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Big but not beautiful …

The Combinatorial Clock Auction (CCA) design has become the format of choice for large multi-band awards over the last few years. It makes bidding decisions simple for bidders and supports flexible lot structures. Bidders do not need to worry that much about how rivals might bid as bid decisions depend primarily on bidders’ own valuations. This increases the chance of an efficient outcome. However, the CCA only works well if bidders can evaluate all the bidding options that are open to them. Such an evaluation will be challenging in the upcoming Canadian and Australian 700MHz auctions owing to the large number of lots on offer. Whether bidders will be able to manage this complexity is unclear. Whilst the CCA is good for solving complex allocation problems, this should not be an excuse for excessive and unnecessary complexity in the design of lots. Allocation mechanisms should be as complex as they need to be – but no more – to have the best chance of achieving an efficient outcome.

Basic features of a Combinatorial Clock AuctionThe CCA is aimed at giving bidders good incentives to reveal their valuations for different combinations of the available lots. Achieving an efficient outcome is then a matter of picking the combination of bids with the highest value that can be satisfied with a given supply. In the CCA, bidders bid on packages of lots. This removes the risk of ending up with unwanted combinations of lots that bidders face in the more traditional simultaneous multi-round ascending (SMRA) format. The second-price rule used in the CCA encourages straightforward bidding. The auction mechanism sets the prices to be paid by winners at the lowest hypothetical bid amount with which they could have still won. The format is ideal if spectrum is to be offered in small slices that are recombined, as bidders have the flexibility to obtain precisely what they need.The CCA begins with one or more clock rounds. Similar lots are grouped into categories. The auctioneer announces a price for each lot category and bidders state how many lots in each category they want. If total demand in a category exceeds the available supply, the price for that category goes up in the next clock round. If there is no lot category with excess demand then the clock rounds end and a single further round – the supplementary bids round – takes place. In this round, bidders can make multiple bids, potentially both raising bids for packages already bid for in the clock rounds and making new bids for additional packages not yet bid for.

All clock bids and all supplementary bids are used for determining winners and prices. Taking at most one bid from each bidder, the auctioneer selects the combination of bids with the highest total value that can be satisfied within the available supply. The auctioneer then calculates the amount that the winners pay according to the second-price rule.

Open bidding over the clock rounds is aimed at mitigating the effect of common value uncertainty, which arises where the valuations of different bidders are affected by common uncertain factors (e.g. by the timely availability of technology or changes in consumer demand). Bidders’ valuations may differ because of different expectations about the common factors, with the most optimistic bidder being the most likely to win. A rational bidder should bid cautiously to avoid over-paying (the so-called ‘winner’s curse’). Information about others’ bids – even aggregate demand each round rather than full transparency of all bids – is helpful for firming up each bidder’s valuations. This both reduces the risks faced by bidders and improves the chances of an efficient outcome as relevant information is pooled across bidders.

The supplementary round is aimed at allowing bidders to express their interest in a wider range of alternative packages. Unlike in the clock rounds, bids are not subject to the constraint that bid amounts have to be based on a common price per lot for individual lot categories. This allows bidders to reflect synergies in combining different lots (i.e. where the value of a combination of lots is higher than the sum of its parts).

The information revealed in the open stage is only valuable if bidders make bids that sufficiently reflect their true valuations. For the auction to achieve an efficient outcome, supplementary bids must reflect the value that bidders place on different packages rather than being driven by a desire to misrepresent valuations for strategic reasons. Activity rules encourage bidders to reveal their demand throughout the open stage. The second-price rule largely removes the incentive to bid strongly below valuation or for fewer lots than actually wanted in order to reduce winning prices.

Valuation, valuation, valuation

The CCA has proven excellent in delivering efficient outcomes for a variety of reasons.

First, the CCA avoids the aggregation risks endemic in the more traditional SMRA. Offering radio spectrum in small slices – and possibly across a number of bands in one auction – gives bidders flexibility to acquire the combination of frequencies that best suits their needs. This is great for efficiency provided the auction format eliminates the risk of ending up with some unwanted subset of the lots sought.

Unfortunately, aggregation risks may be substantial in an SMRA, as standing high bidders are determined separately for each lot in each round. Bidders win their standing high bids when the auction ends, giving rise to the possibility of winning some lots they do not want because they have failed to win other complementary lots. This risk is hard to manage. It distorts bidding incentives and generally means that SMRAs cannot be expected to generate efficient outcomes where there are strong synergies between lots (as is typical in spectrum auctions). Aggregation risk is entirely absent in the CCA as bids are made for packages of lots, rather than individual lots (see box overleaf). In a CCA bidders can freely express their valuations for different packages without the fear of ending up winning something unusable.

Second, the approach used to determine winning bidders and prices in a CCA greatly reduces the decision-making burden on bidders. Unlike in an SMRA, there is no incentive to reduce the quantity bid for prematurely (so called strategic demand reduction). Straightforward bidding – bidding on the most preferred package in each clock round and then making supplementary bids according to valuations – is hard to beat in a CCA. Indeed, the activity rules and pricing rules are designed specifically to encourage such behaviour. The incentive for straightforward bidding also means that the bids made in the clock auction are likely to be informative about bidders’ underlying valuations and so the clock rounds can reduce common value uncertainty.

Removing the need to think hard about bid strategy and making truthful bidding the path of least resistance allows bidders to focus on the key task of determining their valuations for different packages of spectrum. This ability to deliver efficient outcomes is why the CCA has become popular for spectrum awards around the world, in particular for large multi-band auctions.

A few thousands are company, millions are a crowd

Of course, simpler decisions for bidders only come at the cost of increased complexity within the auction mechanism. In particular, incentives for straightforward bidding and the CCA’s ability to deliver efficient outcomes rely on the ‘black box’ of winner determination and second pricing that relies on some sophisticated mathematics.

As the number of lot categories and lots within each category increases, the number of possible packages of lots balloons exponentially. In turn, this creates an exponential ramp-up in the computational demands of determining the winning bids and prices.

Many CCAs place a cap on the number of distinct packages that a bidder may bid for, primarily for reasons of practicality. However, where the lot structure becomes complex, this cap may well be needed to rein in the computational demands of determining the winners and prices within a reasonable time. For example, in the Swiss multi-band auction held at the beginning of the year, bidders could in theory bid on up to 2.8 million different packages. Allowing bidders to submit 2.8 million bids could potentially lead to scenarios where it would become computationally infeasible to find the winning outcome within a reasonable time. The maximum number of bids during the supplementary round was therefore restricted to 3,000.

Do such caps on the number of submitted bids undo much of the flexibility given to bidders in the first place? Usually not, as the efficiency of the CCA does not require bidders to make bids on all possible packages, but only those that are likely to be potential winning outcomes. The clock rounds provide a rough indication of likely market-clearing prices, which helps bidders to narrow down the packages on which they should focus their attention. Also, many theoretically possible packages would not make commercial sense anyway. This is how “big” multiple band auctions – such as the recent Irish and Swiss auctions – have been successful despite the large number of potential packages.

The more you need, the less you get …

As the lot structure becomes more complex, there are more choices about how to combine individual lots creating an exponential blow-up in the number of possible packages. As a result, caps on numbers of bids may need to be tightened for practical reasons. At the same time bidders may require bids on many packages in order to express their preferences across reasonable alternatives.

The more complex the lot structure, the larger the number of combinations on which a bidder might reasonably bid. Even if a complex lot structure introduces distinctions that do not matter to a bidder, this still increases the number of bids needed even to express a lack of preference. For example, if a single lot now comes in the seven colours of the rainbow, expressing the fact that any colour would do takes seven bids. If we started with two lots (and the bidder wants both) and then make each one available in seven colours, the poor bidder has to make 49 bids to express the fact she does not care about the colour.

Offering spectrum on a regional basis is a particular problem in this regard. For example, the Australian and Canadian regulators have recently published their auction designs for awarding spectrum in the 700MHz band, which both feature a very complex lot structure.

The Australians combine the award of national licences in the 700MHz band with that of regional licences in the 2.5GHz band. Given the proposed spectrum caps, a national operator who is interested in acquiring either a national or a regional footprint of 2.5GHz spectrum alongside 700MHz spectrum might need to evaluate up to 156 billion packages.
The Canadians are planning to offer the 700MHz spectrum in regional blocks. Given the spectrum caps, a large wireless provider who is interested in either a national or a regional footprint may have valuations for up to 370 million billion packages. To put this in context, this means that if a bidder were presented with prices for each lot category and asked which package it preferred, the question is effectively unanswerable within any reasonable time unless simplifying assumptions are made (such as that categories are independent of each other). Therefore, the auction design is providing flexibility that could never practically be used by any bidder.
To reduce the computational load for determining the winning bids in the Australian and Canadian auctions, bidders are only allowed to submit up to 500 bids in total. This is a very limited number compared with the potential 156 billion or 370 million billion packages a bidder may be interested in.

How relevant is this? To a large part the answer depends on how informative the clock rounds are. In particular, the clock rounds must effectively provide bidders with the opportunity to identify the packages they are most likely to win. Bidders will truly need to find a needle in a haystack, or in the Canadian case, an atom in a needle in a haystack.

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New activity rules to the rescue?

What if we tighten up the activity rules to increase the role of the open rounds and limit the impact of supplementary bids on the outcome? The open rounds at least allow bidders another shot if lots are oversubscribed.

The rules proposed for the Canadian and Australian auctions include activity rules that place great emphasis on the requirement that bids submitted during the auction need to be consistent with stable and consistent preferences maintained over all clock rounds. The proposed activity rules largely cement the final clock round outcome in place, meaning that bidders will have the option of guaranteeing that they obtain at least the lots on which they bid in the last clock round, regardless of the supplementary bids made by others. This means that limitations on the number of supplementary bids that a bidder is allowed to make have little impact on the outcome, as this is strongly fixed by the final clock round outcome. It also means that bidders better not make any errors during the clock rounds. Because any round could be the last, not bidding on the most preferred package at any point in time could do serious damage to a bidder and the efficiency of the outcome.

At first sight, that looks helpful; after all, we want strong incentives for bidders to bid straightforwardly as this promotes efficiency. However, there is a catch. Penalising bidders for deviating from their preferences is a good idea if they can reasonably be expected to work out exactly how they should value the various lot combinations on which they might bid, and to identify the best combination of lots at any particular set of prices (i.e. through global optimisation, not heuristics). If they can do this only approximately due to the intrinsic difficulty of answering the question “what do I want?”, they may become tangled up in the web of activity constraints intended to promote straightforward bidding. This approach creates immense practical issues for bidders, contrary to the underlying ethos of the CCA that the auctioneer gathers complexity unto itself to make life easy for bidders.

Furthermore, this approach is inconsistent with the very fact that the CCA is a multiple round auction which seeks to mitigate common value uncertainty by allowing preference updating. Bidders may update their valuations during the clock rounds in light of information they receive about what other bidders are doing. If activity rules are too onerous, bidders may not be able to change their valuations in light of information received during the open rounds due to the constraints created by their earlier bids. If activity rules allow so little latitude that preference updating is effectively impossible, then there is little reason for an open auction at all.

Although the Canadian and Australian awards are substantially more complex for bidders than the Swiss auction, the activity rules that constrain bidding in the clock rounds and link the supplementary bids to clock bids are significantly more restrictive and unforgiving. Any bidding mistake during the clock rounds can have serious consequences, not only for the bidder, but also for the efficiency of the outcome.

Know thy limitations

There is no solution to the conundrum that greater flexibility implies greater complexity, which needs to be dealt with by either bidders or the auctioneer. Making the lot structure more differentiated means that bidders need to value a greater number of potential packages, and may need to make more bids. At the same time, there are constraints on the computational complexity of finding the winning outcome, which means that stricter limits may need to be placed on the number of bids.

The inherent trade-offs have to be acknowledged. Shifting complexity back on bidders certainly is not an easy way out. With so many packages on offer, telling bidders that all they need to do is simply to bid on their most preferred package in each clock round is perhaps a touch too simplistic.

Sophisticated auction designs have greatly assisted regulators by reducing their need to make administrative decisions on lot packaging. The CCA has tremendous potential to allow the market to explore alternative outcomes, for example choosing between different band plans or technologies that might have otherwise required a poorly informed administrative decision. However, the tool should not be imposed to allow regulators to skip all decisions on the lot structure and push unwarranted complexity back to bidders as a result.