Consultation on a Licensing Framework for Mobile Broadband Services (MBS) — 700 MHz Band (sf10370)

 

Annex A — Glossary

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 MHzband. A CCA is a bidding process that includes a price discovery stage, similarto the SMRA auction format. However, the CCA format also has attributes whichremove or reduce some design concerns associated with the SMRA format. Inparticular, in a CCA, bidders are able to bid for packages of licences insteadof individual ones, eliminating the risk that bidders may win some but not allof the licences that they desire. This is particularly important given theregional nature of the licences to be auctioned and the complementarities thatexist 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 ofthe combinatorial clock auction (CCA) process and portraying the sequence ofsteps included in the process. The CCA is comprised of two stages, the allocationstage and the assignment stage.

The allocation stage includes two steps, the first of whichis 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 oncategories of licences. In any round, if there is excess demand in any categoryof licences, the price of those licences will increase and the clock roundswill continue until such a time as there is no excess demand in any category oflicences. When there is no longer excess demand in any category of licences,the process will move to the supplementary round. The supplementary round is asingle round where bidders have the opportunity to make additional bids.

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

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

If there were any generic licences offered and won in the allocationstage, the process then moves to the assignment stage. At the end of theassignment stage, winning assignments and final prices are determined. Thissignifies 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 pricesa ccordingly, shifting their bids to licences that continue to be consistent with their business objectives.

6. During each clockround, 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 spectrumcap of two blocks of paired spectrum in each service area. Therefore, bidderswill be unable to bid on more than two licences of paired spectrum in eachservice area. Large wireless service providers are further limited in that theycan only bid on one paired licence in each service area among Blocks B, C, C1and C2. This cap on large wireless service providers, however, does not includeBlock A. The auction software will not allow bidders to submit a bid thatexceeds their spectrum cap(s).

3. Clock Rounds

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

9. For the 700 MHzauction, Industry Canada is proposing four categories of licences in each ofthe 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 isreferred to as a product. Given the proposal of four categories of licences ineach of the 14 service areas, 56 products (4x14) are proposed for the 700 MHz auction.

11. The licences are auctioned simultaneouslyover multiple clock rounds. In each round and for each product, biddersindicate the number of licences in each product on which they would like to bidgiven the prevailing prices. For a product in any of the categories containingtwo generic licences, the bid is “0,” “1” or “2.” For a product in the Block Acategory, which contains only one licence, the bid is “0” or “1.” All of the individualbids placed by a bidder in a given round are considered to be a single packagebid, creating an all-or-nothing bid. The price of the package bid is equal tothe sum of the bids for individual products, evaluated at the prevailing clockprices.

12. When there is excess demand for aproduct, its price increases in the next round. There is excess demand for aproduct when the number of bids exceeds the number of licences available.

13. To remain in the auction, a bidder mustsubmit a valid bid for at least one licence in the first clock round. This bidcannot be withdrawn and will be part of the bids considered in determining theassignment of licences at the end of the allocation stage. All valid bidssubmitted during the clock rounds are binding and will be considered indetermining both winning packages and base prices after the supplementary roundends.

14. Bidding remains open on all productsuntil 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 around in which there is no excess demand for any of the products. This round isreferred to as the final clock round. The package on which a bidder placed abid in the final clock round is referred to as its final clock package. At thispoint, Industry Canada will announce that the clock rounds have ended andthat the auction will proceed to the supplementary round (see Section 9).

16. In the final clock round, all licencesmay be tentatively allocated. Conversely, there may be some unallocatedlicences 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 tentativelyallocated, then the bids placed in the final clock round are the provisionalwinning bids. If there are still some unallocated licences, a bidder canguarantee that it will win its final clock package by submitting asupplementary bid that increases the dollar amount of its final clock packagebid by at least the final clock price of the 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.

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 informtheir bidding strategy. This information includes their own bids from theprevious round and the number of eligibility points that they will have in thenext round, as well as the aggregate demand for each product from the previousround, and the prices for each product in the next round. Bidders are notinformed about the individual bids submitted by other bidders or the remainingeligibility of other bidders. This should address some of the concerns raisedduring previous auctions regarding the potential for gaming.

6. Bid Increments

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

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

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

7. Eligibility Points

22. Each of the 98 licences has been assigneda specific number of eligibility points (points) that are related to thepopulation covered by the licence, its bandwidth and the estimated value of thespectrum. Generally, one point has been assigned per 5 MHz of spectrum per100,000 in population count. The five service areas of Southern Quebec, EasternOntario and Outaouais, Southern Ontario, Alberta and British Columbia are theexception. For these five service areas, the eligibility points per pairedspectrum block have been adjusted in proportion to the opening bid prices. Section 7.3 of the main document lists the proposed eligibility points associated withthe paired and unpaired blocks of spectrum being auctioned, as well as the populationof their respective service areas.

23. In their application, each applicant mustindicate the total number of “points” worth of licences on which they wish tobid. This number defines a bidder’s initial level of eligibility points andhence, the maximum number of licences a bidder is eligible to bid on at thestart of the auction. Eligibility points are also used to determine thefinancial deposit that must be submitted with the application.

24. Bidder eligibility points cannot beincreased once the auction has started.

8. ActivityRules in the Clock Rounds

25. Activity rules have been established toencourage truthful bidding throughout the clock rounds. This facilitates theprice discovery process, allowing bidders to make changes to their biddingstrategies dynamically throughout the auction, in response to increasingprices. The activity rules discourage a bidder from misrepresenting its truedemand, as doing so will limit the bidder’s ability to bid on what it reallywants later in the auction.

26. The activity rules in the clock roundsare comprised of an eligibility point rule and a revealed preference rule. Thetwo rules work in combination to accommodate their relative shortcomings. Themotivation for using both rules is to ensure that the activity rules do notprohibit bidders from bidding on their most preferred package.

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

28. The eligibility pointrule considers the size of the package that the bidder is bidding on, wheresize is the sum of the eligibility points for each licence in the package. Theeligibility point activity rule requires bidders to bid on packages of thesame size or smaller as prices rise. When a bidder switches to a package thatis smaller than the package it has previously bid on, (that is, has fewereligibility points worth of licences), its eligibility is reduced. A round inwhich a bidder’s eligibility is reduced is called an eligibility-reducinground. 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 establishedby its pre-auction financial deposit submitted at the time of application. Insubsequent rounds, a bidder’s eligibility is determined by its activity levelin the previous round. Therefore, if a bidder wishes to maintain the sameeligibility level as in the previous round, its activity level must correspondto the same number of eligibility points in each round. A bidder’s eligibilitypoints can never increase.

30. If a bidder falls short of the requiredactivity 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 nextround are limited in relation to its actual activity level in the currentround. For example, consider an eligibility point rule where the activity levelis 100%. If a bidder starts the round with 100 eligibility points but bidson licences worth only 80 eligibility points, in the subsequent round that bidder’seligibility will drop to 80 points. The bidder’s eligibility remains at 80points until a round in which it bids on a package worth fewer than 80 points, atwhich time its eligibility would be reduced accordingly.

31. However, there are some shortcomings withusing only the eligibility point rule. Price discovery might be lessened, asthere is an incentive for bidders to choose only larger packages when pricesare low, rather than a package that may work better for them, so that theymaintain a higher number of eligibility points for later in the auction. Furthermore,an eligibility point rule may prevent a bidder from making a desirablesubstitution to a package that is larger in terms of associated eligibilitypoints, but which has become relatively less expensive. In such a case, theeligibility point rule would prevent the bidder from bidding on its mostpreferred package.

32. A revealed preference rule would lessenthese problems, as it allows bidders to exceed their eligibility points inorder to bid on packages that have become comparatively less expensive.Revealed preference refers to the information that a bidder discloses regardingits inclination toward one package versus another. In particular, if a bidderchooses one package over another given a certain price differential between thetwo packages, then the bidder should always choose the same package given thesame price differential. Thisrule would afford bidders greater flexibility to fully express theirpreferences in the clock rounds of the auction, ensuring that activity rules donot prevent a bidder from bidding on its most preferred package.

33. For example, suppose that a bidderdesires either a smaller package, X, or a larger package, Y, but not both. Atthe current prices, X is preferred, but in subsequent rounds, the prices forthe 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 revealedpreference rule allows the bidder to switch from X to Y because Y is now thebetter value. In contrast, theeligibility point rule wouldnot allow the switch because Y is larger than X. This example illustrates theproblem with using the eligibility point rule exclusively and the advantage ofusing the eligibility point rule in combination with the revealed preferencerule.

Revealed Preference/Eligibility Point Hybrid Activity Rule

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

35. The proposed eligibility point activityrequirement for the 700 MHz auction is 100%. Specifically, in each round, abidder is required to bid on licences whose total sum of associated points isequal to 100% of their eligibility points if they wish to maintain thateligibility level in the subsequent round.

36. The bidder can always place a bid for anypackage that is within its current eligibility. However, as prices increase, abidder’s eligibility is generally reduced. There may be a point in the auctionwhere the bidder wishes to switch to another package that is larger, but isrelatively less expensive. With the revealed preference rule, in any round, thebidder can bid on a larger package than would be permitted by the bidder’scurrent eligibility provided that the package satisfies the revealed preferencerule with respect to each prior eligibility-reducing round.

37. However, bidding on a larger package willnot increase the bidder’s eligibility in subsequent rounds. Furthermore, abidder will be unable to bid on a package with associated eligibility pointsthat exceeds its initial eligibility. For an algebraic description of the revealedpreference rule in the clock rounds, see Annex D. For an example of the revealedpreference rule in the clock rounds, refer to Annex C.

38. The combination of the two activity ruleswill 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 bidon a larger package provided that the bid on the larger package satisfiesrevealed preference, i.e. the bid involves a switch to a package that has become relatively less expensive.

39. As a result, price discovery is improvedand the final clock allocation becomes a better predictor of the auctionoutcome.

9. Supplementary Round

40. The second phase of the allocation stageis 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 clockrounds (Section 10 of Annex B). These additional bids could be used to improvebids on packages previously submitted in the clock rounds and/or to submit bidsfor which they were eligible to bid on, but unable to in the clock rounds.

41. In the clock rounds, a bidder is allowedto bid on only one package of licences per round. As there may be otherpackages that a bidder would be interested in winning, the supplementary roundprovides bidders with an opportunity to submit bids on multiple packages that theywere willing and eligible to bid on in the clock rounds, but did notnecessarily bid on.

42. If there are licences that remainunallocated at the end of the clock rounds, the supplementary round providesbidders with the opportunity to win some or all of the unallocated licences.Bidders also have the opportunity to guarantee that they win their final clockpackage by submitting a supplementary bid that increases the dollar amount oftheir final clock package by at least the value of the unallocated licences as evaluatedat 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 atthe end of the clock stage, then the supplementary round will not affect thefinal clock allocation. However, the supplementary round provides anopportunity for bidders to be reassured that they themselves were not preparedto pay more than the winning bidders for the licences in question.

10. Activity Rules in the Supplementary Round

44. Activity rules in the supplementary roundencourage truthful bidding throughout the allocation stage of the auction, notjust in the latter stages. The proposed activity rules ensure that supplementarybids are consistent with bids from the previous rounds.

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

46. All licences are available for bidding inthe supplementary round so that bidders can improve on bids submitted duringthe clock rounds, or submit bids for packages of licences not expressed in theclock rounds.

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

48. The bid amount for a supplementary bidmust be at least the sum of the opening bid prices for all the licencesincluded in the package. Furthermore, if a bidder submitted a bid for a certainpackage in the clock rounds, the supplementary bid amount must be at least thebidder’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 supplementarybid amount for the final clock package, which is the package that the bidderbid on in the final clock round. All other supplementary bids must satisfyrevealed preference with respect to the final clock round, regardless ofwhether the supplementary bid package is larger or smaller than the final clockpackage.

51. In addition, supplementary bids forpackages that are larger than the final clock package, as measured by eligibilitypoints, must satisfy revealed preference with respect to eacheligibility-reducing round, beginning with the last round in which the bidderhad sufficient eligibility to bid on the package. The application of therevealed preference limit to limit bids on packages larger than the final clockpackage could have the effect of creating a chain of constraints on the dollaramount of a supplementary bid relative to the dollar amount of othersupplementary bids submitted by the bidder.

52. There is an exception to the above. A supplementarybid for a package comprised solely of the bidder’s final clock package plussome or all of the unallocated licences only needs to satisfy revealedpreference with respect to the final clock round. This is to provide bidders withadditional flexibility in bidding on licences that are unallocated as of thefinal clock round. By relaxing the constraints on bids for such packages, theprobability of awarding unallocated licences can be improved without reducingthe probability that any bidder receives its final clock package.

53. These activity rules guarantee that thefinal clock allocation will not change if there are no unallocated licences. Eachwinner is guaranteed to win its final clock package without making anysupplementary bids. If there are unallocated licences, each winner is guaranteedto win its final clock package by submitting a supplementary bid thatincreases the dollar amount of its final clock package by at least the value of theunallocated 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 respectto the final clock package provides the bidder with an incentive to bid on themost preferred package throughout the clock rounds. This is becausesupplementary bids are limited by bids submitted in the clock rounds. Giventhat the bidder does not know which round will be the final clock round, thebidder will be motivated to always bid truthfully to improve its chance ofwinning its most preferred package, otherwise the bidder will be constrained inthe supplementary round.

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

11. Determining the Winning Packages in the Allocation Stage

56. All valid bids received from bidders inthe clock rounds and the supplementary round are considered for thedetermination of winning packages. In addition, a reserve bid for everylicence, at the opening bid price, will be included in the determination of winning biddersat 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 theincremental value that a bidder would be prepared to pay for an additionallicence is at least the opening bid price of that licence. The reserve bidswill not be treated as a package, but rather as having been placed by differentbidders so that any number of reserve bids can be selected in the winningcombination.

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

58. If there is more than one set of validbids having the equal highest value, the tie will be resolved, first, by minimizingthe number of “lost licences,” where a lost licence is a licence that wasincluded in the bidder’s final clock package but is not included in analternate package that could be assigned to the bidder. The rationale forselecting the combination of valid bids that minimizes the number of lostlicences 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 secondtie-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 pointsassociated with the reserve bids will not count towards the eligibility pointsof the winning combination. This is to maximize the quantity of spectrum thatis allocated. If, subsequently, there is still a tied outcome, the tie will bebroken by a pseudo-random number generator built into the auction software.

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

12. Determiningthe Base Price in the Allocation Stage

61. The base price is the minimum amount thatthe winning bidders will pay for their generic winning packages; it does notinclude the additional, incremental amount that winning bidders may pay forspecific licences in the assignment stage should there be generic licencesincluded in the winning allocation stage package. The base price is determinedusing 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, individuallyand collectively, will pay the lowest amount that they could have bid on theirpackage of licences and still have won. In other words, a winning bidder willpay an amount that is sufficient to ensure that there is no other bidder orgroup of bidders prepared to pay more for the licences. This amount istypically less than the actual winning bid submitted in the allocation stage,either in the clock rounds or the supplementary round, and must be greater thanor equal to the total sum of the opening bid prices for the combination oflicences included in their winning package. The benefit of using a second-pricerule is that it encourages bidders to bid truthfully, potentiallyleading to a more efficient outcome.

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

13. Information at the end of the Allocation Stage

64. At this point, bidders will know withcertainty the number of licences that they have won; however, where there aregeneric licences, they will not necessarily know the specific licences thatthey have won.

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

14. The Assignment Stage

66. As there are generic licences, theauction will then advance to the assignment stage, where the specificassignment of the generic licences will be determined. Only bidders that havewon one or more generic licences during the allocation stage will have theoption to participate in the assignment stage.

67. Industry Canada is proposing to run threesequential assignment rounds (i.e. one for each category of generic licences): blocksB and C; blocks D and E; and blocks C1 and C2. This is to allow bidders that havewon licences in the same category of generic licences across multiple serviceareas to express their preference for particular licences.

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

69. Winning bidders do not have to place bidsin the assignment stage if they do not have an assignment preference, as theyare guaranteed the number of generic licences that they have already won. Eachwinning bidder has both a right and an obligation to purchase one of thelicences in each category presented to it in the assignment round(s). Forexample, in the 700 MHz auction, if two bidders each won a licence in the C1and C2 category in a given service area, then each would have an opportunity tosubmit an additional bid for either the C1 or the C2 licence, depending on itspreferred assignment. However, if one of the two bidders did not have apreference between the two licences, it would not have to submit assignmentbids.

70. An algorithm will be used to identify thecombination of specific assignments of licences that result in the highest bidamount subject to the proposed assignment stage restriction (Section 15).In the event of a tied outcome with more than one specific assignment producingthe same total value, the tie will be broken by a pseudo-random numbergenerator built into the auction software.

71. Similar to the determination of baseprices in the allocation stage, a second-price rule will be used to determinethe assignment price to be paid for the assignment of specific licences suchthat winning bidders will pay an amount sufficient to ensure that there is noother bidder or group of bidders prepared to pay more for the licence(s).

72. The additional amount paid for the assignmentof specific licences, known as the assignment price, is calculated for a packageof licences within one category, not the individual licences. In general, giventhe pricing rules, the assignment price for each winning assignment stage bidwill be equal to or less than the corresponding winning bid amount; however, itis likely that it will be less than the winning bid amount and could even bezero.

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

15. Restrictionsin the Assignment Stage

74. Industry Canada is proposing that theassignment option be limited such that where a bidder wins Block A and one of blocksB and C in a given service area, then the bidder will automatically be assignedblocks A and B.

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

16. Final Price

76. Following the determination of the winningassignment bids, Industry Canada will then determine the final price to be paidby each winning bidder. The final price to be paid by a winning bidder is equalto the base price plus any associated assignment prices for a bidder’s winningpackage.

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 oflicences that they have won, as well as the final price to be paid by eachwinning bidder.

18. Information at the end of the Auction

78. Industry Canada is proposing to make the following information publicly available following theconclusion 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 ofthis example, only a single service area and two categories within the 700 MHzband will be considered: blocks C1/C2 and blocks D/E. Within the given servicearea, suppose that each C1/C2 licence has an eligibility of 50 points, whereas eachD/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 licencesof C1/C2. This package will be denoted as (2, 0). However, if the price of thepackage with two licences of C1/C2 exceeds the price of a package with oneC1/C2 licence and one D/E licence by more than $500,000, then Bidder A wouldprefer a package with one C1/C2 licence and one D/E licence, denoted as package(1, 1).

3. Eventually, if theprices become too high, Bidder A will be unable to afford two licences and willneed to reduce its demand to one licence. In this case, Bidder A again prefersone licence from C1/C2, but will switch to one D/E licence if the price of oneC1/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 totalbudget is $2,800,000. If the price of obtaining two licences becomes greaterthan this, Bidder A must reduce its demand to one licence.

Round 1

5. In Round 1, the openingbid prices are announced; the opening bid price for C1/C2 is $1,000,000 perlicence, and for D/E, it is $600,000 per licence. The price of a package withtwo C1/C2 licences is $2,000,000, whereas the price of a package with one C1/C2licence and one D/E licence is $1,600,000 (a price difference of $400,000). AsBidder 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, severalother bidders shared Bidder A’s preference for C1/C2, whereas few bidders bidon D/E. As a result, the prices in Round 2 are $1,200,000 for C1/C2 and $650,000for D/E. The price for a package with two C1/C2 licences is $2,400,000, whereasthe 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 oneD/E licence when the price difference is greater than $500,000, Bidder A nowbids on one licence of each category, package (1, 1), thereby reducingeligibility 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 lowprice of D/E caused many bidders to switch demand to that category. As aresult, the price of D/E increased at a faster rate than the price of C1/C2. TheRound 3 prices are $1,250,000 for C1/C2 and $800,000 for D/E. The price for apackage with two C1/C2 licences is $2,500,000, whereas the price for a packagewith one C1/C2 licence and one D/E licence is $2,050,000. This price differenceis only $450,000, so Bidder A would prefer to switch back to bidding on twoC1/C2 licences, package (2, 0).

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

9. With a revealed preference/eligibilitypoint hybrid activity rule, however, Bidder A is free to switch back as long asthe package satisfies revealed preference with respect to each prioreligibility 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 abid with eligibility points greater than its current eligibility (75 points),Bidder A must meet the revealed preference constraint with respect to eachprior eligibility-reducing round. In this case, the only eligibility-reducinground is Round 2, where Bidder A decreased its eligibility from 100 points to75 points. In other words, in order for Bidder A to be able to switch its bidfrom (1, 1) to (2, 0), the (2, 0) package had to become relatively cheaper thanthe (1, 1) package. Mathematically, the revealed preference constraint isstated 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 ofpackage (1, 1) increased by $200,000. Therefore, the constraint is satisfiedand Bidder A is permitted to place the bid for the package (2, 0).

Round 4

12. In Round 4, the priceof 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 theprice 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 asin 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’seligibility is still only equal to 75, so it must meet the revealed preferenceconstraint 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 (ascompared 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 constraintcontinues to be satisfied, that is, the price of the package (2, 0) increasedby $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 ispermitted to place this bid for the package (2, 0).

Round 5

15. In Round 5, the pricecontinues 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) nowexceed Bidder A’s budget of $2,800,000. Bidder A must decrease its demand toone licence. As the price of C1/C2 ($1,650,000) is $450,000 greater than theprice 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 oneC1/C2 licence exceeds the price of one D/E licence by less than $500,000.

16. This bid further reducesBidder 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 priceon 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 toone D/E licence, package (0, 1) as Bidder A prefers one D/E licence when theprice 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 priceon D/E increases at a faster rate than C1/C2. At Round 7 prices, Bidder Aprefers one C1/C2 licence, as the price of one C1/C2 licence exceeds the priceof one D/E licence by less than $500,000, causing Bidder A to again desire toswitch:

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 placethis bid, Bidder A must satisfy revealed preference with respect to every roundin which it has reduced its eligibility. Bidder A reduced its eligibility inRound 2, Round 5 and Round 6. It is helpful to summarize the prices and bidsplaced 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 thepackage (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, wherepackage (1, 1) is the packagethat Bidder A bid on in Round 2.

Constraintwith 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 thepackage (1, 0) increased by $200,000 from Round 5 to the current round, Round7, which is no more than the increase in the price of the package (1, 0), wherethe 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), wherethe 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 afinal clock package of one C1/C2 licence. Note that if there had only been an eligibilitypoint activity rule in the clock stage, Bidder A would likely have, instead, afinal 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 unallocatedlicences in the final clock round, Bidder A can still guarantee winning itsfinal clock package by submitting a bid, increasing the dollar amount by at least thefinal 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 clockpackage, as well as with respect to each eligibility-reducing round beginning with the last round inwhich 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) inR7) ≤ (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) inR6) ≤ (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) inR5) ≤ (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 amountis $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 inwhich Bidder A had sufficient eligibility to bid on the (0, 1) package, as wellas in the final clock round. In this example, the last round in which Bidder Ahad sufficient eligibility to bid on the (0, 1) package was Round 7, which isalso 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) inR7) ≤ (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 anysupplementary bids placed on the final clock package, the highest supplementarybid that Bidder A can place on the (0, 1) package is $1,400,000 because BidderA bid $1,850,000 for (1, 0) in the final clock round. However, if for exampleBidder 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 andthe Supplementary Round

Revealed Preference in theClock Rounds

The activity rule in the clock rounds allows for a bidder toalways be able to place a bid on any package that is within the bidder’scurrent eligibility. As well, in any round, the bidder can bid on a largerpackage than would be permitted by the bidder’s current eligibility providedthat the package satisfies revealed preference with respect to each prioreligibility-reducing round. However, bidding on a larger package does notincrease the bidder’s eligibility in subsequent rounds. A bidder will never beallowed to place a bid on a package that exceeds its initial eligibility.

A product refers to a particular category in a given servicearea. Industry Canada is proposing 56 products in the 700 MHz auction. The56 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 clockround t satisfies revealed preference with respect to an earlier clockround s for a given bidder if the bidder’s package Qt hasbecome relatively less expensive than the package on which the bidder bid inclock round s, Qs, as the clock prices have progressedfrom the clock prices in clock round s to the clock prices in clockround t. Algebraically, the revealed preference constraint is thecondition 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 ofthe ith product bid in clock round t;

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

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

Ps,iis 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 clockrounds if it satisfies the revealed preference constraint with respect to alleligibility-reducing rounds prior to clock round t for the given bidder.

RevealedPreference in the Supplementary Round

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

In addition, supplementary bids on packages that are largerthan the final clock package must satisfy the revealed preference limit withrespect to each eligibility-reducing round, beginning with the last round inwhich the bidder had sufficient eligibility to bid on the package, unless theincrease in package size is due to placing bids on unallocated licences, whereunallocated licences are those that are unsold or categories where supply isgreater than aggregate demand in the final clock round.

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

4. A supplementary bid, B,for the package Q satisfies the revealed preference limit with respectto a clock round s, if B is less than or equal to the highestdollar amount bid on the package bid in clock round s, that is, Bsplus the price difference in the respective packages, Q and Qs,using the clock prices of clock round s. Algebraically, the revealed preferencelimit 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 ofthe ith product in the package Q;

Qs,i is the quantity ofthe ith product in the package Qs of clockround s;

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

B is the dollar amount of thesupplementary 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 bidpackage Q, let T(Q) denote the last clock round in whichthe bidder’s eligibility was at least the number of eligibility pointsassociated 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 preferencelimit with respect to another package. Thus, the rule may have the effect ofcreating a chain of constraints on the dollar amount of a supplementary bid fora package Q relative to the dollar amounts of other clock bids orsupplementary 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 payfor their winning packages; and second, at the end of the assignment stage todetermine the incremental payments for specific licences, known as assignmentprices. 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. Thefinal price paid by a winning bidder is the sum of the base price and theassignment 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 eachwinning 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 asVickrey 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 isfound by solving the winner determination problem (see Annex B) with Bidder J’sbids removed. Next, take the sum of the winning allocation stage bids for allbidders other than Bidder J. The Vickrey price for Bidder J is defined to bethe maximum bid value with Bidder J’s bids removed minus the sum of the winningallocation stage bids for all bidders other than Bidder J.

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

6. The set of baseprices for the winning allocation stage bids must satisfy the followingconditions:

  • (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 conditionscharacterize a unique set of base prices such that each winning bidder pays nomore than the dollar amount of its winning bid and pays at least the aggregatevalue of the opening bid prices for the package of licences.

8. A software algorithmwill be used to determine the set of base prices that meets the conditionsoutlined above.

9. The following is an example of how base prices are calculated. This example isbased on the 2012 Spectrum Auction Design.

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

b1{A}= $28

b2{B}= $20

b3{AB}= $32

b4{A}= $14

b5{B}= $12

The bids of thefive bidders are represented in Figure 2.

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

To calculate theVickrey price for Bidder 1, Bidder 1’s bid is removed. The best assignmentwithout Bidder 1 assigns licence A to Bidder 4 at $14 and licence B to Bidder 2at $20, resulting in $34. The sum of the winning bids for all bidders otherthan Bidder 1 is $20 ($48 – $28). Thus, theVickrey price for Bidder1 is $14 ($34 – $20). Similarly, if Bidder 2’s bid isremoved, then the best assignment is to assign licence A to Bidder 1 andlicence B to Bidder 5, resulting in a value of $40. The sum of the winning bidsfor 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 Vickreyoutcome is for Bidder 1 to pay $14 for licence A and for Bidder 2 to pay $12for licence B. Total revenues with these payments are $14 + $12 = $26. As shownin Figure 2, this means that Bidder 1 can reduce its bid to $14 before beingdisplaced by Bidder 4. Similarly, Bidder 2 can reduce its bid to $12 beforebeing displaced by Bidder 5.

The problem is that these payments sum to $26, which lessthan Bidder 3’s bid of $32 for both licences A and B. Therefore, Bidder 1 andBidder 2 must split an additional payment of $6 ($32 – $26), to ensure that their combinedpayment is greater than that of Bidder 3, satisfying the condition that that noother bidder or group of bidders were prepared to pay more for the licences inquestion. That is, Bidder 1 and Bidder 2 must pay, collectively, at least $32.

Figure 2 - Example of Calculating Base Prices

Figure 2 - Example of Calculating Base Prices (the long description is located below the image)
Description of Figure 1

This figure is a graph illustrating the example in paragraph 9 of Annex 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 arethe same amount, the additional payment of $6 is split equally between the twobidders. Each bidder is therefore paying an additional $3 above its Vickreyprice, 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 licencesare different amounts, the two bidders must split the extra paymentproportionately, in reference to the opening bid amounts (the fourthcondition). For example, if the opening bid price for licence A is $8 and theopening bid price for licence B is $4, then the opening bid price of Bidder 1’spackage is twice as large as that of Bidder 2. Therefore, Bidder 1 would paytwice as much as Bidder 2 of the extra payment, with Bidder 1 paying anadditional $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 threesequential assignment rounds, if necessary, one for each category of genericlicences, blocks B and C, blocks D and E and blocks C1 and C2. This is to allowbidders that have won licences in the same category of generic licences acrossmultiple service areas to have the opportunity to express their preference forparticular licences.

11. For each categorythat includes two generic licences, that is, blocks B and C, blocks D and E andblocks C1 and C2, assignment prices will be determined from the set ofassignment stage bids for the category of licences. The assignment bid isessentially 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. Theassignment price is attributable to the entire collection of licences within acategory and is not separable between given service areas. For example, if abidder wins one B/C licence nationwide in the B/C assignment round, the bidder isable to submit a single bid to be assigned the same licence in every servicearea. In this case, the assignment price is for the group of licences ratherthan the specific licence in each service area.

13. For the purpose of calculatingassignment prices, the Vickrey price for each winning bidder is defined asfollows. First, determine the maximum bid value that can be achieved when allof Bidder J’s bids are replaced by bids with dollar amounts of zero. This isfound by solving the winning assignment bid problem with Bidder J’s bidsreplaced by bids of zero amounts, indicating that the bidder does not have apreference. Then the Vickrey price for Bidder J is defined to be the maximumbid value with Bidder J’s bids replaced by bids of zero amounts minus the sumof the winning assignment bids for all bidders other than Bidder J.

14. The assignment stageprices 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 algorithmwill be used to determine the set of assignment prices that meet the conditionsoutlined above.