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

This document supplements Appendix C to the September 28, 2012 NPRM, titled: “Incentive Auction Rules Option and Discussion.” It provides additional details about several of the more novel aspects discussed in connection with the Forward Auction, including the use of intra-round bidding, managing the shifting of demand between categories of licenses and the forward auction closing rule.

We first offer a non-technical characterization of the main problems that the forward auction algorithm described below is designed to solve. There are three such issues.

A first issue in a standard clock auction is price overshooting. As an example, suppose that there are five licenses for sale in some category and that at the current price of 100, the total demand across all bidders is for six licenses. Suppose that at the next round the price is raised to 105 and the total demand at that price falls to just four: raising the price to 105 overshoots the market-clearing price. Because large increments make the substantial price overshooting more likely, standard clock auctions typically employ small bid increments that require more rounds and longer times to completion.

The design described in this document uses intra-round bidding to allow larger price increments in a round without the risk of price overshooting, thus resolving this first problem. With intra-round bidding, each bidder can specify the price point(s) at which it wishes to reduce its demand. In the example of the preceding paragraph, it might be that one bidder would specify that it wishes to reduce its demand by one at a price of 102 and another would specify the same at a price of 104. Our algorithm would determine that the clock should stop ticking up at a price of 102, when demand falls to be just equal to the supply. The reduction planned for the price of 104 would then not be implemented, so demand would be exactly equal to supply at the end of the round. Generally, if a round begins with aggregate demand at least as high as the target supply for a license category, our proposed intra-round bidding rules ensure that the round also ends with demand at least as high as supply. Intra-round bidding is illustrated by an example later in this document.

A second problem that can arise in clock auctions (regardless of whether they incorporate intra-round bidding) arises when a bidder proposes to increase demand for one product category while reducing demand for another. In a standard clock auction, the auctioneer cannot distinguish whether the bidder wishes to increase one demand only if it can reduce the other, or whether the bidder wishes to make those changes independently. The proposed design remedies that problem by allowing packaging of demand changes. To illustrate, we revisit the example of the preceding paragraph but suppose that the second bidder, with price limit 104, is also interested in buying an additional license in second category, but does not have sufficient authorized budget to buy both. Suppose that the beginning and end of round prices for the second category are 80 and 84. In the proposed auction, a bidder’s intra-round bid would specify that at the 80% price point (when the prices reach 104=100+.8x(105-100) for the first category and 83.2= 80+.8x(84 80) for the second category, it would reduce its demand for the first category and increase its demand for the second category. The proposed rules package changes at a single price point, so the increased demand for the second category would apply only if the bidder is permitted to reduce demand for the first category. In the example, the reduced demand for the first category is rejected, so that increased demand for the second category is not applied. In the same example, if the bidder wishes to delink the two changes, then it can make them at price points of 80% and 81%. Since the bids apply at different price points, the two would then be evaluated separately and the demand increase for the second category would be applied regardless of any restriction of the reduction for the first category

A rule allowing bidders to specify combinations in this way is particularly valuable for this auction, in which there are multiple license categories and an activity rule. For example, suppose that a bid specifies reducing the quantities bid for categories A and B while increasing the quantities for categories C and D, but that the rules require that the reduction for A is rejected to avoid creating a situation in which demand falls below supply. Then, applying the activity rule, it may be that at least one of the increases must also be rejected, but which one? In the rule described here, it is the bidder itself who answers that question, as is necessary to promote efficiency of the final result. For example, if the bidder had bid to reduce the quantity for A and increase that for D at the 50% price point and to reduce the quantity for B and increase that for C at the 60% price point and the reduction for A were rejected, then the increase for D would also be rejected.

A third problem, which is novel in the context of the Incentive Auction, is that the supply of licenses in the reverse auction also depends on prices in the forward auction. In a standard clock auction, prices stop rising as soon as the demand falls to the target supply. In the Incentive Auction, such a rule could lead to prices that are too low to elicit the target supply from broadcasters, even if the bidders, if given another chance, would be willing to raise their bids enough to produce sufficient revenue to elicit the target supply. In the implementation described below, in such an event, prices continue to rise in the Forward Auction even when there is no excess demand relative to the target supply.

The algorithm described in the next section addresses each of the three problems described above. Choices about alternative rules, where applicable, have been made to encourage serious bidding and to allow the auction to progress as quickly as reasonably possible.