 700 MHz auction, if two bidders each win a licence in the C1 and C2 category in a given service area, then each will have an opportunity to submit an additional bid for either the C1 or the C2 licence, depending on its preferred assignment. However, if one of the two bidders does not have a preference between the two licences, it does not have to submit assignment bids.

62. A solver will be used to identify the combination of specific assignments of licences that result in the highest bid amount subject to the assignment stage restriction (see Section 15 of this annex). In the event of a tied outcome with more than one specific assignment producing the same total value, the tie will be broken by a pseudo-random number generator built into the auction software.

63. Similar to the determination of base prices in the allocation stage, a second-price rule will be used to determine the assignment price to be paid for the assignment of specific licences such that winning bidders will pay an amount sufficient to ensure that there is no other bidder or group of bidders prepared to pay more for the licence(s).

64. The additional amount to be paid for the assignment of specific licences, known as the assignment price, is calculated for a package of licences within one category, not the individual licences. In general, given the pricing rules, the assignment price of each winning assignment stage bid will be equal to or less than the corresponding winning bid amount; however, it is likely that it will be less than the winning bid amount and could even be zero.

65. Industry Canada will apply bidder-optimal core prices and use a “nearest Vickrey” approach to determine assignment prices. In the event that an additional payment above Vickrey prices is required, the portion of the additional payment to be paid by each winning bidder will be weighted based on the winning package sizes evaluated at the opening bid prices. Further information on the determination of assignment prices can be found in Annex E.

### 15. Restrictions in the Assignment Stage

66. The assignment options will be limited such that where a bidder wins block A and one of blocks B and C in a given service area, then the bidder will automatically be assigned blocks A and B in that service area.

67. Further information on the process for submitting assignment round bids will be available in the information package provided to qualified bidders.

### 16. Information at the end of each Assignment Round

68. Following the end of each assignment round, after the results have been verified, participating bidders will be notified of the specific licences that they have won and the assignment price to be paid. This will allow bidders who have won licences across multiple categories to know their own results from one assignment round before participating in a subsequent assignment round.

### 17. Final Price

69. Following the determination of the winning assignment bids, Industry Canada will determine the final price to be paid by each winning bidder. The final price to be paid by a winning bidder is equal to the base price plus any associated assignment prices for a bidder’s winning package.

### 18. Information at the end of the Assignment Stage

70. Following the end of the assignment stage, winning bidders will be notified of the specific licences that they have won, as well as the final price to be paid.

### 19. Information at the end of the Auction

71. The following information will be made publicly available following the conclusion of the auction:

• the list of winning bidders, licences won and prices to be paid;
• the bids submitted by each bidder in every clock round, including their identity;
• the supplementary bids submitted by each bidder, including their identity; and
• the assignment bids submitted by each bidder, including their identity.

top of page

## Annex C — Example of the Activity Rules

1. For the purposes of this example, only a single service area and two categories within the 700 MHz band will be considered: blocks C1/C2 and blocks D/E. Within the given service area, suppose that each C1/C2 licence has an eligibility of 50 points, whereas each D/E licence has an eligibility of 25 points.

2. A single bidder, Bidder A, will also be considered. Bidder A would like to obtain two C1/C2 licences. This package will be denoted as (2, 0). However, if the price of the package with two C1/C2 licences exceeds the price of a package with one C1/C2 licence and one D/E licence by more than $500,000, then Bidder A would prefer a package with one C1/C2 licence and one D/E 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 C1/C2, but will switch to one D/E licence if the price of one C1/C2 licence, denoted as package (1, 0), exceeds the price of one D/E 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 blocks C1/C2 is$1,000,000 per licence, and for D/E, it is $600,000 per licence. The price of a package with two C1/C2 licences is$2,000,000, whereas the price of a package with one C1/C2 licence and one D/E licence is $1,600,000 (a price difference of$400,000). As Bidder A prefers two C1/C2 licences unless the price difference is greater than $500,000, Bidder A will bid on two C1/C2 licences, package (2, 0): Table 1 — Round 1 CategoryPriceBidEligibility Points C1/C2$1,000,0002100
D/E$600,00000 Total Package$2,000,000(2, 0)100

### Round 2

6. In Round 1, several other bidders shared Bidder A’s preference for C1/C2, whereas few bidders bid on D/E. As a result, the prices in Round 2 are $1,200,000 for C1/C2 and$650,000 for D/E. The price of a package with two C1/C2 licences is $2,400,000, whereas the price of a package with one C1/C2 licence and one D/E licence is$1,850,000 (a price difference of $550,000). As Bidder A prefers one C1/C2 licence and one D/E licence when the price difference is greater than$500,000, Bidder A now bids on one licence from each category, package (1, 1), thereby reducing eligibility from 100 to 75 points.

Table 2 — Round 2
CategoryPriceBidEligibility Points
C1/C2$1,200,000150 D/E$650,000125
Total Package$1,850,000(1, 1)75 ### Round 3 7. In Round 2,the low price of D/E caused many bidders to switch demand to that category. As a result, the price of D/E increased at a faster rate than the price of C1/C2. The Round 3 prices are$1,250,000 for C1/C2 and $800,000 for D/E. The price of a package with two C1/C2 licences is$2,500,000, whereas the price of a package with one C1/C2 licence and one D/E licence is $2,050,000. This price difference is only$450,000, so Bidder A would prefer to switch back to bidding on two C1/C2 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 on 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‑reducing round:

Table 3 — Round 3
CategoryPriceBidEligibility Points
C1/C2$1,250,0002100 D/E$800,00000
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 on the package (2, 0). ### Round 4 12. In Round 4, the price of C1/C2 increases to$1,400,000, whereas the price of D/E increases to $1,000,000. The price of a package with two C1/C2 licences is$2,800,000, whereas the price of a package with one C1/C2 licence and one D/E licence is $2,400,000. This price difference is only$400,000 so Bidder A prefers the same package as in Round 3:

Table 4 — Round 4
CategoryPriceBidEligibility Points
C1/C2$1,400,0002100 D/E$1,000,00000
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 categories, with C1/C2 at$1,650,000 and D/E at $1,200,000. As a result, both of the 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 C1/C2 ($1,650,000) is$450,000 greater than the price of D/E ($1,200,000), Bidder A places a bid on one C1/C2 licence, package (1, 0), given that Bidder A prefers one C1/C2 licence when the price of one C1/C2 licence exceeds the price of one D/E 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.

Table 5 — Round 5
CategoryPriceBidEligibility Points
C1/C2$1,650,000150 D/E$1,200,00000
Total Package$1,650,000(1, 0)50 ### Round 6 17. In Round 6, the price on C1/C2 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 D/E licence, package (0, 1), as Bidder A prefers one D/E licence when the price of one C1/C2 licence exceeds the price of one D/E licence by more than$500,000. This bid further reduces Bidder A’s eligibility to 25 points:

Table 6 — Round 6
CategoryPriceBidEligibility Points
C1/C2$1,800,00000 D/E$1,250,000125
Total Package$1,250,000(0, 1)25 ### Round 7 18. In Round 7, the price of D/E increases at a faster rate than C1/C2. At Round 7 prices, Bidder A prefers one C1/C2 licence, as the price of one C1/C2 licence exceeds the price of one D/E licence by less than$500,000, causing Bidder A to again desire to switch:

Table 7 — Round 7
CategoryPriceBidEligibility Points
C1/C2$1,850,000150 D/E$1,400,00000
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, Bidder A’s eligibility and its bids placed up to this point: Table 8 — Summary Category Price Round 1 Round 2 Round 3 Round 4 Round 5 Round 6 Round 7 C1/C2$1,000,000 $1,200,000$1,250,000 $1,400,000$1,650,000 $1,800,000$1,850,000
D/E $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) (1, 0) Eligibility 100 100 75 75 75 50 25 Activity 100 75 100 100 50 25 50 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 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 C1/C2 licence. Note that if there had only been an eligibility point activity rule in the clock stage, Bidder A would likely have a less desirable final clock package of one D/E licence. ### Revealed Preference Constraints for the (1,1) Package 26. Now, suppose that Bidder A wishes to increase its bid on the package (1, 1) (i.e. one C1/C2 licence and one D/E licence) to its maximum budget of$2,800,000. This package is worth 75 eligibility points, which exceeds Bidder A’s eligibility of 25 eligibility points in the final clock round. Therefore, Bidder A must satisfy revealed preference with respect to the final clock round 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). The last round in which Bidder A had sufficient eligibility to bid on the package (1, 1) was Round 5 and it subsequently reduced eligibility in Round 6. Therefore, Bidder A’s supplementary bid on the package (1, 1) must meet the revealed preference constraints with respect to Round 5Round 6 and Round 7.

27. The revealed preference constraints are as follows:

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

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 7

(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

28. Without submitting a supplementary bid increasing the amount bid for its final clock package (1, 0) or for the (0, 1) package, the highest supplementary bid that Bidder A can place on the (1, 1) package is $3,050,000, allowing Bidder A to place the$2,800,000 bid.

### Revealed Preference Constraints for the (0, 1) Package

29. The (0, 1) package is also subject to revealed preference constraints. 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

30. So, without submitting a supplementary bid to increase the amount bid for its 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 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.

top of page

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

### Revealed Preference in the Clock Rounds

1. Under the activity rule in the clock rounds, a bidder may, at any time during the clock rounds, place a bid on any package that is within its 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 and as long as the bidder still has some eligibility points. 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. There will be 56 products in the 700 MHz auction representing the four categories of licences, block A, blocks B and C, blocks D and E and blocks C1 and C2 in each of the 14 Tier 2 service areas.

3. As per the equation below, 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:

$\sum^m_{i=1} (Q_{t,i} ×(P_{t,i} - P_{s,i})) \leq \sum^m_{i=1} (Q_{s,i} ×(P_{t,i} - P_{s,i}))$

where:

• i” indexes the products;
• m” is the number of products, where the number of products for the 700 MHz auction is 56;
• 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. This exception also applies where a bidder’s final clock package exceeded its eligibility in the final clock round due to the revealed preference activity rule.

6. All supplementary bids must satisfy revealed preference with respect to the final clock round regardless of whether the supplementary bid package is smaller or larger, in terms of eligibility points, than the bidder’s eligibility in the final clock round.

7. In addition, supplementary bids for packages that exceed the bidder’s eligibility in the final clock round must satisfy revealed preference with respect to the last clock round in which the bidder was eligible to bid on the package and every subsequent clock round in which the bidder reduced eligibility.

8. 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 on package Qs, whether the highest dollar amount was placed in a clock round or the supplementary round.

9. A supplementary bid B on package Q satisfies revealed preference 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 round s, 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 package Q;
• Qs,i is the quantity of the ith product in 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 on package Q; and
• Bs is the highest dollar amount bid on package Qs either in a clock round or in the supplementary round.

10. 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 package Q.

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

1. for any package Q, the dollar amount B must satisfy the revealed preference constraint, as specified in paragraph 8 above with respect to the final clock round and with respect to every eligibility-reducing round equal to T(Q) or later.

12. Note that, in the application of paragraph 8, the package Qs may itself be subject to a revealed preference constraint 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.

13. See Annex C for an example of the revealed preference limit in the supplementary round.

top of page

## Annex E — Pricing Rules

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 will use a second‑price rule to determine the prices to be paid by winning bidders. More specifically, Industry Canada will 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. A second‑price rule will be used 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 individual 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, subtract Bidder J’s winning bid (value A). Next, recalculate the winning combination of packages for the hypothetical situation in which all of Bidder J’s bids are excluded, as if Bidder J had not participated (Value B). The Vickrey price for Bidder J is calculated 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. This determines the minimum amount that the winning bidder could have bid and still have won the package, given the bids of all other bidders.

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 so that it is 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:

1. 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 bid.
2. 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 meets the first and second conditions, this determines the base prices for the allocation stage.
3. Third condition:  If there is more than one set of base prices that fulfils the first and second conditions, the set (or sets) of base prices minimizing the sum of base prices across winning bidders is (are) selected. If there is only one set of base prices satisfying these three conditions, this set determines the base prices for the allocation stage.
4. Fourth condition:  If there is more than one set of base prices that satisfies 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 bid 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 Spectrum Auction Design paper by P. Cramton (http://www.cramton.umd.edu/papers2005 -2009/cramton-spectrum-auction-design.pdf).

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 The bids of the five bidders are represented in Figure 2. 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.

To calculate the Vickrey price for Bidder 1, its winning bid ($28) is subtracted from the value of the winning combination ($48), resulting in $20. Next, the winning combination of packages is recalculated for the hypothetical situation in which Bidder 1’s bids are excluded. The best assignment, excluding Bidder 1, assigns licence A to Bidder 4 at$14 and licence B to Bidder 2 at $20, resulting in$34. The Vickrey price for Bidder 1 is the value of the winning combination of packages with all Bidder 1’s bids excluded ($34) less the sum of the winning allocation stage bids for all bidders other than Bidder 1 ($20), that is, its Vickrey price is $14 ($34 – $20). Similarly, to calculate the Vickrey price for Bidder 2, its winning bid ($20) is subtracted from the value of the winning combination ($48), resulting in$28. Next, the winning combination of packages is recalculated for the hypothetical situation in which Bidder 2’s bids are excluded. The best assignment, excluding Bidder 2, assigns licence A to Bidder 1 and licence B to Bidder 5, resulting in a value of $40. The Vickrey price for Bidder 2 is the value of the winning combination of packages with all Bidder 2’s bids excluded ($40) less the sum of the winning allocation stage bids for all bidders other than Bidder 2 ($28), that is, its Vickrey price is$12 ($40 –$28).

### Assignment Prices

10. Industry Canada will run three sequential assignment rounds, if necessary, one for each category of generic licences, blocks B and C, blocks D and E and blocks C1 and C2. This is to allow bidders that have won licences in the same category of generic licences across multiple service areas to have the opportunity to express their preference for particular licences.

11. The assignment bid is essentially a package bid for the locations of all licences within a category. For each category that includes two generic licences, that is, blocks B and C, blocks D and E and blocks C1 and C2, assignment prices will be determined from the set of assignment stage bids for the category of licences.

12. A second‑price rule will be used to calculate assignment prices. The assignment price is attributable to the entire collection of licences assigned within a given assignment round and not to individual licences that comprise the package. For example, if a bidder wins one B/C licence nationwide, in the B/C assignment, round the bidder is able to submit multiple bids to be assigned specific licences in every service area. In this case, the assignment price is for the group of licences rather than the specific licence in each service area.

13. 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, 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 that 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.

14. The assignment stage prices for each winning assignment bid must satisfy the following conditions:

1. First condition: The assignment prices must be greater than or equal to zero, and not more than the dollar amount of the winning assignment stage bid.
2. 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.
3. Third condition: If there are many sets of assignment prices that fulfil the first and second conditions, the set (or sets) of assignment prices minimizing the sum of assignment prices across winning assignment stage bids is (are) selected. If there is only one set of assignment prices that satisfies these three conditions, this determines the assignment prices.
4. 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.

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

Date modified: