Licensing Framework for Broadband Radio Service (BRS) — 2500 MHz Band (sf10730)

Annex D — The Combinatorial Clock Auction (CCA) Format

Industry Canada will use a combinatorial clock auction (CCA) format for the 2500 MHz band auction. A CCA involves a bidding process that includes a price discovery stage, which is similar to the simultaneous multiple round ascending (SMRA) auction format. However, the CCA format also has attributes that remove or reduce some design concerns associated with the SMRA format. In particular, in a CCA, bidders are able to bid on packages of licences instead of individual licences, 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.

Generic licences and anonymous bidding will also be used in the 2500 MHz auction. Generic licences are blocks of spectrum that are of comparable value and are similar in terms of frequency location in the band, block size, technology and interference constraints, 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 products to bid on in the auction, and will enhance the possibility of substitution among licences. The use of anonymous bidding will reduce the potential for gaming. Pricing rules and activity rules that encourage truthful bidding throughout the auction process (i.e. bidding in a manner that is consistent with how a bidder truly values the package) will further improve the process.

The licences have been separated into two categories, paired and unpaired, with the following blocks available in each service area of the identified regions (Table D1):

Region A (43 service areas):

• Blocks C/C’ to G/G’ (five paired generic licences of 10 + 10 MHz);

• Block I (one unpaired licence of 25 MHz);

Region B (16 service areas):

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

Region C (two service areas):

• Blocks A/A’, B/B’ and E/E’ to G/G’ (five paired generic licences of 10 + 10 MHz); and

• Block H (one unpaired licence of 25 MHz).

Note: The unpaired blocks, H and I, will be auctioned as 20 MHz blocks but will be licensed as 25 MHz blocks, which will include a 5 MHz restricted band. For the purposes of calculating spectrum aggregation limits, these blocks are counted as 20 MHz blocks.

The set of licences in the same category and within the same service area is referred to as a product. Given that there will be two categories in Region A (43 service areas), one category in Region B (16 service areas) and two categories in Region C (two service areas), there will be a total of 106 products in the 2500 MHz auction. The licences available in the auction may be subject to change following the deadline (60 calendar days after the publication of this Framework) for the return of existing licences in the 2500 MHz band.

1. Overview of the CCA

A CCA usually consists of two stages, the allocation stage and the assignment stage (Figure D1). In the allocation stage, the number of spectrum licences that a bidder will win in each service area as well as the base price to be paid by each winning bidder are determined. Where generic licences are offered, an additional stage is needed to determine the specific frequencies that will be assigned to each winning bidder. This stage is referred to as the assignment stage.

Figure D1 — CCA Process

2. The Allocation Stage

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

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 price changes accordingly, shifting their bids to licences that continue to be consistent with their business objectives.

8. During each clock round, bidders are able to bid only 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 on bids that they placed in the clock rounds and/or to submit bids on packages that they were eligible to bid on, but did not submit, during the clock rounds.

All bidders will be subject to a spectrum aggregation limit of 40 MHz in each service area, with the exception of the Northwest Territories, the Yukon and Nunavut, where no aggregation limit will apply. The aggregation limit includes both the paired and the unpaired spectrum available for auction, along with any spectrum licence holdings that bidders already have, but excludes the restricted bands at 2570-2575 MHz and 2615-2620 MHz. Therefore, with the exception of the Northwest Territories, the Yukon and Nunavut, bidders will not be permitted to bid on additional licences in a service area where their spectrum aggregation limit would be exceeded. The auction software will not allow bidders to submit a bid that exceeds their spectrum aggregation limit.

3. Clock Rounds

The allocation stage begins with the clock rounds.

The licences will be auctioned simultaneously over multiple clock rounds. In each round, bidders indicate the number of licences in each product on which they would like to bid, given the prevailing prices. The bid could be for "0," "1" or "2" licences for a product in any category containing multiple generic licences, except for products in the Northwest Territories, the Yukon and Nunavut, where bids of "3," "4" or "5" licences are also permitted (since these service areas are not subject to the spectrum aggregation limit of 40 MHz in the 2500 MHz band). For a product in an unpaired block category, which contains only one licence, the bid could be for "0" or "1" licence. 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.

The price of a product increases in the subsequent round when there is excess demand for it. There is excess demand for a product when the number of licences that are bid on, exceeds the number of licences available.

To remain in the auction, a bidder must submit a valid bid with a value greater than zero for at least one licence in the first clock round. The last valid bid that a bidder submits during each clock round will be binding and will be considered in determining both winning packages and base prices at the end of the allocation stage. However, bidders may increase their bids from the clock rounds in the supplementary round, subject to the activity rules.

The clock rounds will continue and bidding will remain open on all products until there is no excess demand for any product.

4. Conclusion of Bidding in the Clock Rounds

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

5. Information in the Clock Rounds

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

6. Bid Increments

In the first clock round, the price of all licences in each product will be equal to the opening bid price listed in Table 4 in Section 4.2 of the Framework.

In subsequent clock rounds, the price of a given product will increase from the previous round when there is excess demand for that product. For a product that has no excess demand, prices will not increase from the previous round.

The bid increments for the 2500 MHz auction will be in the range of 1-20% of prices in the previous clock round (rounded to the nearest thousand). Throughout the course of the auction, Industry Canada reserves the right to adjust the bid increments to facilitate an efficient and timely auction.

7. Eligibility Points

Each of the 318 licences has been assigned a specific number of eligibility points in proportion both to the population covered by the licence and to the estimated value of the spectrum. One eligibility point has been assigned per 50,000 in population for each 20 MHz block of spectrum (either paired or unpaired) in a service area. The eligibility points have also been adjusted to reflect the estimated value of the spectrum licences as indicated by the opening bid prices. Section 4.3 of this document lists the eligibility points associated with the paired and the unpaired blocks of spectrum being auctioned, as well as the population of the respective service areas.

Eligibility points are used in the determination of the pre-auction financial deposits and in the activity rules applied during the auction, which influence the bids that bidders can submit. In their applications, each potential bidder must indicate the total number of "points" worth of licences on which they wish to bid. A bidder’s initial eligibility, which is based on its pre-auction financial deposit, defines an upper limit on the number of licences for which the bidder can bid. Subsequent levels of eligibility are based on bids in previous clock rounds. All clock rounds in which the bidder does not bid on licences worth the full amount of its eligibility in that round are considered eligibility-reducing rounds.

Bidders will not be able to increase their eligibility points once the auction has started.

8. Activity Rule in the Clock Rounds

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

The activity rule has been established to promote truthful bidding throughout the clock rounds, facilitating the price discovery process and allowing bidders to make changes to their bidding strategies dynamically during the auction, in response to increasing prices. The activity rule discourages biddersfrom misrepresenting their true demand, as doing so will limit their ability to bid on what they really want later in the auction.

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

The eligibility point activity requirement for the 2500 MHz auction is 100%. Specifically, in each round, a bidder will be required to bid on licences whose total sum of associated points is equal to 100% of its eligibility points if it wishes to maintain that eligibility level in the subsequent round.

The eligibility-based activity component considers the size of the package of licences that the bidder is bidding on, where the size is the sum of the eligibility points for each licence in the package, and requires bidders to bid on packages of licences that are the same size or smaller as prices rise. When a bidder switches to a package of licences that is smaller than the one it has previously bid on (that is, a package with fewer eligibility points worth of licences) the bidder’s eligibility is reduced. A clock round in which a bidder reduces its eligibility is called an eligibility-reducing round. These rounds play a special role in the activity rules of the 2500 MHz auction.

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

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

Revealed preference refers to the information that a bidder discloses during the auction 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. The revealed preference component of the activity rule will allow bidders to exceed their eligibility points in order to bid on packages that have become comparatively less expensive, affording bidders greater flexibility to bid on their preferred packages and therefore lessening the shortcomings of only using an eligibility point rule.

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

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

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

9. Supplementary Round

The second phase of the allocation stage is the supplementary round. This is a single round process where bidders have the opportunity to place additional bids for packages of licences at prices they choose, subject to constraints based on the bids that they submitted during the clock rounds (see Section 11 of this annex). Supplementary bids are critical to ensuring both that the licences are allocated to the bidders who value them the most and that winning bidders pay an amount that is sufficient to ensure that no other bidder or group of bidders was willing to pay more for the licences. The supplementary round will still be held even when all licences are provisionally allocated at the end of the clock rounds.

During each clock round, bidders are limited to submitting a single package bid at the announced prices for that round. However, bidders may want to increase their bids in order to reflect their own values for those packages of licences. Furthermore, bidders may be interested in winning other packages that they were eligible for in the clock rounds, but have yet to bid on. The supplementary round provides bidders with an opportunity to submit their best and final bids on packages that they have previously bid on and to submit new bids on the other packages that they are interested in.

In the typical CCA design, bidders submit all-or-nothing, mutually exclusive package bids on the combinations of licences that they are interested in winning, called "standard package bids." In other words, each bid is either won or lost as a whole, and each bidder can win no more than one of its package bids. It also requires the bidder to explicitly bid on each of the packages that it is interested in winning. These two features serve to eliminate exposure risk and to reduce uncertainty about the potential combinations of licences that a bidder may win. However, the number of conceivable combinations that could result from the number of products in the auction may make it difficult for bidders to specifically identify each package that they are interested in winning.

To facilitate bidding on many more packages, Industry Canada is providing bidders with another means of submitting bids in the supplementary round, known as "OR bidding". OR bidding allows bidders to submit individual bids on additional licences without having to explicitly bid on each package that they are interested in. The use of OR bidding in combination with standard package bidding will provide bidders with greater bidding flexibility and should lead to a more efficient auction outcome.

All bidders that are eligible to participate in the supplementary round will have the option to submit standard package bids, OR bids, or both. Section 10 of this annex describes the rules as well as the process for OR bidding.

10. OR Bidding

OR bidding allows bidders to implicitly express interest in many more packages by adding a licence or combination of licences to a base package (see paragraphs 40 and 41 below). OR bids indicate that, in addition to its base package, the bidder wants Licence A at a certain price and / or Licence B at a certain price, and so on.

Base Package

For each bidder, the base package will always be the bidder’s final clock package with an associated bid amount that is equal to the bidder’s highest submitted bid on its final clock package.

A bidder without a final clock package will still be able to submit OR bids in the supplementary round. In this case, its base package is the package consisting of no licences (known as the "zero package").

OR Bids

An "OR bid" refers to an incremental bid on one licence, or combination of licences, within a single service area that a bidder wants to add to its base package. OR bids are non-exclusive in nature, meaning that all feasible combinations of submitted OR bids will be considered with the base package.

Bidders will be allowed to submit more than one OR bid in each service area, subject to the aggregation limit and the rules for OR bidding (see paragraphs 50 and 51 below).

Collections of OR bids

Bidders express their OR bids in collections. A collection of OR bids is defined as an independent set of one or more incremental OR bids. Bidders will have the option to submit a maximum of three different collections of OR bids. Each collection is considered independently of other collections submitted by the same bidder, meaning that OR bids from different collections will not be considered together. See paragraphs 48 and 49 below for examples of collections of OR bids.

Base + OR Package

The bidder’s OR bids are applied additively to its base package to form implied base + OR package bids. The set of implied base + OR package bids consists of all packages formed by combining the base package with all feasible combinations of the submitted collection(s) of OR bids. However, each base + OR package will consist of OR bids from only one collection and will consist of no more than one OR bid from any service area.

In addition, each base + OR package bid is subject to the following restrictions: the aggregation limit, any bidder-defined constraints (see paragraphs 52-55 below) and the activity rules for base + OR package bids (see paragraphs 62-68 below).

The bid amount associated with each base + OR package is equal to the sum of the bid for the base package and the bids for the included OR components, subject to the bidder-defined constraints and the activity rules.

Examples of Collections of OR Bids

The following examples illustrate four different ways that bidders will be able to use collections of OR bids to express their preferences for additional licences. In examples 1-3, suppose the bidder has a base package consisting of two paired FDD licences in five service areas, SA1 to SA5, for which it has bid $200 million.

Example 1 — One OR bid in multiple service areas

Example 2 — Multiple OR bids within a service area

Example 3 — More than one collection of OR bids

Collection 1

Collection 2

In example 4, suppose the bidder has a base package consisting of one FDD licence in five service areas, SA1 to SA5, for which it has bid $100 million.

Example 4 — OR bids in multiple service areas

Rules for Submitting OR Bids

As mentioned, the bidder’s collection of OR bids must satisfy some rules and constraints. When submitting collections of OR bids, bidders will not be permitted to submit any single OR bid that, when combined with the base package as a base + OR package bid, exceeds the aggregation limit for any service area or the bidder’s initial eligibility. To provide bidders with additional flexibility in expressing their incremental OR bids, it may be possible to submit a collection that implies base + OR package bids that exceed one or more of the constraints. However, only base + OR package bids that satisfy all applicable constraints can form part of the solution to the determination of winning bidders and prices.

For each incremental OR bid in a collection, the submitted bid amount must be no less than the opening bid price of the licence(s) and no more than the final clock price of the licence(s). It is possible that a collection of OR bids could imply a bid amount that exceeds the amount allowable by the activity rules for OR bidding (as described in paragraphs 64-68 of this annex) or that exceeds the bidder-defined maximum bid amount (as described in paragraphs 52-55 below). However, the bid amount for all base + OR package bids will automatically be reduced as needed in order to satisfy both the activity rules and any bidder-defined maximum bid amount when considered in the winner determination and pricing processes.

Bidder-defined Constraints on Base + OR Package Bids

Since it is possible that the base + OR packages implied by a single collection of OR bids could vary significantly in terms of size and bid amounts, bidders will have the option to exercise greater control over the base + OR packages they could win by specifying more restrictive constraints on their implied bids. In particular, bidders will be able to specify both an eligibility point limit and a maximum bid amount for each collection of OR bids. These constraints can only be used to limit the bids considered, not to relax any existing constraints.

Any bidder-defined eligibility point limit cannot exceed the bidder’s initial eligibility. Furthermore, any bidder-defined eligibility point limit must be at least equal to the eligibility point value of the base package. For each collection where a bidder has not defined an eligibility point limit, the default eligibility point limit for base + OR package bids implied by the collection is the bidder’s initial eligibility.

For each collection where a bidder has not defined a maximum bid amount, the maximum bid amount for each base + OR package bid implied by the collection will only be limited by the activity rules.

If a bidder specifies an eligibility point limit for a collection of OR bids, then only base + OR package bids that satisfy the eligibility point limit will be considered in the winner determination and pricing processes. If a bidder defines a maximum bid amount for a collection of OR bids, then the implied bid amount for any base + OR package bid will automatically be reduced, as needed, to satisfy the maximum bid amount when considered in the winner determination and pricing processes. If a bidder specifies both an eligibility point limit and a maximum bid amount for a collection of OR bids, then: 1) only base + OR package bids that satisfy the eligibility point limit will be considered in the winner determination and pricing processes and 2) the implied bid amount for a base + OR package bid will automatically be reduced, as needed, to satisfy the maximum bid amount when considered in the winner determination and pricing processes. In addition, all base + OR packages must also satisfy the activity rules in the supplementary round.

11. Activity Rules in the Supplementary Round

The activity rules for bids on standard packages and base + OR packages in the supplementary round complement the activity rule in the clock rounds, encouraging truthful bidding throughout the allocation stage of the auction by ensuring that supplementary bids are consistent with preferences expressed in the clock rounds.

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

All licences are available for bidding in the supplementary round, so that bidders will be able to improve on bids submitted during the clock rounds or to submit bids for packages of licences that they were eligible to bid for in the clock rounds but did not.

A bidder will be able to submit a standard supplementary bid for any given package of licences within its initial eligibility. However, bidders will not be allowed to submit a bid on the zero package, as the only allowable bid amount is zero ($0). The limit on the number of different supplementary round packages that a bidder will be allowed to place will be announced after the bidder qualification has occurred, but will be no less than 500 different packages. The addition of OR bidding will have no impact on the number of standard supplementary bids that each bidder will be allowed to submit.

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

Revealed Preference Limit for a Standard Supplementary Bid

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

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, unless the final clock package is the zero package. All other standard supplementary bids must satisfy revealed preference with respect to the final clock round, regardless of whether the supplementary bid package has more or less eligibility points than the bidder’s eligibility in the final clock round. The revealed preference limit with respect to the final clock package provides the bidder with an incentive to bid on its 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 will not know which round will be the final clock round, the bidder will be encouraged to always bid on its most preferred package; otherwise, the bidder will be constrained in the supplementary round.

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

Revealed Preference Limit for a Base + OR Package

Each supplementary bid on a base + OR package must satisfy the following revealed preference limit activity rule.

Revealed preference limit: All base + OR package bids implied by a given collection of OR bids , must satisfy revealed preference with respect to the final clock round and with respect to:

• i. all eligibility-reducing rounds starting with the last round in which the bidder had eligibility of at least its bidder-defined eligibility point limit for the given collection of OR bids; or
• ii. all eligibility-reducing rounds, if the bidder has not defined an eligibility point limit for the given collection of OR bids.

For the purposes of calculating the revealed preference constraints on base + OR package bids from a given collection, it will be assumed that the bidder has submitted the highest allowable standard supplementary bid on each constraining package, subject to the bidder’s highest bid on its final clock package. In this way, the revealed preference constraints for base + OR package bids will be determined solely by the bidder’s clock round bids and its highest bid amount on its final clock (base) package, and will not be affected by other base + OR package bids implied by the collections of OR bids.

In addition, if a base + OR package bid exceeds the amount that would be allowed by the revealed preference limit, the implied bid amount will automatically be reduced, as needed, to satisfy the activity rules when considered in the winner determination and pricing processes.

It is possible that a base + OR package bid may duplicate other bids that were submitted as either a standard package bid or implied by other collections of OR bids. In those instances, the bid amount used in the winner determination and pricing processes will be the highest bid amount that satisfies the activity rules as well as all relevant bidder-defined constraints. However, implied bid amounts will never be used as constraining bids for the purposes of calculating revealed preference limits.

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

The structure of the supplementary round bidding constraints guarantees that the final clock allocation will not change if there are no unallocated licences. If there are unallocated licences, each bidder will be allocated its final clock package if it has submitted a supplementary bid that increases the dollar amount of its final clock package by at least the value of the unallocated licences as evaluated at the final clock prices less the opening bid prices of the unallocated licences. However, as the aggregate demand in the final clock round will not be available to bidders as they go into the supplementary round, the bidder should be motivated to always bid truthfully to improve its chance of winning its most preferred package. Furthermore, the ability to ensure this allocation may be compromised if any other supplementary bid does not include, at a minimum, all of the licences contained in the bidder’s final clock package.

The revealed preference limit in conjunction with the non-disclosure of the final clock round aggregate demand provides a strong incentive for truthful bidding during the supplementary round, encouraging bidders to bid based on their valuations rather than on any expected guarantee of winning their final clock package.

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

12. Determining the Winning Packages in the Allocation Stage

All valid bids received from bidders in the clock rounds and in the supplementary round are considered for the determination of winning packages. In determining the winning packages and the associated prices, the following constraints will apply to each collection of OR bids: the aggregation limit, the bidder’s initial eligibility, any bidder-defined constraints and the activity rules for OR bidding. If a bidder has specified both an eligibility point limit and a maximum bid amount for a given collection of OR bids, then both constraints will be applied in the winner determination and pricing processes.

A reserve bid for every licence, at the opening bid price, will be included in the determination of winning bidders at the end of the allocation stage. In this process, it is as though Industry Canada is a bidder in the auction, placing a bid on every licence at the opening bid price. The purpose of including a reserve bid for every licence is to ensure that the incremental value that a bidder would be prepared to pay for an additional licence is at least the opening bid price of that licence. The reserve bids will not be treated as a package, but rather as having been placed by different bidders so that any number of reserve bids can be selected in the winning combination.

A solver will be used to identify the highest value combination of valid bids subject to the requirements that each bidder wins no more than one of its packages and that each licence is allocated no more than once. If there is only one combination of bids that meets the criteria, this will be the winning outcome that determines the winning packages and the winning bidders.

If more than one combination of valid bids have the same highest value, the tie will first be resolved 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 so that an allocation that is the most similar to the final clock allocation is selected.

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

13. Determining the Base Price in the Allocation Stage

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

Industry Canada will use a second-price rule to calculate the base prices such that winning bidders, individually and collectively, will pay an amount that is sufficient to ensure that there is no other bidder or group of bidders prepared to pay more for the licences. This amount will typically be 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.

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

14. Information at the End of the Allocation Stage

At the end of the allocation stage, each bidder will be informed of its own winning package, along with the base price that it will pay for its package.

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

15. The Assignment Stage

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.

The assignment stage will only be used to determine the specific assignments within the paired category of licences. Since there is no more than one unpaired licence available in any given service area, there is no need for an assignment round for the unpaired licences.

The assignment stage will consist of a sequence of assignment rounds. In each assignment round, bidders will be presented with a set of options available to them for the products being assigned, taking into consideration the number of licences that the bidder won in the allocation stage, the number of licences allocated to other bidders and the number of licences that remain unallocated, subject to the assignment stage restrictions (see Section 16 of this annex).

The assignment rounds will be run product-by-product in descending order of the populations of the associated service areas, possibly conducting a separate round for each product. This could potentially result in up to 61 assignment rounds. This process will enable bidders to know which specific frequencies they have won in the most populated service areas prior to their participation in the assignment rounds for the other less populated service areas.

In support of simplifying the assignment stage and facilitating the assignment of contiguous spectrum across service areas, two or more products will be combined into a single assignment round when the products are in the same Region (i.e. Region A, Region B or Region C), when their service areas form a contiguous geographic area and when the winners, and the number of licences they have won, are the same in the service areas to be combined (see Section 16 of this annex). Only products that are in the same Region will be considered for being combined, as the service areas in different regions have different blocks available in the auction. See Annex A for the licences available in the service areas of each region.

For example, the two contiguous service areas shown in the tables below would be eligible to be combined into a single assignment round.

One possible assignment could be:

In addition, products in the same Region may also be combined into a single assignment round when the winners, and the number of licences they have won, are sufficiently similar. For example, products in the same Region may be combined if a single winner in one service area is replaced by a different winner in the other service area(s) or if a licence is unallocated in the other service area(s). Consideration may also be given to combining service areas that are within the same Region, whether or not they form a contiguous geographic area, provided the winners and the number of licences they have won in each service area are sufficiently similar.

For example, the two service areas shown in the tables below would also be eligible to be combined into a single assignment round.

One possible assignment could be:

With the combined products, bidders will only be permitted to bid for and win assignments that would give them the exact same blocks in each service area.

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 been allocated. Each winning bidder has both a right and an obligation to purchase one of the frequency range options presented to it in the assignment round.

For each assignment round, a solver will be used to identify the combination of specific assignments of licences that result in the highest bid amount. 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.

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).

The additional amount to be paid for the assignment of specific licences, known as the assignment price, is calculated for the package of specific licences bid for in the round, not for the individual licences. Given the pricing rules, the assignment price of each winning assignment stage package will be equal to or less than the corresponding winning bid amount, and could even be zero.

Industry Canada will apply bidder-optimal core prices and use a "nearest Vickrey" approach to determine assignment prices. In the event that an additional payment above Vickrey prices is required, the calculation of the additional payment to be paid by each winning bidder will be weighted based on the relative size of the package it is being assigned in the given assignment round, evaluated at the opening bid prices. Further information on the determination of assignment prices can be found in Annex G.

16. Restrictions in the Assignment Stage

Recognizing the efficiency gains from having contiguous blocks of spectrum, Industry Canada will assign bidders contiguous spectrum within a product whenever possible. As such, bidders will only be presented with the assignment options that satisfy the following rules, applied in order:

• (a) Bidders that win more than one licence in the same product will be assigned licences that are contiguous to each other;
• (b) A bidder that wins one or more licences in a product where they have an existing licence will have its new licence assigned as contiguous to its existing licence, provided it is feasible to do so after ensuring the first contiguity rule;
• (c) Finally, licences that remain unallocated within a product will be retained by Industry Canada as contiguous blocks, provided it is feasible to do so after ensuring the first and second contiguity rules.

Note that the contiguity rules may affect the specific frequency options that are available to bidders in the assignment round and may prevent bidders from obtaining the same frequency options across service areas. It is also possible that the application of these contiguity rules would prevent Industry Canada from combining some products into a single assignment round.

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

17. Information at the end of each Assignment Round

Following the end of each assignment round, after the results have been verified, participating bidders will be notified of the specific licences that they have won and the assignment price to be paid. In this way bidders will know their own results from one assignment round before participating in a subsequent assignment round.

18. Final Price

At the end of the assignment stage, Industry Canada will determine the final price that each winning bidder will be required to pay for the package of licences it has won. This final price will be equal to the base price plus any associated assignment price(s).

19. Information at the end of the Assignment Stage

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

20. Information at the End of the Auction

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

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

Annex E — Example of the Activity Rules for the Clock Rounds and Supplementary Round

For the purposes of this example, consider ten (10) service areas (SA1 to SA10) with two paired (FDD) licences available in each service area. In SA1 to SA5, the licences are worth 20 points; while, in SA6 to SA10, the licences are worth 14 points. A spectrum aggregation limit of 40 MHz in each service area allows a bidder to submit bids for either one licence, two licences or no licences in any given service area.

Suppose a bidder wants to obtain two licences in five service areas, SA1 to SA5 (Package A). However, if the price of Package A exceeds the price of a package with two licences in SA6 to SA10 (Package B) by more than $400,000, then the bidder prefers Package B.

Eventually, if the prices become too high, the bidder will be unable to afford either Package A or Package B and will need to reduce its demand to one licence. In this case, the bidder prefers one licence in SA1 to SA5 (Package C), but will switch to one licence in SA6 to SA10 (Package D) if the price of Package C exceeds the price of Package D by more than $200,000.

Suppose the bidder has an initial budget of $1,600,000 and 200 eligibility points.

CLOCK ROUNDS

Given this bidder’s preferences, consider the following clock round bidding history.

Note that rounds 2, 7 and 8 (in bold) were eligibility-reducing rounds, and that round 8 was also the final clock round.

In rounds 1, 2, 3, 6, 7 and 8 the bidder’s activity was within its eligibility so revealed preference constraints were not enforced. However, in rounds 4 and 5, the bidder’s activity exceeded its eligibility points. Therefore, to bid on its most preferred package in rounds 4 and 5, each bid had to satisfy revealed preference with respect to the previous rounds in which it reduced its eligibility (round 2).

With a purely eligibility-based rule, the bidder is never able to switch to a larger package once it reduces its eligibility. This may therefore encourage a bidder to bid on less profitable packages in order to maintain its eligibility for bids in later rounds.

However, the revealed preference / eligibility point hybrid activity rule allows a bidder to switch back freely, as long as the package satisfies the revealed preference constraints with respect to each previous round in which the bidder reduced its eligibility points. In other words, the package the bidder wants to bid on has to have become relatively less expensive compared to the packages the bidder has bid on in previous rounds.

The revealed preference calculations for rounds 4 and 5 are as follows:

Round 4

In round 4, prices increased on licences in SA6 to SA10. At these prices, the price difference between Package A and Package B was $300,000 ($1,400,000 compared to $1,100,000). Therefore, the bidder preferred bidding on Package A. However, the bidder already reduced its eligibility from 200 points to 140 points in round 2. Therefore to bid on Package A, the bid had to satisfy the revealed preference constraint with respect to round 2. Mathematically, the constraint was as follows, where R refers to the round:

(Price of Package A in R4) – (Price of Package A in R2) ≤ (Price of Package B in R4) – (Price of Package B in R2)
($1,400,000 - $1,200,000) ≤ ($1,100,000 - $700,000)
$200,000 ≤ $400,000

The price of Package A increased by $200,000 from round 2 to round 4, while the price of Package B increased by $400,000. Therefore, the constraint was satisfied and the bidder was permitted to bid on two licences in SA1 to SA5 (Package A). Note that this bid did not increase the bidder’s eligibility back to 200 points.

Round 5

In round 5, prices increased by the same amount on licences in all service areas. Since the relative price difference ($300,000) had not changed, the bidder still preferred to bid on the same package as in round 4, Package A. Since the bidder’s eligibility in this round was only 140 points, the bid again had to satisfy the revealed preference constraint with respect to round 2, given by:

(Price of Package A in R5) – (Price of Package A in R2) ≤ (Price of Package B in R5) – (Price of Package B in R2)
($1,600,000 - $1,200,000) ≤ ($1,300,000 - $700,000)
$400,000 ≤ $600,000

The revealed preference constraint continued to be satisfied since the price of Package A increased by $400,000, while the price of Package B increased by $600,000. Therefore the bidder was again permitted to bid on Package A.

SUPPLEMENTARY ROUND

The following table summarizes the bidder’s highest bid on each standard package that it bid on in the clock rounds. These four bids will be carried into the supplementary round.

Since Package D is the bidder’s final clock package, the bid amount for Package D is unlimited. However, for this example, suppose that the bidder does not revise its bid for its final clock package or for any of its other constraining packages.

Standard Package Supplementary Bids

For each standard package bid, the revealed preference limit requires that each bid satisfy revealed preference with respect to the final clock round, and with respect to each eligibility-reducing clock round starting with the last round in which the bidder had eligibility points equal to the eligibility of the package being bid on.

Suppose that the bidder is now also interested in a package consisting of one licence in all service areas (SA1 to SA10), called Package S1, and wants to submit a bid on S1 up to its maximum budget of $1,600,000. Package S1 is associated with 170 eligibility points. The bidder last had sufficient eligibility to bid on S1 in round 2, when it had 200 eligibility points. Therefore, a valid bid on S1 must satisfy revealed preference with respect to the final clock round (round 8) and with respect to round 2 and all subsequent rounds where the bidder reduced its eligibility (rounds 7 and 8).

The revealed preference constraints for Package S1 are as follows:

Revealed preference with respect to round 2 (first eligibility-reducing round, Package B)

(Sup. Bid on S1) – (R2 Price of S1) ≤ (Highest bid on B) − (R2 Price of B)
(Sup. Bid on S1)  ≤  (Highest bid on B) – (R2 Price of B) + (R2 Price of S1)
(Sup. Bid on S1)  ≤  $1,500,000 - $700,000 + $950,000
(Sup. Bid on S1)  ≤  $1,750,000

Revealed preference with respect to round 7 (second eligibility-reducing round, Package C)

(Sup. Bid on S1) – (R7 Price of S1) ≤ (Highest bid on C) – (R7 Price of C)
(Sup. Bid on S1) ≤ (Highest bid on C) – (R7 Price of C) + (R7 Price of S1)
(Sup. Bid on S1) ≤ $1,000,000 - $1,000,000 + $1,850,000
(Sup. Bid on S1) ≤ $1,850,000

Revealed preference with respect to round 8 (final clock round and last eligibility-reducing round, Package D)

(Sup. Bid on S1) – (R8 Price of S1) ≤ (Highest bid on D) – (R8 Price of D)
(Sup. Bid on S1) ≤ (Highest bid on D) – (R8 Price of D) + (R8 Price of S1)
(Sup. Bid on S1) ≤ $850,000 - $850,000 + $1,950,000
(Sup. Bid on S1) ≤ $1,950,000

Without submitting a supplementary bid that increases the bid amount on its constraining packages, the bidder would be allowed to submit a supplementary bid with a maximum bid amount of $1,750,000 on Package S1. Therefore, the bidder would be allowed to submit its bid of $1,600,000 on Package S1.

Note that the revealed preference activity rule results in a chain of constraints that begins with the final clock package. By increasing the bid on its final clock package, a bidder can increase its maximum allowable bid amount for constraining packages; by increasing its bids on constraining packages, a bidder can then increase its maximum allowable bid amount for other packages, including constraining packages from earlier clock rounds. The calculations in paragraph 23, for the maximum allowable bid on the constraining packages, demonstrate how constraints are chained to one another.

Base + OR Package Supplementary Bids

The activity rules require that all base + OR package bids implied by a given collection of OR bids must satisfy revealed preference with respect to the final clock round and with respect to:

• a. All eligibility-reducing rounds starting with the last round in which the bidder has eligibility of at least its bidder-defined eligibility point limit; or
• b. All eligibility-reducing rounds, if the bidder did not define an eligibility point limit for the given collection of OR bids.
• c. In calculating these constraints, it is assumed that the bidder submitted the highest allowable standard package bid on each constraining package (the package bid on in each eligibility-reducing round).

In this example, the bidder did not increase its bid on Package D, so the maximum possible standard package bids for the constraining packages (Packages B, C and D) are given by the following revealed preference constraints.

• (a) Highest bid on the final clock package, Package D, is $850,000.
• (b) Maximum allowable bid on Package C is $1,100,000, as given by the following constraint.

• Revealed preference with respect to round 8 (final clock round and last round eligible to bid on Package C)

(Sup. Bid on C) – (R8 Price of C) ≤ (Highest bid on D) – (R8 Price of D)
(Sup. Bid on C) ≤ (Highest bid on D) – (R8 Price of D) + (R8 Price of C)
(Sup. Bid on C) ≤ $850,000 - $850,000 + $1,100,000
(Sup. Bid on C) ≤ $1,100,000

• (c) With the assumption that the bidder submitted $1,100,000 on Package C, the maximum allowable bid on Package B is $1,700,000, as given by the following constraints related to both round 8 (the final clock round) and round 7 (the last round the bidder was eligible to bid on Package B). Note that round 8 is the most constraining round.

Revealed preference with respect to round 8 (final clock round)

(Sup. Bid on B) – (R8 Price of B) ≤ (Highest bid on D) – (R8 Price of D)
(Sup. Bid on B) ≤ (Highest bid on D) – (R8 Price of D) + (R8 Price of B)
(Sup. Bid on B) ≤ $850,000 - $850,000 + $1,700,000
(Sup. Bid on B) ≤ $1,700,000

Revealed preference with respect to round 7 (last round eligible to bid on Package B)

(Sup. Bid on B) – (R7 Price of B) ≤ (Highest bid on C) – (R7 Price of C)
(Sup. Bid on B) ≤ (Highest bid on C) – (R7 Price of C) + (R7 Price of B)
(Sup. Bid on B) ≤ $1,100,000 - $1,000,000 + $1,700,000
(Sup. Bid on B) ≤ $1,800,000

Based on the above constraints, the revealed preference limit for base + OR package bids assumes the following highest bids for the constraining packages:

• Package B - $1,700,000
• Package C - $1,100,000
• Package D - $850,000

Note: For Package D, the highest bid amount is an actual bid; while for Packages B and C, the highest bid amount is assumed based on the above constraints. These bid amounts are assumed regardless of the bidder’s budget constraint.

Now suppose that the bidder submits the following collection of OR bids, without specifying any bidder-defined limits (eligibility point limit or maximum bid amount) for this collection of OR bids. The base package is the bidder’s final clock package, Package D.

This collection represents a bid on one additional licence in each of SA6 to SA10 at the final clock prices. These bids express the bidder’s interest in all base + OR packages that are implied by combining the base package with any combination of these OR bids (up to 31 different packages).

Since the bidder did not include any bidder-defined constraints with this collection of OR bids, the activity rules require that all base + OR package bids satisfy revealed preference with respect to the final clock round and all eligibility-reducing rounds.

Rounds 2, 7 and 8 are eligibility-reducing rounds. Round 8  is also the final clock round.

The following provides an example of the constraints that would be applied to one possible base + OR package bid.

Consider the bid combining the base package with all of the OR bids in the collection. This package includes two licences in five service areas, SA6 to SA10, and will be referred to as OR1. Note that OR1 also duplicates Package B, on which the bidder bid $1,500,000 in the clock rounds.

Based on the collection of OR bids, the implied bid amount for this package is $1,700,000.

Revealed preference with respect to round 2 (first eligibility-reducing round)

(Sup. Bid on OR1) – (R2 Price of OR1) ≤ (Highest bid on B) – (R2 Price of B)
(Sup. Bid on OR1) ≤ (Highest bid on B) – (R2 Price of B) + (R2 Price of OR1)
(Sup. Bid on OR1) ≤ $1,700,000 – $700,000 + $700,000
(Sup. Bid on OR1) ≤ $1,700,000

Revealed preference with respect to round 7 (second eligibility-reducing round)

(Sup. Bid on OR1) – (R7 Price of OR1) ≤ (Highest bid on C) – (R7 Price of C)
(Sup. Bid on OR1) ≤ (Highest bid on C) – (R7 Price of C) + (R7 Price of OR1)
(Sup. Bid on OR1) ≤ $1,100,000 – $1,000,000 + $1,700,000
(Sup. Bid on OR1) ≤ $1,800,000

Revealed preference with respect to round 8 (final clock round)

(Sup. Bid on OR1) – (R8 Price of OR1) ≤ (Highest bid on D) – (R8 Price of D)
(Sup. Bid on OR1) ≤ (Highest bid on D) – (R8 Price of D) + (R8 Price of OR1)
(Sup. Bid on OR1) ≤ $850,000 – $850,000 + $1,700,000
(Sup. Bid on OR1) ≤ $1,700,000

Therefore, the revealed preference constraints would allow a maximum bid amount of $1,700,000 for Package OR1, and the bid amount does not need to be reduced. Note that the bid of $1,700,000 is more than the bidder’s highest clock round bid of $1,500,000 on Package B. As a result, this base + OR package bid of $1,700,000 would be used in the winner determination and pricing processes. However, the bid of $1,500,000 would still be used to calculate the revealed preference limit for any standard package bid in the supplementary round that is for more than 140 eligibility points.

In addition to the specific example, the following generalizes the three constraints that each base + OR package bid would need to satisfy, where OR represents any possible base + OR package bid implied by the base package and the given collection of OR bids.

Revealed preference with respect to round 2 (first eligibility-reducing round)

(Sup. Bid on OR) – (R2 Price of OR) ≤ (Highest bid on B) – (R2 Price of B)
(Sup. Bid on OR) ≤ (Highest bid on B) – (R2 Price of B) + (R2 Price of OR)
(Sup. Bid on OR) ≤ $1,700,000 – $700,000 + (R2 Price of OR)
(Sup. Bid on OR) ≤ $1,000,000 + (R2 Price of OR)

Revealed preference with respect to round 7 (second eligibility-reducing round)

(Sup. Bid on OR) – (R7 Price of OR) ≤ (Highest bid on C) – (R7 Price of C)
(Sup. Bid on OR) ≤ (Highest bid on C) – (R7 Price of C) + (R7 Price of OR)
(Sup. Bid on OR) ≤ $1,100,000 – $1,000,000 + (R7 Price of OR)
(Sup. Bid on OR) ≤ $100,000 + (R7 Price of OR)

Revealed preference with respect to round 8 (final clock round)

(Sup. Bid on OR) – (R8 Price of OR) ≤ (Highest bid on D) – (R8 Price of D)
(Sup. Bid on OR) ≤ (Highest bid on D) – (R8 Price of D) + (R8 Price of OR)
(Sup. Bid on OR) ≤ $850,000 – $850,000 + (R8 Price of OR)
(Sup. Bid on OR) ≤ (R8 Price of OR)

Since the bidder did not define any additional constraints, all implied base + OR package bids had to satisfy revealed preference with respect to the final clock round and all eligibility-reducing rounds; and the implied bid amount for each base + OR package bid is the sum of the highest bid on the final clock package and the amount of the OR bid components, subject to the activity rules.

As indicated in paragraph 22 (a), if the bidder had defined a maximum eligibility point limit with this collection, its bids would have to satisfy revealed preference with respect to the final clock round and all eligibility-reducing rounds, starting with the last round in which the bidder’s eligibility was at least its bidder-defined eligibility point limit.

For example, if the bidder had defined a maximum eligibility point limit of 140 points or less, all implied base + OR package bids would only be subject to the revealed preference constraints with respect to rounds 7 and 8, as round 7 was the last round in which the bidder had at least 140 eligibility points.

Additionally, if the bidder had defined a maximum bid amount with its collection of OR bids, the bid amount for each base + OR package bid would have been capped to either the bidder-defined maximum bid amount or the maximum allowable amount according to the activity rules, whichever is lower. In other words, when the activity rule allows a bid amount that exceeds the bidder-defined maximum bid amount for a collection, the bid will be reduced to the bidder-defined maximum bid amount.

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

Revealed Preference in the Clock Rounds

Under the activity rule in the clock rounds, a bidder may, at any time, place a bid on any package that is within its current eligibility. In addition, in any round, the bidder is also permitted to bid on a package that exceeds its current eligibility provided that the package satisfies revealed preference with respect to each prior eligibility-reducing round. Bidding on a larger package does not increase the bidder’s eligibility in subsequent rounds. A bidder will not be able to submit a clock round bid that exceeds its initial eligibility, as determined by its pre-auction financial deposit.

Licences have been grouped into two categories, paired and unpaired. A category in a given service area is referred to as a product. In total, 106 products will be available in the 2500 MHz auction, with the following blocks and quantities available in each Region.

Region A — 86 products

• Blocks C/C’ to G/G’ (five generic licences of 10 + 10 MHz);

• Block I (one licence of 25 MHz);

Region B — 16 products

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

Region C — 4 products

• Blocks A/A’ to B/B’ and E/E’ to G/G’ (five generic licences of 10 + 10 MHz); and

• Block H (one licence of 25 MHz).

As per the equation below, a package in clock round t satisfies revealed preference with respect to an earlier clock round s for a given bidder if the bidder’s package Q_t has become relatively less expensive than the package bid on in clock round s, Q_s, as clock prices have progressed from the clock prices in clock round s to the clock prices in clock round t. Algebraically, the revealed preference constraint is the condition that:

\[\sum^m_{i=1} (Q_{t,i} *(P_{t,i} - P_{s,i})) \leq \sum^m_{i=1} (Q_{s,i} *(P_{t,i} - P_{s,i})) \]

where:

"i" indexes the products;
"m" is the number of products, where the number of products for the 2500 MHz auction is 106;
Q_t,i is the quantity of the i^th product bid in clock round t;
Q_s,i is the quantity of the i^th product bid in clock round s;
P_t,i is the clock price of the i^th product bid in clock round t; and
P_s,i is the clock price of the i^th product bid in clock round s.

A bidder’s package, Q_t, 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

Under the activity rule for the supplementary round, there is no limit on the supplementary bid amount for the final clock package, unless the final clock package is the zero package. This exception also applies when a bidder’s final clock package exceeds its eligibility in the final clock round due to the application of the revealed preference component of the clock round activity rule. However, a bidder will never be allowed to submit a supplementary bid on the zero package.

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

A bidder will not be allowed to submit a standard supplementary bid on a package that exceeds its initial eligibility. In addition, standard supplementary bids on packages (other than the final clock package) that exceed the bidder’s eligibility in the final clock round must satisfy revealed preference with respect to the last clock round in which the bidder was eligible to bid on the package as well as all subsequent clock rounds in which the bidder reduced eligibility.

When submitting collections of OR bids, bidders will not be permitted to submit any single OR bid that, when combined with the base package as a base + OR package bid, exceeds any aggregation limit for any service area or the bidder’s initial eligibility.

To provide bidders with additional flexibility in expressing their incremental OR bids, it may be possible to submit a collection that implies base + OR package bids that exceed one or more of the constraints. However, only base + OR package bids that satisfy all applicable constraints can form part of the winning solution.

Furthermore, all base + OR package bids implied by a given collection of OR bids must satisfy revealed preference with respect to the final clock round and with respect to:

• a) all eligibility-reducing rounds starting with the last round in which the bidder had eligibility of at least its bidder-defined eligibility point limit for the given collection of OR bids; or
• b) all eligibility-reducing rounds, if the bidder has not defined an eligibility point limit for the given collection of OR bids.

For the purposes of calculating revealed preference for base + OR package bids from a given collection, it is will be assumed that the bidder has submitted the highest allowable standard supplementary bid for on each constraining package (packages bid on in eligibility-reducing rounds), subject to the bidder’s highest bid on its final clock package.

Let Q denote the package on which the bidder wishes to place a supplementary bid, whether it is a standard supplementary bid or a base + OR package bid. Let Q_s denote the package on which the bidder bid in clock round s and let B_s denote the bidder’s highest dollar amount bid in the auction for package Q_s, whether the highest dollar amount was placed in a clock round or the supplementary round.

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

\[B \leq B_S + \sum^m_{i=1} (P_{s,i} *(Q_{i} - Q_{s,i})) \]

where:

"i" indexes the products;
"m" is the number of products;
Q_i is the quantity of the i^th product in package Q;
Q_s,i is the quantity of the i^th product in package Q_s of clock round s;
P_s,i is the clock price of the i^th product in clock round s;
B is the dollar amount of the supplementary bid on package Q; and
B_s is the highest dollar amount bid on package Q_s either in a clock round or in the supplementary round.

For a standard supplementary bid on a 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. For a base + OR package bid implied by a given collection, let T(Q) denote the last clock round in which the bidder’s eligibility was at least its bidder-defined eligibility point limit for that collection of OR bids. If the bidder has not defined an eligibility point limit, then T(Q) is the first round in which the bidder reduced its eligibility.

A given bidder’s supplementary bids are consistent with revealed preference if the bidder’s supplementary bid for package Q, with a dollar amount, B, satisfies the following condition:

For a supplementary bid on any package Q, the dollar amount B must satisfy the revealed preference constraint, as specified in paragraph 13 above with respect to the final clock round and with respect to every eligibility-reducing round equal to T(Q) or later.

Note that, in the application of paragraph 13 to standard supplementary bids, the package Q_s 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.

However, the revealed preference constraints for base + OR package bids will be determined solely by the bidder’s clock bids and its highest bid on the final clock package since it is assumed that the bidder has submitted the maximum allowable bid on its constraining packages. The revealed preference constraint will not be affected by other base + OR package bids implied by the collection of OR bids.

See Annex E for an example of the revealed preference activity rules for the clock rounds, for standard supplementary bids, and for OR package bids.

Annex G — Pricing Rule

Prices are determined at two points in the auction, in the following order: first, at the end of the allocation stage, in order to determine the base prices, which are the minimum that winning bidders will pay for their winning packages; and second, in the assignment stage at the end of each assignment round in order to determine the incremental payments for specific licences, known as assignment prices. Industry Canada will use a second-price rule to determine the prices to be paid by winning bidders. More specifically, Industry Canada will apply bidder-optimal core prices and 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

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.

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

The Vickrey price for each winning bidder (known as "Bidder J" in this explanation) is calculated as follows. First, from the value of the winning combination of packages, subtract Bidder J’s winning bid (value A). Next, recalculate the winning combination of packages for the hypothetical situation in which all Bidder J’s bids are excluded, as if Bidder J had not participated (value B). The Vickrey price for Bidder J is calculated as the value of the winning combination of packages with all Bidder J’s bids excluded (value B) minus the sum of the winning allocation stage bids for all bidders other than Bidder J (value A), that is, value B minus value A. This is the minimum amount that the winning bidder could have bid in order to still have won the package, given the bids of all other bidders.

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 relative to the size of the bidder’s package, as measured by the bidder’s winning package evaluated at the opening bid prices.

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 bid.
• (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 minimizing the sum of base prices across winning bidders is (are) selected. If there is only one set of base prices satisfying these three conditions, this set determines the base prices for the allocation stage.
• (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 as 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.

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.

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

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 (https://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 G1.

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

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

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

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

However, these payments sum to $26, which is 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) in order to ensure that their combined payment is greater than that of Bidder 3, satisfying the condition that no other bidder or group of bidders were prepared to pay more for the licences in question. To do so, Bidder 1 and Bidder 2 must pay, collectively, at least $32.

Figure G1 — Example of Calculating Base Prices (Annex G)

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 in this example. Each bidder is therefore paying an additional $3 above its Vickrey price, with Bidder 1 paying $17 ($14 + $3) and Bidder 2 paying $15 ($12 + $3), as shown in Figure G1.

However, if the opening bid prices for the two licences are different amounts, the two bidders must split the extra payment proportionately, in reference to the opening bid amounts (the fourth condition). For example, if the opening bid price for Licence A is $8 and the opening bid price for Licence B is $4, then the opening bid price of Bidder 1’s package is twice as large as that of Bidder 2. Therefore, in this example, 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

The assignment stage will only be used to determine the specific assignments within the paired category of licences. Since there is no more than one unpaired licence available in any given service area, there is no need for an assignment round for the unpaired licences.

The assignment rounds will be run product-by-product in descending order of the populations of the associated service areas, and possibly conducting a separate round for each product will be conducted. This could potentially result in up to 61  assignment rounds.

In support of simplifying the assignment stage and facilitating the assignment of contiguous spectrum across service areas, two or more products will be combined into a single assignment round when the products are in the same Region (i.e. Region A, Region B or Region C), when their service areas form a contiguous geographic area and when the winners and the number of licences they have won are the same, whenever possible given the assignment stage restrictions (see Annex C, Section 16).

Products in the same Region may also be combined into a single assignment round when the winners, and the number of licences they have won, are sufficiently similar, whether or not they form a contiguous geographic area.

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

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

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

The assignment prices from each assignment round must satisfy the following conditions:

• (a) First condition: The assignment prices must be positive or zero and not more than the dollar amount of the winning assignment stage bid.
• (b) Second condition: The set of assignment prices must be sufficiently high that there is no alternative combination of valid assignment bids that sum to more than the winning assignment bids. If there is only one set of assignment prices that satisfies the first two conditions, this determines the assignment prices.
• (c) Third condition: If there are many sets of assignment prices that fulfil the first and second conditions, the set(s) of assignment prices minimizing the sum of assignment prices across winning assignment stage bids is (are) selected. If there is only one set of assignment prices that satisfies these three conditions, this determines the assignment prices.
• (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 being assigned in the given assignment round, 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.

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