A Practical Guide to the Combinatorial Clock Auction

A Practical Guide to the Combinatorial Clock Auction Lawrence M. Ausubel * and Oleg V. Baranov June 2014 Abstract The Combinatorial Clock Auction (CCA) is an important recent innovation in auction design that has been utilised for many spectrum auctions worldwide. While the theoretical foundations of the CCA are described in a growing literature, many of the practical implementation choices are omitted. In this paper, we review and discuss the most critical practical decisions for a regulator implementing the CCA. Topics include: implementation of reserve prices; accommodation of technological choice; activity rules; price incrementing policy; incorporation of competition policy objectives; and bidding language and pricing rule. We illustrate our discussion with examples from recent CCA spectrum auctions. * Department of Economics, University of Maryland, College Park, MD 20742, USA. Email: ausubel@econ.umd.edu Department of Economics, University of Colorado, Boulder, CO 80309, USA. Email: oleg.baranov@colorado.edu

Since its proposal in a 2006 academic paper, 1 the combinatorial clock auction (CCA) has rapidly established itself as one of the leading formats for government auctions of telecommunications spectrum. Its initial implementations were for relatively small auctions and some of these applications may be viewed as experimental. However, in the past few years, usage of the CCA has gained substantial momentum. From 2012 to this writing in June 2014, the CCA has been used for no fewer than 10 major spectrum auctions worldwide, allocating prime sub-1-ghz spectrum on three continents and raising approximately $20 billion in revenues. (See Table 1.) Despite the presence of an existing auction format the simultaneous multiple round auction (SMRA) which often performs reasonably well, the CCA has the potential of displacing it and becoming the new standard design choice for spectrum auctions. Table 1: Combinatorial Clock Auctions to date, as of May 2014 Country and Auction Year Revenues Trinidad and Tobago Spectrum Auction 2005 $25.1 million ($US) UK 10 40 GHz Auction 2008 1.43 million UK L-Band Auction 2008 8.33 million Netherlands 2.6 GHz Spectrum Auction 2010 2.63 million Denmark 2.6 GHz Spectrum Auction 2010 DKK 1.01 billion Austria 2.6 GHz Spectrum Auction 2010 39.5 million Switzerland Spectrum Auction 2012 CHF 996 million Denmark 800 MHz Spectrum Auction 2012 DKK 739 million Ireland Multi-Band Spectrum Auction 2012 482 million Netherlands Multi-Band Spectrum Auction 2012 3.80 billion UK 4G Spectrum Auction 2013 2.34 billion Australia Digital Dividend Spectrum Auction 2013 $1.96 billion ($AU) Austria Multi-Band Spectrum Auction 2013 2.01 billion Slovakia 800, 1800 and 2600 MHz Spectrum Auction 2013 164 million Canada 700 MHz Spectrum Auction 2014 $5.27 billion ($CA) Slovenia Multi-Band Spectrum Auction 2014 149 million The CCA design consists of a two-stage bidding process. The first stage, known as the clock rounds, is a multiple-round clock auction. In each round, the auctioneer announces prices for all items and bidders respond 1 The CCA format was proposed by Ausubel, Cramton and Milgrom (2006), first presented at the FCC s Conference on Combinatorial Bidding in Wye River, Maryland in November 2003. See: http://wireless.fcc.gov/auctions/default.htm?job=conference_summary&y=2003&page=summary. 1

with quantities demanded at these prices. If aggregate demand exceeds available supply for any items, the auctioneer announces the next round with higher prices for these items. The bidding process continues until prices reach a level at which aggregate demand is less than or equal to supply for every item. The second stage, known as the supplementary round, is a sealed-bid auction in which bidders can improve their bids made in the first stage and submit additional bids as desired for other combinations of items. Throughout the whole auction, all bids are treated as all-or-nothing package bids. To determine winnings and associated payments, all bids placed during the clock rounds and all bids placed in the supplementary round are entered together into a standard winner determination problem (WDP). Winning allocations are determined by finding an allocation that maximizes the total value (as reflected in bids) subject to feasibility constraints. Associated payments are found by solving a series of counterfactual WDPs that identify the relevant opportunity costs (second prices) imposed by winners on other participants. In current practice, it is standard for the CCA also to include a third bidding stage, known as the assignment stage. This stage is added to the CCA in order to significantly simplify bidding in the first two stages. The main idea is to treat several closely-related items as completely identical during the clock and supplementary rounds. For example, the European digital dividend auctions auctioned six distinct licenses in the 800 MHz band. In these auctions, bidders were typically asked to bid on generic 800 MHz spectrum blocks during the first two stages of the auction. In a third stage that takes the winning allocations of the generic spectrum as given, bidders had the opportunity to compete for specific frequencies within the 800 MHz band. The assignment stage, usually implemented as a sealed-bid auction, determines the mapping from generic spectrum to physical frequencies. Due to its growing adoption, the CCA format has attracted substantial interest from academic researchers who are studying its theoretical properties and suggesting further improvements. With this level of attention, it is not at all surprising that the CCA has been in almost continual evolution and improvement since its first implementations. Despite recent innovations, the current generation of the CCA design still has a number of theoretical issues that will need to be addressed in future generations. 2 Varying experiences in recent spectrum auctions utilising the CCA format have vividly demonstrated a significant gap between theory and practice. Regulators, in charge of setting rules for spectrum auctions, routinely face difficult implementation choices when trying to customise the CCA format for the specific objectives and unique environments of their auctions. While the CCA is a highly versatile design, the introduction of any novel auction feature needs to be evaluated carefully against the main guiding principles. A small overlooked detail can easily turn out to be a major mistake with serious consequences. In this paper, 2 See Ausubel and Baranov (2014a, b). 2

we take a closer look at some of the most critical implementation issues typically faced by a regulatory authority when adopting the CCA format for its spectrum auctions. This paper attempts to fill some of the gap between theory and practice. As such, it should be useful both for researchers and practitioners. The literature on CCAs is growing rapidly. Ausubel and Baranov (2014a) summarize the recent history of the CCA, including expected innovations to the design. Cramton (2013) outlines the flaws in the SMRA design and argues how the CCA design solves them. Various pricing mechanisms for combinatorial auctions and their properties, including the pricing rules currently used for CCAs, have been studied by Parkes (2001), Ausubel and Milgrom (2002), Day and Raghavan (2007), Day and Milgrom (2008), and Day and Cramton (2012). We begin our discussion with reserve price policy. Unlike the traditional SMRA format, there are multiple ways to implement reserve prices in the CCA. Furthermore, it is not entirely clear what objectives the reserve prices should meet in spectrum auctions. Recent CCA implementations have adopted different treatments of reserve prices, including ones that appear to be imperfect. The CCA is an extremely flexible auction design that allows for many useful extensions. One of the most attractive customisations is to build in technological neutrality allowing bidders to compete not only for the quantity of spectrum but also for the intended use of the spectrum. We point out some critical issues in designing a CCA with endogenous band plan. Activity rules for multi-item auctions have begun to receive a lot of attention. The activity rules currently used in CCAs, despite some recent innovations, are known to be imperfect. Making matters worse, the CCA design as a whole has a fundamental theoretical issue that sometimes is mistakenly attributed to the strictness of its activity rules. To mitigate this flaw, regulators frequently adopt weaker activity rules that exacerbate opportunities for strategic bidding. We illustrate the major shortcomings of current activity rules. One of the most overlooked questions in the related auctions literature is the price incrementing policy. We discuss the relevant objectives and considerations that the auctioneer should have in mind when deciding how to increment prices in the clock stage of the CCA. We consider the question of achieving competition policy objectives (or any other side objectives) and we emphasise the important properties of the CCA design that need to be preserved when such policies are integrated into the design. Some recent European CCAs appear to have had incomplete integrations. We provide a short discussion about the bidding language. In January 2014, the Canadian Government announced that it will adopt an OR bidding enhancement (a more compact bidding language) for its upcoming 2500 MHz auction. The strong need for bidding language innovations is well justified there, as with 318 licenses, grouped into 106 product categories, the Canadian 2500 MHz auction will be the largest CCA (in the 3

number of offered items) to date. Finally, we talk briefly about the various pricing rule alternatives available in the CCA environment. 1 Reserve Prices Reserve prices have been utilised in the majority of spectrum auctions, irrespective of their formats. The main rationale for reserve prices in public auctions is generally to internalise the societal opportunity cost of selling assets to private parties rather than retaining them for future use. A second rationale is less fundamental but still very important. Adequate reserve prices improve bidder discipline in the auction by reducing the possible gains from various strategic manipulations. Before deciding on the implementation, the auctioneer needs to think about the underlying meaning of the reserve prices for its auction application and its objectives. The most straightforward interpretation of the reserve prices is to enforce a lower bound on auction revenues. Under such an interpretation, the auctioneer simply enforces that the payment for any bundle should be at least the sum of the reserve prices of its component elements. However, there is another way to interpret reserve prices. Reserve prices can be viewed as minimum incremental costs of acquiring additional items. The auction format should guarantee that the incremental prices of winning additional items for any bidders are at least the reserve prices of these items, in all possible contingencies. These alternative approaches are formalized by the following definitions: Bundle Reserve Prices: A pricing rule implements bundle reserve prices if a bidder s payment for a package x is at least the reserve price of the package x, i.e. p( x) r( x). Incremental Reserve Prices: A pricing rule implements incremental reserve prices if, for any package x and associated payment of px, ( ) the payment py ( ) for any incremental package y x, 0, is greater than px ( ) by at least the reserve price of the incremental items, i.e. p( y) p( x) r( ). It is straightforward to see that any pricing rule that enforces incremental reserve prices also enforces bundle reserve prices. However, the converse is not true. A pricing rule that enforces bundle reserve prices does not necessarily enforce incremental reserve prices. The traditional SMRA format utilises linear pricing, separately for every item. Hence, in the SMRA format, setting the opening prices of the bidding process equal to the reserve price levels the most naïve implementation directly implements incremental reserve prices. By contrast, the CCA uses opportunitycost-based pricing on packages of items. Hence, opening the clock stage at the reserve prices is insufficient to enforce either treatment of reserve prices. Auctioneers need to strengthen the pricing rule in order to enforce incremental reserve prices or even bundle reserve prices. 4

To implement bundle reserve prices, the auctioneer might employ an approach known as bounds only the submitted bid for any package must be at least the reserve price and, if the opportunity-cost-based price for a bidder ends up being too small, the final payment for any package won is increased to its reserve price. In order to implement incremental reserve prices, the auctioneer might use an approach known as reserve bidders fictitious bidders who bid for all available items at the reserve prices are added to the winner and price determination processes, thus explicitly applying opportunity costs at the reserve price level to all possible combinations of items. It might seem that the incremental reserve approach would necessarily generate at least as much revenue as the bundle reserve approach, but Day and Cramton (2012) showed that there is no general revenue ranking between the two treatments. The incremental approach would indeed generate at least as much revenue as the bundle approach when they both allocate the same set of items to actual bidders. However, the incremental approach may generate lower revenues if it results in fewer items being allocated. There are two clear benefits to bundle reserve prices. First, the bundle approach should always result in a weakly larger set of items being sold. Note that the number of unallocated items is frequently viewed by regulators as a measure of failure. Second, with the bundle approach, the final payments by bidders are less sensitive to the choices of reserve prices, which may make it seem a less intrusive implementation of the reserve prices. In other words, reserve prices serve only as a safety net for the auctioneer once opportunity cost calculations have become sufficiently high, the exact choice of reserve prices has no further effect on final payments. The impact of bundle reserve prices on final payments is smaller than that of incremental reserve prices. However, incremental reserve prices are strongly preferable from the perspective of bidder incentives. With the bundle approach, it is possible that bidders effective incremental costs are lower than the reserve prices, especially in the early clock rounds. When this happens, bidders may find themselves with unspent reserve capacity that can be used to subsidise the cost of acquiring extra items. Bidders have every incentive to bid above their marginal values, betting that any extra nominal costs will be absorbed by their reserve capacities and will not translate to any extra real costs. If a particular auction environment facilitates large reserve capacities, the price discovery yielded in the clock stage can be significantly impaired by these strategic incentives. By way of contrast, under the incremental reserve price approach, opportunity costs are always at least as high as the reserve price. There is no longer any concept of unspent reserve capacity, and bidders will be at risk of overpayment when making incremental bids exceeding their marginal values. This is illustrated in a hypothetical scenario patterned after the Slovakian 4G spectrum auction of 2013. While only limited information about the actual auction is available, it appears that a bundle reserve approach was taken. In the 1800 MHz band, three large B blocks were set aside for an entrant. In the prime 800 MHz 5

band, the supply of A blocks was six, and the three incumbents were subject to spectrum caps of two blocks each. In the less valuable 2.6 GHz band, the supply of C blocks was 14, and there was no spectrum cap. The reserve price on each A block was 19 million and the reserve price on each C block was 1 million. 3 Observe that, in such a scenario, if only incumbents competed for the A blocks, there would be no opportunity cost associated with winning 800 MHz spectrum (since the aggregate demand would never exceed the supply). The clock price for the A blocks would stall at the reserve price, and the true underlying payment would arise only through the bundle reserve. Meanwhile, the bidders might have expected to be fully priced on their C blocks. Suppose that an incumbent was considering whether to purchase a package of (2,4) or (2,6), where the first number of the pair denotes the quantity of A blocks and the second number denotes the quantity of C blocks. At a clock price of 6 million for the C blocks, the (2,4) package would generate opportunity cost of 24 million, while the (2,6) package would generate opportunity cost of still only 36 million. Since bidder payments were floored by the bundle reserve prices of 42 million and 44 million, respectively, the incremental cost faced by an incumbent would be only 1 million per C block. Even at a clock price of 9 million for the C blocks, the opportunity costs for the packages would be only 36 million and 54 million respectively, and so the incremental cost would be only 6 million per block. The effective incremental costs are summarised in Error! Reference source not found.. Table 2: Unspent reserve capacity in a hypothetical auction scenario Price of C Package = (2,4) Package = (2,6) Opp. Cost Payment Opp. Cost Payment Difference 1 mil 4 mil 42 mil 6 mil 44 mil 2 mil 6 mil 24 mil 42 mil 36 mil 44 mil 2 mil 9 mil 36 mil 42 mil 54 mil 54 mil 12 mil In short, in this hypothetical scenario, an incumbent would possess unspent reserve capacity of 38 million from the A blocks. Consequently, the calculations of the previous paragraph would indicate that an incumbent with a marginal value (for a fifth and sixth C block) of 1 million would bid up to 6 million, and an incumbent with a marginal value of 6 million would bid up to 9 million. The CCA, intended to give incentives for truthful bidding, would instead create incentives for massive overbidding. While we do not know whether bidders had these incentives in the actual Slovakian auction, we know that a single entrant won the large B blocks and that only incumbents won the A and C blocks, and we know that the allocation payments equaled the reserve prices for all but one of the winners, lending some credence to this scenario. 4 3 See the published auction rules at http://www.teleoff.gov.sk/data/files/35571.pdf and http://www.teleoff.gov.sk/data/files/33771.pdf (last accessed on 24 June 2014). 4 See the published auction results at http://www.teleoff.gov.sk/index.php?id=8261 (last accessed on 24 June 2014). 6

2 Accommodation of Technological Choice There are many ways to use spectrum. It is often attractive for the regulator to replace any administrative decision over the future use of spectrum with a market decision. This becomes even more important when the regulator and possibly the industry itself do not have a clear picture about the best use for this valuable but scarce resource. Highly customizable package auction designs, such as the CCA, make it exceptionally easy for the auctioneer to accommodate technology choices within the auction framework. However, allowing such flexibility might end up damaging the auction rather than achieving its noble purpose. A classic example of technological choice within a CCA is the initial UK design for the 2.6 GHz auction in 2007. This design was never actually implemented as the auction was later superseded by the 2013 multi-band auction that additionally included the 800 MHz and 1800 MHz bands. The expansion of the supply coupled with a significant time delay warranted a complete redesign of the 2.6 GHz auction. The original proposal for the 2.6 GHz auction was to offer 38 blocks (5 MHz each) in the 2.6 GHz band, with endogenous determination of the number of paired lots (spectrum blocks suitable for frequency division duplex or FDD) versus unpaired lots (blocks suitable for time division duplex or TDD). According to the auction rules, bidders would submit bids specifying both the number of blocks they wanted and whether they wanted them in paired, unpaired, or combined configurations. The auctioneer would then determine the actual split between two technologies by maximizing the total value of the allocation. A more exotic example of technological choice is the actual UK 4G Auction s determination of whether any spectrum would be allocated for low-power shared use. Up to four of the paired lots in the 2.6 GHz band were made available alternatively for both low-power shared use (as D1 or D2 lots) and high-power non-shared use (as C lots). In the low-power use, up to 10 different operators would share the same frequencies. In the highpower use, each C lot would be owned and operated by a single operator. The final decision between the lowpower and high-power usage was to be determined by comparing the sum of bids from the low-power bidders with the bids from high-power bidders. In general, the auctioneer should be aware of the possibility of at least three types of complications when introducing the possibility of an endogenous band plan. Interaction with Reserve Prices We have already discussed that implementing reserve prices in the CCA is by itself a nontrivial task. When the auctioneer incorporates additional design elements such as endogenous technological choice, the interaction of the reserve price policy with the new design elements requires a careful reexamination. For example, Ofcom in its UK 4G auction decided to use the reserve bidders approach for all lots except the lots designated for the low-power shared use (D1 and D2). Instead, the low-power lots were subject to a bounds only approach. The 7

rationale behind Ofcom s decision appears to be reasonable. On the one hand, Ofcom avoided situations in which the fictitious reserve bidders for D lots would have helped actual bidders bidding on D lots to compete against the C lot bidders. On the other hand, the policy introduced a positive bias into any technological neutrality: the approach might have resulted in the withholding of D lots from the actual bidders in favor of fictitious reserve bidders. Free-Rider Problems Core-selecting pricing rules, typically used in CCAs, are known to induce certain free-riding incentives in bidders. While theoretically curious, the presence of free-riding incentives was never a major concern in the recent CCAs for spectrum. The typical market structure of the wireless industry, with 3 to 4 major incumbents, combined with common spectrum caps almost always guaranteed that bidders would not benefit from such free-riding strategies. The only potential exceptions to date may have been auctions with regional licenses in countries with strong regional bidders, which naturally may create a free-rider problem. However, auctioneers must recognize that facilitating technology choice may artificially create the free-riding problem for bidders. If one set of bidders bids on blocks with a technology A and another set of bidders bids for the same licenses for use with a technology B, bidders within one group might have strong incentives to free-ride on the bids made by other members of their technology team. In the first example above, where marginal choices by the auctioneer between one paired and two unpaired lots are possible, free-riding incentives do not seem to be very significant. A free-rider problem would technically exist if there were two bidders who each wanted to buy only one unpaired lot, competing against another bidder for a paired lot. But, typically, real-world bidders want several unpaired lots or several paired lots, substantially reducing any free-rider issues. The free-riding incentives drastically change in the low-power / high-power example. There, up to 10 bidders for low power were effectively invited to compete jointly against one or two bidders for high power, inducing a severe free-rider problem among the low-power bidders. All would have strong incentives to bid very conservatively and let other low-power bidders pick up the tab. Therefore, from the planning stages of this auction, it should have been understood that the low-power shared technology was unlikely to prevail as an outcome. In fact, the bidding data from the auction shows that one bidder, Niche (BT), did place a substantial number of supplementary bids that were suggestive of extreme free-riding tendencies. 5 Strategic Manipulations 5 Niche placed 54 bids (out of 89) for packages that included either a D1 or D2 lot, that were just a minimal increment ( 1000 or 2000) over its corresponding base bids without D lots. The amounts of the base bids were at least 20 million. 8

Another important issue that arises in the context of endogenous supply is unintended opportunities for strategic manipulations. As will be noted later (see Section 4), in certain circumstances, bidders in a CCA may find it beneficial to influence relative prices during the clock rounds. By affecting the price trajectory, the bidder can put itself in a better position for the supplementary round. For example, the bidder might be able to exploit weaknesses in the activity rules that would enhance its ability to place surprise bids in the supplementary round. The UK 4G auction was ripe for such strategies. In some circumstances, a bid for a single low-power D2 block in combination with the price incrementing policy that was used in the auction would reduce the endogenous supply of high-power C blocks by four units, resulting in an artificial excess demand and increasing the price. 3 Activity Rules The imposition of activity rules in dynamic auctions has been one of the most influential recent innovations in auction design. Generally speaking, activity rules are intended to prevent bid sniping, that is, bidders concealing their true intentions until the very end of the auction. If activity rules in the CCA are weak, bidders will generally try to avoid revealing any useful information to their opponents during the clock stage. This causes the auction effectively to collapse into a sealed-bid auction, defeating the purpose of running the dynamic stage in the first place. Furthermore, a dynamic auction with weak activity rules may take an excessive time to conclude. In single-item auctions, bid sniping literally means attempting to win at the last second. Recall that, in an ebay auction with an ending time of 9 pm, a participant may bid snipe by placing its first and only bid at 8:59.59, In multi-item auctions, bid sniping (to the extent permitted) may include richer approaches intended to mislead opponents about one s future intentions. This includes both early drops to unattractive packages with the hope of stealing a better one later, as well as continuing to bid too long on large valuable packages with the intention of sharply dropping demand later to end the clock stage. In the CCA, where winners losing bids can determine other winners payments, bidders may place high bids for packages without intending to win them, but simply to increase payments of other winners by increasing their opportunity costs. The standard CCA rules contain several provisions that attempt to make bid sniping unattractive for bidders. They include: (1) a clock-round activity rule that limits the size of packages on which the bidder can bid in later clock rounds, based on bids in earlier rounds; (2) a supplementary-round activity rule that limits the amounts that the bidder can bid during the supplementary round; and (3) a rule that treats all clock bids to be live at the time that the winner-determination problem is solved. 9

Historically, spectrum auctions have utilised points-based activity rules. The auctioneer assigns a number of points to each item in the auction. The standard activity rule for the SMRA is a variant on the requirement that a bidder s total number of points associated with each successive bid must not increase as the auction progresses. For the clock rounds of the CCA, sometimes a points-based approach is also taken. More recently, a hybrid approach, based both upon points and revealed-preference considerations, is often adopted. For the supplementary round, the CCA s activity rule is also based on a combination of points and revealedpreference ideas. Standard implementations of activity rules rely on the concepts of the Relative Cap, the Intermediate Cap and the Final Cap. All of them are defined in terms of revealed-preference constraints. Revealed-Preference Constraint: The revealed preference constraint for package x with respect to the clock round t is b( x) b( x ) p ( x x ), where bxis ( ) the bid amount for package x, xt is the package demanded t t t in Round t, bx ( t ) is the final bid amount for package x t, and pt is the vector of clock prices for Round t. 6 Intuitively, the revealed-preference constraint states that it is unreasonable for the bidder to claim a high value for package x relative to package x t, given that the package x t was revealed to be preferred to package x in Round t. The Relative Cap, Intermediate Cap and Final Cap rules are defined in terms of revealed-preference constraints with respect to certain clock rounds as follows: Relative Cap: A bid for the package x should satisfy the revealed-preference constraint with respect to the last clock round in which the bidder s eligibility, as measured by points, was at least the total points associated with package x. Intermediate Cap: A bid for the package x should satisfy the revealed-preference constraint with respect to all eligibility-reducing rounds starting from the last clock round in which the bidder s eligibility, as measured by points, was at least the total points associated with package x. Final Cap: A bid for the package x should satisfy the revealed-preference constraint with respect to the final clock round. The Final Cap appears to be the most natural implication of revealed preference theory that comes out of the clock rounds. Yet many regulators decide against the Final Cap for their CCAs relying on the Relative Cap only, viewing the Final Cap as giving excessive allocation stability between the clock stage and the supplementary round. In the extreme case, it may be impossible for the supplementary bids to change the allocation of the final clock round; consequently, opportunity cost pricing based on these bids may become unreliable. Recently, both the ACMA (the Australian regulator) and Ofcom (the UK regulator) used this 6 More precisely, this is the constraint imposed by the Weak Axiom of Revealed Preference (WARP) for a bidder with quasilinear payoff function. 10

rationale to decide against the Final Cap. The limitation to opportunity cost pricing is a fundamental issue of the current CCA design that requires a complex resolution. It should involve major rules changes affecting both activity rules and the pricing rule simultaneously. The omission of the Final Cap is a costly shortcut that partially mitigates the bidder incentive issues at the expense of leaving substantial bid-sniping opportunities and thus risking elimination of many advantages of a dynamic auction. The following bidding history illustrates differences in bid limits (and bid sniping opportunities) arising under several activity rules in a simple three-product example (A, B and C, each assigned 10 eligibility points): Table 3: Bidding History Round Clock Price Bidder (in millions) Demand Eligibility Activity 1 (10, 10, 10) (1, 0, 2) 30 30 2 (10, 50, 10) (1, 0, 1) 30 20 3 (100, 50, 10) (0, 1, 0) 20 10 4 (100, 100, 10) (0, 1, 0) 10 10 To calculate bid limits under different activity rules, we are going to assume that the bidder continues to bid 100 million for its final clock package, (0, 1, 0), in the supplementary round. Furthermore, maximum possible bid amounts are used for all constraining packages in all subsequent calculations. Table 4 compares the bid limits for two packages: (1, 0, 1) and (0, 1, 2): Table 4: Calculations of Bid Limits for Two Packages: (1, 0, 1) and (0, 1, 2) Package Relative Cap Intermediate Cap Relative Cap + Final Cap (1, 0, 1) R3: 100 + (110-50) = 160 R3: 100 + (110-50) = 160 R3: 100 + (110-50) = 160 R4: 100 + (110-100) = 110 (0, 1, 2) R2: 160 + (60-10) = 210 R2: 160 + (60-10) = 210 R3: 100 + (20-0) = 120 R2: 110 + (60-10) = 160 R4: 100 + (20-0) = 120 Under the Relative Cap, the highest supplementary bid that the bidder can place for (1, 0, 1) is 160 million and the highest possible amount for (0, 1, 2) is 210 million. With the Final Cap in place, these limits are reduced to 110 million and 120 million, respectively. The Relative Cap leaves room for an extra 90 million for the (0, 1, 2) package, which can be used by the bidder for various purposes including bid sniping. In this example, the Intermediate Cap was successful in limiting the bid for (0, 1, 2), but not for the (1, 0, 1) package. This example was specifically constructed to highlight the differences between activity rules and may appear artificial. Next, we compare the extent of bid sniping opportunities available to bidders in the supplementary round under several activity rules in an actual high-stakes CCA. 11

For the UK 4G auction, we have calculated theoretical 7 bid amounts needed to protect final clock packages for all major bidders 8 under the Relative Cap (the actual activity rule used in the auction), the Intermediate Cap (considered, but never used), the Relative + Final Cap (used in Ireland), and the Intermediate + Final Cap (used in Canada). The exposure numbers were generally high in the UK auction, mostly due to the large value of unsold lots at the end of the clock stage. For this reason, we report two sets of numbers. Exposure provides the theoretical amounts required to protect the package using the actual level of unsold lots in the auction, while Net Exposure provides the theoretical amounts when the effect of unsold lots on exposure is removed (as if the auctioneer had placed a bid for all unallocated lots at the final clock prices, effectively removing them from the auction). All exposure numbers are reported as a percentage of the bidders final clock prices. As can be seen from the table, the Final Cap consistently reduces the amount that the bidder needs to bid to guarantee its winnings, due to reduced bid sniping opportunities. Furthermore, the reduction is rather significant. Even in situations without undersell (Net Exposure), bidders might need to increase their bids substantially in order to protect their clock packages under the Relative Cap. For example, Niche would have needed to increase its bid by almost a factor of seven in order to assure that it won its final clock package At the same time, with the Final Cap, Niche would have already bid a sufficient amount. Table 5 shows that the Relative Cap by itself is a relatively weak protection against bid sniping in the realistic setting of the UK auction. Bidder/ Final Clock Package Vodafone (2 A1, 3 - C) Telefonica (1-A2, 1- D2) EE (9 - E) Niche(BT) (2 - C) Table 5: Exposure Calculation for the UK 4G Auction (2013) Relative Cap + Relative Cap Intermediate Type Final Cap (used in UK) Cap (used in Ireland) Intermediate Cap + Final Cap (used in Canada) Exposure 245% 184% 166% 166% Net Exposure 179% 118% 100% 100% Exposure 282% 206% 183% 183% Net Exposure 199% 123% 100% 100% Exposure 697% 438% 438% 438% Net Exposure 359% 100% 100% 100% Exposure 1092% 616% 504% 504% Net Exposure 688% 212% 100% 100% At this point in the CCA s development, it appears that an advance in the activity rule may be one of the next evolutionary steps. One idea, which we advocate in Ausubel and Baranov (2014b), is to completely replace points-based activity rules with a rule based upon the Generalized Axiom of Revealed Preference (GARP) one of the tests for rationality used in economics. Unlike both the Relative Cap and Intermediate Cap, which 7 These theoretical exposures are calculated as maximum incremental values that the bidder s opponents can place on the lots in the bidder s final clock package. 8 They are calculated for all major bidders with the exception of Three UK. Due to the competition policy used in the UK auction, Three UK never needed to protect its bid for any of the designated minimum spectrum portfolios. 12

enforce revealed-preference constraints only with respect to rounds in which the bidder reduces the size of its demanded package, GARP imposes revealed-preference constraints against every clock round. To assure that the system of revealed-preference constraints stays feasible, all clock bids made by a bidder are required to be consistent with some valuation profile at all times. To put it differently, the GARP activity rule requires that bidders demonstrate rational behavior throughout its demand choices in clock rounds. One shortcoming of points-based activity rules is that it is impossible to make an assignment of points guaranteeing that bidders will always be able to bid straightforwardly according to their values. Moreover, the auctioneer will often miss the mark widely. One case in point is the 2013 UK 4G Spectrum Auction. There, the point ratio between A blocks and C blocks was set at 15-to-1. However, the effective price ratio ended up at about 4-to-1. In this auction, bidders were only able to switch from the A blocks to C blocks, and they were unable to switch back. In other forthcoming work, we show that in order to avoid constraining bidders from straightforward bidding in the actual auction, it appears that the point ratio would have needed to have been set at only about 2-to-1, quite different from what was used empirically. To put it differently, one significant advantage of the GARP activity rule is that it completely eliminates the need for points and therefore it completely eliminates the need for the regulator to assign appropriate points. 4 Price Increments for the Clock Rounds CCA auctioneers are frequently unconcerned with the way in which they should be incrementing clock prices during the dynamic part of the CCA. Among all design decisions that need to be made prior to the auction, this question is considered relatively unimportant and is often overlooked by the design team. To make matters worse, the academic literature provides little guidance about the price increments as well. Yet the clock stage is built on the assumption that the auctioneer increments clock prices in a meaningful way that guides bidders towards efficient assignments. The underlying objective behind the clock stage is often described as price discovery a dynamic process that involves identifying the efficient allocation of items among bidders and the supporting prices. If bidders were to bid straightforwardly (i.e., bid for the profit-maximizing bundle given clock prices) and if all items were claimed in the final clock round, the final clock allocation would be optimal. 9 And, if the final clock allocation resulting from straightforward bidding is not optimal, any possible welfare gain cannot exceed the value of the unallocated lots evaluated at the final clock prices. These two observations suggest that the auctioneer should select clock price increments so as to minimize the value of unallocated lots in the final clock round. 9 This follows from the First Fundamental Welfare Theorem. 13

It is well known that bidders are unlikely to bid completely straightforwardly during the clock stage, especially if they can improve their positions for the supplementary round by misreporting their preferences. Therefore, another important objective for setting price increments is to mitigate any potential gains from such misreports. This is especially relevant for current CCA designs that employ relatively weak activity rules and present multiple opportunities for bidders to profit from untruthful bidding. An ill-designed price incrementing policy might easily invite additional bidder manipulations and promote bid sniping. Finally, auctioneers should not lose track of that bidding in high-stake auctions requires appropriate time for bidders to make hard decisions. For planning purposes, bidders should be able to forecast dynamics and magnitude of future price changes in order to make sure that their internal procedures do not get in the way of their bidding in the auction. The total time length of the auction is also important. Many spectrum auctions require much in the way of human and capital resources, so a timely end to the auction process is desirable. One substantive decision is whether to use differential price increments for each good (for example, a price increment proportional to excess demand) or whether simply to use flat price increments (for example, a constant 5% increase in price for any good that is in excess demand, and a 0% increase otherwise). It is tempting to use proportional price increments, as this follows closely to Walras original analysis, and increments that are more finely tuned to excess demand would seemingly produce faster price discovery. Unfortunately, differential price increments create extra strategic opportunities for bidders, for exactly the same reasons. With greater ability to control price trajectories, a bidder might try to manipulate them in its favour by driving relative clock prices on a desired path. Mainly due to this last argument, the majority of recent CCAs have adopted flat price incrementing policies. Since classical results on convergence to Walrasian equilibrium hold not only for price adjustment processes proportional to excess demand, but also for continuous sign-preserving transformations of these processes, the flat price incrementing policy does not necessarily sacrifice any desirable convergence properties. Smart Price Trajectory In the future, auctioneers might consider using more sophisticated price incrementing policies. Such policies would use all available information to guide the clock stage towards efficient assignments. In our current working paper (Ausubel and Baranov 2014b), we propose new activity rules based on GARP. If adopted, these activity rules may create intriguing possibilities for smart price increments. A GARP activity rule guarantees that each bidder s demands can be explained with a rational valuation profile. Making use of these value profiles, the auctioneer may be able to set increments in a way that more effectively minimizes the value of unallocated lots one of the objectives outlined above. 14

5 Incorporation of Competition Policy Objectives When we speak of incorporating competition policy into spectrum auctions, we are generally not referring to introducing competition into the spectrum auctions themselves, but to injecting competition into the downstream market for mobile voice and data services. Spectrum is a scarce input into the provision of mobile voice and data services, and concentration in mobile spectrum holdings would generally lead to concentration in the downstream market for wireless services. Meanwhile, to the extent that the spectrum auction facilitates new entry and reduces concentration in mobile spectrum holdings (and to the extent that mergers and acquisitions outside of the auction are limited), the spectrum auction can help to improve the competitive performance of the downstream market. Historically and generally in conjunction with use of the SMRA format the two most frequent devices for competition policy in spectrum auctions have been the set-aside and the spectrum cap: Set-aside: One or more spectrum blocks are reserved for a particular class of bidders. The most common form that this has taken is that a specific block of spectrum is set aside for entrants ; while incumbents are excluded from bidding on the set-aside block. 10 Spectrum cap: A limit is placed on the quantity of spectrum within a given group of bands that a bidder is permitted to acquire or hold. Spectrum caps may be applied to winnings within a given auction or they may apply cumulatively to specified existing holdings as well as to acquisitions within the given auction. In countries such as the US, India, Canada and Australia, where spectrum licenses are regional, spectrum caps have been applied to each and every geographic region. 11 10 Set-asides have been used in auctions in many countries, including the US and the UK. In the US Broadband PCS spectrum auctions which began in 1994, the FCC set aside two of the original six blocks of broadband PCS spectrum for designated entities in an effort to promote small business ownership of spectrum. The implementation of set-asides did not work out well, as the set-aside was bundled with other policy instruments, such as instalment payments, that were intended to favour small businesses. The result of this exercise was that one of the largest winners of set-aside spectrum entered into bankruptcy, and there was a roughly ten-year period where most of the set-aside spectrum went unused. By way of contrast, the UK had an apparently successful experience with set-asides. In the UK 3G auction in 2000, Ofcom set aside one of the 3G licenses for a new entrant. This resulted not only in fostering actual entry and hence competition in the downstream market for wireless services, but in increasing competition in the auction and probably increasing auction revenues. 11 Spectrum caps have been prevalent in spectrum auctions worldwide. At the time of the US Broadband PCS spectrum auctions, the FCC established a 45-MHz cap for commercial mobile radio spectrum, including both existing cellular licenses and the new PCS licenses being auctioned. By contrast, in many of the European 3G auctions in 2000, bidders were limited to winning at most a specified number of spectrum blocks, irrespective of their existing spectrum holdings. In recent 4G auctions, bidders have often been subject to an overall constraint on existing and new holdings for spectrum generally, together with a tighter constraint on the prime sub-1-ghz spectrum. For example, in the 2013 UK 4G spectrum auction, there was both a 105-MHz overall cap on existing and new holdings (which proved to be binding for incumbent Everything Everywhere) and a 27.5-MHz cap on sub-1-ghz spectrum (which proved to be binding for incumbents Vodafone and Telefonica). 15

However, due to the nature of the SMRA format, there have been two frequent limitations on these devices. First, since the bids in the SMRA have been for specific licenses, the set-asides in SMRAs have been for specific licenses. This required regulators to make decisions that may have been undesirably specific (e.g., whether or not dirty blocks that are subject to interference should be included within the set-aside). Second, since the evaluation of highest bids in the SMRA is done at the individual license level, the spectrum cap was applied individually for each incumbent (as opposed to establishing an aggregate cap on the aggregate acquisitions or holdings of all incumbents). This potentially has the effect of impeding competition in the auction among incumbent bidders and thereby depressing auction revenues. Virtual set-asides/aggregate spectrum caps In auction formats such as the CCA, in which bidders bid on generic spectrum rather than on specific licences, it is possible to go beyond the two aforementioned limitations and to provide for a virtual set-aside (which may equivalently be viewed as an aggregate spectrum cap): Virtual set-aside/aggregate spectrum cap: If a quantity of N generic spectrum blocks is offered, then a particular class of bidders (e.g. incumbents ) is limited, in aggregate, to winning a quantity of K of these blocks. A policy following this first description can be called an aggregate spectrum cap. Equivalently, this can be viewed as reserving a quantity of N K generic spectrum blocks for another class of bidders (e.g. entrants ). A policy following this second description can be called a virtual set-aside. One key advantage of this device (as compared to reserving spectrum implicitly via the standard spectrum cap) is that, for any fixed quantity reserved for entrants, there can be greater competition among incumbents. For example, suppose that there are two incumbent mobile operators and six blocks of spectrum available. The regulator can implicitly reserve two blocks for entrants by limiting each incumbent to an in-auction spectrum cap of two blocks. However, unless entrants demand greater than two blocks, this competition policy would have eliminated all competition for the incumbents. Instead, the regulator can establish an aggregate cap of four blocks on the incumbents. Each one is free to bid for and win up to four blocks. With this device, there are still two blocks reserved for entrants, but competition between the two incumbents is permitted to occur. A virtual set-aside in the CCA has several advantages over the standard set-aside in the SMRA. First, it is more flexible, and allows the market to determine which specific frequency blocks are won by entrants. Second, with the CCA s price determination mechanism rather than implicit uniform pricing, a single entrant may be capable of winning the entire set-aside, as opposed to being vulnerable to pressure from a second entrant who may force it to surrender some of the set-aside. (And the regulator may, for competition reasons, prefer that a single entrant win the entire set-aside, as a single substantial entrant is likely to pose a greater competitive threat to incumbents than a diffuse competitive fringe.) Third, in some situations, a standard set- 16

aside may be viewed as an excessively strong policy and of questionable legality. While the aggregate spectrum cap is isomorphic to a virtual set-aside, the aggregate spectrum cap (as a limit on incumbents, rather than a reservation for entrants) may be considered more acceptable and less subject to legal challenge. Spectrum Floor The UK s 4G auction in 2013 went a step further beyond a virtual set-aside and established a spectrum floor. The regulator decided that either a 2x5 MHz block of 900 MHz spectrum or a 2x20 MHz block of 2.6 GHz spectrum would be reserved for an entrant. This went further than a virtual set-aside in two respects. First, it allowed the market to determine not only which frequency blocks would constitute the set-aside, but whether they would belong to the more valuable 900 MHz band or the less valuable 2.6 GHz band. Second, it institutionalized that the entire set-aside would be required to be won by a single entrant. Spectrum floor: Two or more alternative sets of spectrum ( minimum spectrum portfolios ) are reserved for a particular class of bidders. The choice of which minimum spectrum portfolio is awarded, and to which bidder, is decided according to the solution to a modified winner determination problem: maximize the value of accepted bids, subject to feasibility and to awarding one of the minimum spectrum portfolios to an eligible bidder. With a CCA, two issues are likely to arise when spectrum is reserved for entrants. The first issue can be referred to as infeasible bids. Given that certain spectrum blocks are reserved for entrants, certain other combinations of blocks might never be part of a feasible winning bid. In this event, placing bids for infeasible combinations of blocks might become a stalling tactic or a way to drive up prices of certain spectrum bands; therefore, it is important that the auction rules prevent bidders from ever submitting such infeasible bids. The second issue relates to the supplementary bids. Under the standard rules used in CCAs today, the bidder is generally permitted to submit a supplementary bid that raises its final clock package (the package that it bid for in the final round of the clock stage) by any arbitrary amount. However, there is one exception: no supplementary bids are permitted to be submitted for the null set, even if it is the bidder s final clock package (i.e. if the bidder has dropped out of the clock stage by the final clock round). When spectrum is reserved for entrants, similar logic would suggest that the bidder should not be allowed to place a supplementary bid on the reserved package. More generally, a clean solution to this problem might be to require the entire collection of highest bids to be consistent with a GARP-based activity rule (see also the discussion in Section 3, above). 17