Appendix C to the Notice of Proposed Rulemaking
Supplement to Appendix C: Auctionomics/Power Auctions Option for Forward Auction (February 1, 2013)

Reverse Auctions

Generally, the major rules of an auction can be described in terms of three elements: the bid collection procedure (how bid information is gathered from bidders), the assignment procedure (who gets what), and the pricing rule (how bids determine the prices). The Reverse Auction option we present here is a descending clock auction defined in the following general way. Bid information is gathered in a series of rounds in which stations are presented with price offers for different options for relinquishing rights (including going off-air or moving to a lower broadcast television band). Prices can fall but cannot rise from round to round. A bid for a station in each round specifies the broadcaster’s preferred option for that station. Whenever the price offer for a broadcaster’s currently preferred relinquishment option is reduced, that broadcaster is given the opportunity to exit the auction and continue broadcasting in its pre-auction band, and may also be given an opportunity to modify its preferred relinquishment option. Generally, the FCC’s algorithm will decrement prices so as to reduce the excess supply of broadcasters willing to relinquish their rights and to make best use of the available broadcast channels. When the auction terminates, every broadcaster that has not exited will receive its last selected relinquishment option and be compensated according to its last accepted price offer for that option.

This description outlines the auction rules, but omits some algorithmic details. Final details will depend on how the FCC decides to measure interference and to determine what collections of broadcast stations can be fit into the remaining broadcast spectrum. To illustrate how the auction would work, consider a simple example. Imagine there are five stations with identical coverage areas currently assigned to channels. The goal is to clear three channels by paying two stations to go off-air. The auction starts by proposing to pay a high price to each station to go offair. Some stations may choose to stay on-air, but assume that more than three offer to go off-air at that price. In subsequent rounds, the price for going off-air is decreased. As the proposed price falls, some stations that were willing to go off-air at a higher price will reject the lower price, instead choosing to stay on-air. When the number of stations assigned to go off-air is down to three, the auction is over: the stations staying on-air are assigned specific channels, and the stations going offair are paid the current price.

The simple example abstracted from the facts that there are multiple bands (UHF and VHF) and that different stations have different coverage areas and create different interference for other stations. With multiple bands, a station may be offered a price not only for going off-air but also for accepting assignment to a lower band. Also, because the stations have different coverage areas and create different interference for other stations, the prices will be station-specific (although, as noted above, prices for two stations in the same band with the same coverage area would be the same). Furthermore, the number of channels to be cleared will not be fixed in advance, but may depend on the bids in the Forward Auction. Therefore, the Reverse Auction will begin by finding the prices at which a large number of channels can be cleared in every area and then, if necessary, will continue by finding the (lower) prices at which a smaller number of channels can be cleared.

Moving beyond the simple to a more general case, there are still multiple rounds of bidding. At the beginning of each round, there is a tentative assignment of stations to bands. Each station has a current offer price for going off-air, and for moving to a lower band, and is told whether these prices will decrease during the round. The station states whether it wants to stay in its currently assigned band, go off-air, or move to a lower band. The station may switch among these options, as prices decline. An activity rule enforces consistent bidding. The activity rule has the property that a station’s decision to be assigned to its pre-auction band is irreversible: once made, the station “exits” the auction. Therefore, as in the simple example, the number of stations agreeing to go off-air or move to a lower band will decrease as the auction progresses.

In each round of the auction, a computer algorithm determines, for each station that has not exited, whether that station still could be assigned to its pre-auction band without violating the interference limits for the other stations already assigned to that band. When a station cannot be assigned a channel in its home band, it is “frozen” – its current assignment and the price for that assignment cannot be changed in this round. All the other prices may be decreased. For any station whose price for its currently preferred relinquishment option is decreased, the station is invited to (a) change its preferred relinquishment option (in a way that may be restricted by an activity rule), (b) exit the auction, or (c) keep its preferred relinquishment option. At the end of the auction, every bidder that has not exited receives its last selected relinquishment option and is compensated according to the last price offer for this option. Bidders that have exited and stations that did not participate will be assigned specific channels in their pre-auction bands.

As described below, if there is insufficient demand in the Forward Auction at prices determined by the Reverse Auction, the FCC may reduce the provisional clearing target and the auction will continue. In that case, the assignments and prices of some stations will change. With a lower provisional clearing target, more stations will be able to be assigned channels in their pre-auction bands and prices paid to go off-air or move to a lower band will fall. We now provide more details for this auction design option, starting with a few definitions.

Definitions
Permissible Bands

A station’s Permissible Bands are the ones it potentially can choose during the auction. <sup>1</sup> For a station whose pre-auction band is UHF, the Permissible Bands are the UHF band and the upper VHF band. For a station currently in the upper VHF only the upper VHF band is permissible.

Provisional Clearing Target

The Provisional Clearing Target is the number of UHF broadcast channels to be cleared. The Provisional Clearing Target may be adjusted downward as the Reverse Auction proceeds. The same Provisional Clearing Target will apply nationally except in the event that broadcaster participation in certain regions is particularly low or Canadian or Mexican television allotments constrain the amount of spectrum that can be made available for flexible use. The FCC may then choose to designate certain geographic areas as Impaired Regions, and seek to clear a smaller number of channels in these areas.

Feasible Assignment

An assignment of stations to bands is feasible given a Clearing Target if every station under consideration can be given a channel in its assigned band in a way that satisfies FCC interference requirements.

Feasibility Checker

The auction computations will rely on a computer algorithm that can check whether any proposed assignment of stations to bands is a Feasible Assignment. The Feasibility Checker also will output a tentative assignment of stations to channels that meets the feasibility requirements. During the auction, the Feasibility Checker will be used repeatedly to determine whether, given a current Feasible Assignment, it would be possible to move a particular station to a different band and still have a Feasible Assignment.

Active

A station that can feasibly be assigned to its pre-auction band, given the current assignments to other stations, is active.

Frozen

A station that cannot feasibly be assigned to its pre-auction band, given the current assignments of other stations, has its price frozen at the last price offer for its last selected relinquishment option (its current tentative assignment).

Exit

A station assigned to its pre-auction band has exited the auction.

Impaired regions

Wireless license areas in which less than the targeted amount of spectrum can be cleared at the reserve prices.

<p class="footnote"><sup>1</sup> For simplicity of exposition we do not consider moves to the lower VHF band. The auction design can easily be extended to include moves to this band.</p>

Description of the Auction
Initial Prices

Prior to the auction, the FCC will announce Initial Prices—the maximum prices the FCC will offer—for each station. A UHF broadcaster will see two prices: a price to go off-air and a price to move from UHF to upper VHF. An upper VHF broadcaster will see one price: a price to go off-air. The Initial Prices may be specified as a multiple of a station’s interference-free population coverage, and may vary by region or depending on a station’s home band. The Initial Price for going off-air will be greater than the Initial Price for moving to a lower band.

Initial Bids

In the initial round of the auction (Round 0), each station’s Initial Bid is a statement of its preferred relinquishment option (go off-air or move to another Permissible Band) at the relevant reserve prices, or alternatively to remain in its pre-auction band. Any station that does not participate will be assigned to its preauction band.

Initial Assignment

The FCC first will determine whether it is feasible to accept all Initial Bids, while assigning all non-participating stations in their home bands. If so, the Initial Clearing Target will be set equal to the maximum number of channels that can be cleared while accepting all the Initial Bids. During this process, certain regions may be designated as Impaired Regions and the number of channels cleared in these regions may be less than the Clearing Target. It also may happen that accepting all Initial Bids is not feasible for any Clearing Target. If this happens because of infeasibility in the VHF band (because too many stations’ Initial Bids select an assignment in that band), there will be an extra round in which VHF prices are decreased until enough stations choose to move out of this band to yield a Feasible Assignment, so that the initial Clearing Target can be set. This process generates a feasible Initial Assignment of stations to bands. Once a tentative Feasible Assignment is generated, a tentative Feasible Assignment will be maintained throughout the auction.

Determining Feasible Moves

Prior to each auction Round t ≥ 1, and later during the bid processing for each Round, the FCC will use the Feasibility Checker to determine, for each station that is not currently assigned to its pre-auction band, which of its Permissible Bands the station could be feasibly reassigned to. A station that can feasibly be assigned to its pre-auction band, given the current auction assignments of other stations, is active. If a station cannot be feasibly assigned to its pre-auction band, the station is frozen. Finally, if a station already is assigned to its pre-auction band, we say the station has exited. A station that has exited submits no further bids and is assigned a channel in its pre-auction band at the end of the auction.

Descending Station Prices

Prior to each Round t ≥ 1, the FCC announces to each station that has not exited whether and by how much its offer prices will decrease in that round. A station may have just one or more of its prices decreased in a given round. Each station is also told its current tentative assignment, whether it is frozen or active, and if it is active, which relinquishment options for the station are feasible given the current tentative assignment. Stations also may be given additional information, for instance information about what fraction of channels are filled in UHF and VHF in the station’s local area given the current assignment.

Bids

In each Round t, all stations that have neither exited nor been frozen are given the opportunity to modify their preferred relinquishment option or to exit.

Activity Rule

Bids will be required to satisfy an Activity Rule that ensures consistent bidding, so that for instance a station that chooses to go off-air rather than move to VHF may be prevented from making the reverse choice in the following round unless its price offer for going off-air is reduced by more than its price offer for moving to VHF. In particular, the Activity Rule will help prevent a station from choosing a band that is currently infeasible for it as its preferred relinquishment option, by reducing the prices for such bands by at least the same amount as the price for the station’s current preferred relinquishment option. (The Activity Rule will never prevent a station from exiting in any round in which its price offer is reduced for its currently preferred relinquishment option.)

Intra-Round Bidding

In order to accelerate the auction without sacrificing efficiency, the following modified bid submission procedure may be used. Instead of a fixed reduction of prices for its relinquishment options, a bidder may be given end-of-round prices for these options that correspond to maximal possible reductions, and invited to submit one or more intra-round bids. Each intra-round bid specifies a price point in the interval between the start- and end-of-round prices in a Permissible Band or off-air at which he would like to modify his preferred option to another Permissible Band or off-air. For example, if the bidder’s current preferred relinquishment option is the upper VHF band, he may specify a price point in this band that is between the start- and end-of-round prices. The bid might specify that when prices progress beyond the price point, the bidder’s preferred relinquishment option should be modified to going off-air. The bidder might also make a second intra-round bid specifying a lower price point below which the bidder would prefer to exit the auction and remain in its pre-auction band. Within each round, a computer algorithm will process such intra-round bids sequentially, and decide which prices are decremented and by how much, and which intra-round bids are accepted as a result of the decrements.

Conditional Termination and Clearing Target Adjustment

The Reverse Auction continues until a point is reached at which every station is either frozen or has exited the auction. The current assignment and prices then become the Conditional Outcome, which will become the Final Outcome if the closing conditions are satisfied. If the closing conditions are not satisfied, then the provisional Clearing Target will be decreased and additional assignments to UHF channels will become feasible so that some frozen stations may become active. The Reverse Auction then continues until again all stations are either frozen or have exited. This generates the Conditional Outcome for the new Clearing Target. Depending on the Clearing Rule for the overall auction, to be discussed in Section 5, the process continues.

Discussion
Bidder Incentives

The Reverse Auction is designed to provide stations with relatively straightforward bidding incentives. A single-station owner that considers only the possibility of going off-air, and not moving to a lower band, cannot do better for itself than to determine a minimal payment it would accept to relinquish its license, and then, during the auction, bid to go off-air until it cannot be assigned a channel in its pre-auction band or the offered price to go off-air falls below its minimal acceptable payment. Exiting earlier means foregoing an opportunity to be paid more than the station’s minimal acceptable payment, while exiting later means getting paid less than its minimum acceptable amount.

There are no “strategic” elements to such a decision. The logic is analogous to a bidder seeking to buy a single item in an ascending clock auction: such a bidder should stay in the auction until the price reaches the bidder’s maximum willingness to pay. In the Reverse Auction, the same logic also applies for a station that considers only the possibility of moving to upper VHF, or only moving to lower VHF, but not moving off-air. An important benefit of this approach is that it makes bidding simple and inexpensive for any broadcaster that chooses to participate in the auction.

For a bidder that is considering multiple options during the auction (e.g. potentially to go off-air or to move to VHF), a natural strategy is to choose the option that looks best given current prices. The auction does not guarantee absolutely that such a strategy will be optimal, but given competition among stations to relinquish their rights, the complexity of the interference constraints that determine feasible assignments, and the limited information that will be available to stations, the scope for such gaming is likely to be very limited. Similarly, for a bidder that owns multiple stations, the scope for gaming would be quite limited, provided that the bidder does not own a sizeable number of stations in any given local area.

Scoring Rule

The algorithm that determines how prices are decremented for each station in each round (and, in the intra-round bidding modification, which intra-round bids are accepted) is an important part of the auction design. This algorithm will rely on a “score” for each bid that accounts for factors like the potential interference created by a station and the population served by the station, as well as the money amount of the bid. The use of population in scoring could reflect the fact that the value of a broadcasting license depends in part on its population served. Ranking bids and paying winning bidders in relation to their population served or other indicators of value may reduce the amount that the Commission would have to pay to repurpose broadcast television spectrum. The details of the scoring will need to be examined further.

Additional Possible Variations
Dynamic Maximum Prices

In the auction design option described above, the maximum price that can be paid to a broadcaster is the Initial Price in the auction. Setting the Initial Price well in this design is an important matter. If the FCC’s choice of Initial Price were too low, the consequence would be to reduce the amount of spectrum that could be cleared in some areas. If it were too high, the consequence would be a higher cost of acquiring spectrum, which in turn could result in fewer channels being cleared. A variation to the design option that could mitigate the problem of setting Initial Prices that are either too high or too low would set the maximum prices (for example, on a per pop basis) paid to broadcasters dynamically during the auction. The dynamic maximum prices would be constructed using the bids in the early rounds of the auction. To implement this variation, the price decrement rules would be modified so that prices offered to bidders that exceed the corresponding dynamic maximum prices are reduced even when there is no excess supply. Just as after any reduction in the offered price, the bidder could reject its reduced price offer and exit to its pre-auction band, even when such exit might necessitate reducing the number of licenses that can be offered in a particular area in the forward auction. The potential advantage of dynamic maximum prices is that the maximum prices paid to broadcasters would be based on actual bids in the auction, rather than on the FCC’s pre-auction price forecasts.