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

## Annex A — 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. 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 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.

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

1. Industry Canada is proposing to use a combinatorial clock auction (CCA) format for the 700 MHz band. A CCA is a bidding process that includes a price discovery stage, similar to the SMRA auction format. However, the CCA format also has attributes which remove or reduce some design concerns associated with the SMRA format. In particular, in a CCA, bidders are able to bid for 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. Other attributes are being proposed for the 700 MHz auction, such as the use of generic licences and anonymous bidding. 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 strategies. 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 is determined, as well as the base price to be paid by each winning bidder. 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 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, however, does not include Block A. The auction software will not allow bidders to submit a bid that exceeds their spectrum cap(s).

### 3. Clock Rounds

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

9. For the 700 MHz auction, Industry Canada is proposing 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)
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 the proposal of four categories of licences in each of the 14 service areas, 56 products (4x14) are proposed for 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 bids exceeds the number of licences available.

13. To remain in the auction, a bidder must submit a valid bid 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. All valid bids submitted during the clock rounds are binding and will be considered in determining both winning packages and base prices after the supplementary round ends.

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

### 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).

16. In the final clock round, all licences may be tentatively allocated. Conversely, there may be some unallocated licences in the final clock round due to a licence never having received a bid, and/or bidders reducing or substituting their demands in any clock round, including the final clock round.

17. If all of the licences are tentatively allocated, then the bids placed in the final clock round are the provisional winning bids. If there are still some unallocated licences, a bidder can guarantee that it will win its final clock package by submitting a supplementary bid that increases the dollar amount of its final clock package bid by at least the final clock price of the unallocated licences Begin new text less the opening bid prices of the unallocated licences. This guarantee 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.

### 5. Information in the Clock Rounds

18. At the beginning of each clock round, bidders have access to sufficient information to permit price discovery and inform their bidding strategy. This information includes their own bids from the previous round and the number of eligibility points that they will have in the next round, as well as the aggregate demand for each product from the previous round, and the prices for each product in the next round. Bidders are not informed about the individual bids submitted by other bidders or the remaining eligibility of other bidders. This should address some of the concerns raised during previous auctions regarding the potential for gaming.

### 6. Bid Increments

19. Industry Canada is consulting on the opening bid amounts for each of the licences being auctioned. The opening bid amounts being proposed can be found in Table 4, Section 7.2 of the main document. In the first clock round, the price for each licence is equal to the decided upon opening bid price to be stated in the final licensing document.

20. During subsequent clock rounds, if there is excess demand for a given product, the prices for the given product increase in the next round. Industry Canada will use activity-based increments as a mechanism to determine the bid increments. The increment for each product is based on the excess demand for the product during the previous round. Products that generate greater excess demand are subject to a larger bid increment than products that generate less excess demand, all other things being equal. Bid increments increase more quickly for products with higher demand, potentially shortening the length of the auction. If there is no excess demand, the price for the product does not increase in the next round.

21. Industry Canada will decide on the bid increments for the 700 MHz auction. Details concerning the calculation of bid increments will be included in the final licensing framework.

### 7. Eligibility Points

22. 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 7.3 of the main document lists the proposed eligibility points associated with the paired and unpaired blocks of spectrum being auctioned, as well as the population of their respective service areas.

23. In their application, each applicant 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 a bidder is eligible to bid on at the start of the auction. Eligibility points are also used to determine the financial deposit that must be submitted with the application.

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

### 8. Activity Rules in the Clock Rounds

25. Activity rules have 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.

26. The activity rules in the clock rounds are comprised of an eligibility point rule and a revealed preference rule. The two rules work in combination to accommodate their relative shortcomings. The motivation for using both rules is to ensure that the activity rules do not prohibit bidders from bidding on their most preferred package.

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

28. The eligibility point 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 point 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 it has previously bid on, (that is, has fewer eligibility points worth of licences), its eligibility is reduced. A round in which a bidder’s eligibility is reduced is called an eligibility-reducing round. These rounds play a special role in the proposed activity rules of the 700 MHz auction.

29. In Round 1, a bidder’s eligibility is established by its pre-auction financial deposit submitted at the time of application. In subsequent rounds, a bidder’s eligibility is determined by its activity level in the previous round. Therefore, if a bidder wishes to maintain the same eligibility level as in the previous round, its activity level must correspond to the same number of eligibility points in each round. A bidder’s eligibility points can never increase.

30. If a bidder falls short of the required activity level in any round, its eligibility point level is reduced accordingly, so that the total points worth of licences on which it can bid in the next round are limited in relation to its actual activity level in the current round. For example, consider an eligibility point rule where the activity level is 100%. If a bidder starts the round with 100 eligibility points but bids on licences worth only 80 eligibility points, in the subsequent round that bidder’s eligibility will drop to 80 points. The bidder’s eligibility remains at 80 points until a round in which it bids on a package worth fewer than 80 points, at which time its eligibility would be reduced accordingly.

31. However, there are some shortcomings with using only the eligibility point 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 point 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 point rule would prevent the bidder from bidding on its most preferred package.

32. A revealed preference rule would 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. This rule would afford bidders greater flexibility to fully express their preferences in the clock rounds of the auction, ensuring that activity rules do not prevent a bidder from bidding on its most preferred package.

33. 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 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 point rule exclusively and the advantage of using the eligibility point rule in combination with the revealed preference rule.

Revealed Preference/Eligibility Point Hybrid Activity Rule

34. A revealed preference/eligibility point hybrid activity rule is being proposed for each clock round. It comprises both an eligibility point rule and a revealed preference rule.

35. The proposed 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 their eligibility points if they wish to maintain that eligibility level in the subsequent round.

36. The bidder can always place a bid for any package that is within its current eligibility. However, as prices increase, a bidder’s eligibility is generally reduced. There may be a point in the auction where the bidder wishes to switch to another package that is larger, but is relatively less expensive. With the revealed preference rule, 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 the revealed preference rule with respect to each prior eligibility-reducing round.

37. However, bidding on a larger package will not increase the bidder’s eligibility in subsequent rounds. Furthermore, a bidder will be unable to bid on a package with associated eligibility points that exceeds its initial eligibility. For an algebraic description of the revealed preference rule in the clock rounds, see Annex D. For an example of the revealed preference rule in the clock rounds, refer to Annex C.

38. The combination of the two activity rules will allow a bidder to bid on its most preferred package in every clock round. A bidder can continue to bid just as it would under the eligibility point rule. The only difference is that the bidder is given some extra flexibility to bid on a larger package provided that the bid on the larger package satisfies revealed preference, i.e. the bid involves a switch to a package that has become relatively less expensive.

39. As a result, price discovery is improved and the final clock allocation becomes a better predictor of the auction outcome.

### 9. Supplementary Round

40. 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 for packages, subject to constraints that are based on the bids that they placed in the clock rounds . 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 in the clock rounds.

41. 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 submit bids on multiple packages that they were willing and eligible to bid on in the clock rounds, but did not necessarily bid on.

42. If there are licences that remain unallocated at the end of the clock rounds, the supplementary round provides bidders with the opportunity to win some or all of the unallocated licences. Bidders also have the opportunity to guarantee that they win their final clock package by submitting a supplementary bid that increases the dollar amount of their final clock package by at least the value of the unallocated licences as evaluated at the final clock prices Begin new textless the opening bid prices of the unallocated licences. This guarantee 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.

43. If all of the licences are allocated at the end of the clock stage, then the supplementary round will not affect the final clock allocation. However, the supplementary round provides an opportunity for bidders to be reassured that they themselves were not prepared to pay more than the winning bidders for the licences in question.

### 10. Activity Rules in the Supplementary Round

44. Activity rules in the supplementary round encourage truthful bidding throughout the allocation stage of the auction, not just in the latter stages. The proposed activity rules ensure that supplementary bids are consistent with bids from the previous rounds.

45. Any bidder that placed at least one valid bid in the clock rounds may submit bids in the supplementary round. A bidder is not required to submit bids in the supplementary round if it does not so desire.

46. 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 not expressed in the clock rounds.

47. A bidder can only make one supplementary bid for a given package of licences. A bidder can submit supplementary bids for up to 500 different packages.

48. 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 for a certain package in the clock rounds, the supplementary bid amount must be at least the bidder’s highest bid for that package.

Revealed Preference Limit

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

50. 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 larger or smaller than the final clock package.

51. In addition, supplementary bids for packages that are larger than the final clock package, as measured by eligibility points, 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 to limit bids on packages larger than the final clock package 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 submitted by the bidder.

52. There is an exception to the above. A supplementary bid for a package comprised solely of the bidder’s final clock package plus some or all of the unallocated licences only needs to satisfy revealed preference with respect to the final clock round. This is to provide bidders with additional flexibility in bidding on licences that are unallocated as of the final clock round. By relaxing the constraints on bids for such packages, the probability of awarding unallocated licences can be improved without reducing the probability that any bidder receives its final clock package.

53. These activity rules guarantee that the final clock allocation will not change if there are no unallocated licences. Each winner is guaranteed to win its final clock package without making any supplementary bids. If there are unallocated licences, each winner is guaranteed to win its final clock package by submitting 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 Begin new textless the opening bid prices of the unallocated licences. This guarantee 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.

54. 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.

55. Industry Canada will decide on the process for submitting supplementary bids. Details concerning the process will be included in the final licensing framework.

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

56. All valid bids received from bidders in the clock rounds and 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. This process will act as though Industry Canada is a bidder in the auction, placing a bid on every licence at the opening bid price. The inclusion of 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.

57. An algorithm will be used to identify the highest value combination of valid bids with each bidder winning at most one of its packages. If there is only one combination of bids that meets the criterion, this will be the winning outcome that determines the winning packages and winning bidders.

58. If there is more than one set of valid bids having the equal 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.

59. If there is still a tie, the second tie-breaking rule is to select the combination of valid bids which includes the greatest quantity of spectrum, measured in terms of 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.

60. Industry Canada will decide how best to validate the results following the use of the algorithm. Further details will be included in the final licensing framework. This will include details of the algorithm to be used and also how Industry Canada intends to validate the results following the use of this applicable algorithm.

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

61. 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 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.

62. Industry Canada is proposing to use a second-price rule to calculate the base prices such that winning bidders, individually and collectively, will pay the lowest amount that they could have bid on their package of licences and still have won. In other words, a winning bidder 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.

63. Industry Canada is proposing to apply bidder-optimal core prices and to use the “nearest Vickrey” approach to determine the base prices. Further information on the determination of base prices can be found in Annex E.

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

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

65. At the end of the allocation stage, bidders will be informed of their own winning packages, along with the base price to be paid for each package. All bidders will be informed of the number of winning bidders and the total number of licences allocated.

### 14. The Assignment Stage

66. 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.

67. Industry Canada is proposing to 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.

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

69. 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. Each winning bidder has both a right and an obligation to purchase one of the licences in each category presented to it in the assignment round(s). For example, in the 700 MHz auction, if two bidders each won a licence in the C1 and C2 category in a given service area, then each would 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 did not have a preference between the two licences, it would not have to submit assignment bids.

70. An algorithm will be used to identify the combination of specific assignments of licences that result in the highest bid amount subject to the proposed assignment stage restriction (Section 15). 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.

71. 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).

72. The additional amount 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 for 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.

73. Industry Canada is proposing to apply bidder-optimal core prices and to use a “nearest Vickrey” approach to determine assignment prices. Further information on the determination of assignment prices can be found in Annex E.

### 15. Restrictions in the Assignment Stage

74. Industry Canada is proposing that the assignment option 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.

75. Industry Canada will decide on the process for submitting assignment bids. Details concerning the process for submitting bids in the assignment stage will be included in the final licensing framework.

### 16. Final Price

76. Following the determination of the winning assignment bids, Industry Canada will then 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.

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

77. Following the end of the assignment stage, all bidders will be notified of the winning bidders and the specific package of licences that they have won, as well as the final price to be paid by each winning bidder.

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

78. Industry Canada is proposing to make the following information 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.

## Annex C — Example of the Proposed 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 licences of C1/C2. This package will be denoted as (2, 0). However, if the price of the package with two licences of C1/C2 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 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 for two C1/C2 licences, package (2, 0): Example of the Proposed Activity Rules - Round 1 Category Price Bid Eligibility Points C1/C2$1,000,000 2 100
D/E $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 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 for a package with two C1/C2 licences is $2,400,000, whereas the price for 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 of each category, package (1, 1), thereby reducing eligibility from 100 to 75 points.

Example of the Proposed Activity Rules - Round 2
Category Price Bid Eligibility Points
C1/C2 $1,200,000 1 50 D/E$650,000 1 25
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 for a package with two C1/C2 licences is$2,500,000, whereas the price for 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 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:

Example of the Proposed Activity Rules - Round 3
Category Price Bid Eligibility Points
C1/C2 $1,250,000 2 100 D/E$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 C1/C2 increases to$1,400,000, whereas the price of D/E increases to $1,000,000. The price for a package with two C1/C2 licences is$2,800,000, whereas the price for 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:

Example of the Proposed Activity Rules - Round 4
Category Price Bid Eligibility Points
C1/C2 $1,400,000 2 100 D/E$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 categories, with C1/C2 at$1,650,000 and D/E 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 C1/C2 ($1,650,000) is$450,000 greater than the price of D/E ($1,200,000), Bidder A places a bid for 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.

Example of the Proposed Activity Rules - Round 5
Category Price Bid Eligibility Points
C1/C2 $1,650,000 1 50 D/E$1,200,000 0 0
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:

Example of the Proposed Activity Rules - Round 6
Category Price Bid Eligibility Points
C1/C2 $1,800,000 0 0 D/E$1,250,000 1 25
Total Package $1,250,000 (0, 1) 25 ### Round 7 18. In Round 7, the price on 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:

Example of the Proposed Activity Rules - Round 7
Category Price Bid Eligibility Points
C1/C2 $1,850,000 1 50 D/E$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: Example of the Proposed Activity Rules - 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) 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 C1/C2 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 D/E 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 Begin new textless the opening bid prices of the unallocated licences. This guarantee 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. 27. 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 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 D — Algebraic Description of Proposed Revealed Preference Activity Rules in the Clock Rounds and the Supplementary Round

### Revealed Preference in the Clock Rounds

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.

A product refers to a particular category in a given service area. Industry Canada is proposing 56 products in the 700 MHz auction. The 56 products represent 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.

1. 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 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.

2. 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

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.

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 that are unsold or categories where supply is greater than aggregate demand in the final clock round.

3. 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.

4. 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 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 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.

5. 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.

6. 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 4, 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 4 with respect to the final clock round and with respect to every eligibility-reducing round equal to T (Q) or later.

7. Note that, in the application of paragraph 4, 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.

8. See Annex C for an example of the revealed preference activity rules.

## Annex E — 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, determine the maximum bid value that can be achieved with all of Bidder J’s bids removed. This is found by solving the winner determination problem (see Annex B) with Bidder J’s bids removed. Next, take the sum of the winning allocation stage bids for all bidders other than Bidder J. The Vickrey price for Bidder J is defined to be the maximum bid value with Bidder J’s bids removed minus the sum of the winning allocation stage bids for all bidders other than Bidder J.

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).

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, 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, theVickrey 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).

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 2, 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. 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 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 2 - Example of Calculating Base Prices Description of Figure 1 This figure is a graph illustrating the example in paragraph 9 of Annex E which demonstrates how to calculate base prices using a second-price rule and why an additional payment beyond second prices is sometimes required. 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 2. 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

10. Industry Canada is proposing to 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. 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. The assignment bid is essentially a package bid for the locations of all licences within a category.

12. 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 within a category and is not separable between given service areas. For example, if a bidder wins one B/C licence nationwide in the B/C assignment round, the bidder is able to submit a single bid to be assigned the same licence 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 is defined as follows. First, determine the maximum bid value that can be achieved when all of Bidder J’s bids are replaced by bids with dollar amounts of zero. This is found by solving the winning assignment bid problem with Bidder J’s bids replaced by bids of zero amounts, indicating that the bidder does not have a preference. Then the Vickrey price for Bidder J is defined to be the maximum bid value with Bidder J’s bids replaced by bids of zero amounts minus the sum of the winning assignment bids for all bidders other than Bidder J.

14. The assignment stage prices for each winning assignment bid 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.

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

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