Introduction

Auctions with multiple items are typically conducted in an environment in which bidders’ values depend on acquiring combinations, e.g. networks of broadcast licenses or timber rights for adjacent tracts of land. Concerns for economic efficiency and revenue enhancement have led the Federal Communications Commission (FCC) to run auctions simultaneously for large numbers of licenses in a series of bidding rounds, with provisional winners being announced after each round. Under the simultaneous multiround auction format (SMR), the highest bid on each license becomes the provisional price that must be topped in a subsequent round. This approach has been copied in other countries with considerable success, but experimental evidence indicates that efficiency and revenue may be reduced when bidders hesitate to incorporate synergy values into their bids for fear that they will end up winning only part of a desired package (see, for instance, the references in Brunner et al., 2010).

The “exposure problem” is a major concern in what is arguably the auction of a lifetime, i.e. the upcoming FCC 700 MHz spectrum auction. This spectrum has better propagation and penetration properties than any spectrum sold before and is extremely valuable for wireless applications (the FCC has set minimum prices at over 10 billion). More importantly, the wireless industry is concentrated and the 700 MHz auction provides the last opportunity for a new firm to enter the market. For an entrant to be successful in the wireless market, however, it has to acquire a nationwide footprint, which is virtually impossible with the current SMR format because of exposure risk.

Some pre-packaging of licenses into larger groups may help solve the exposure problem. In FCC Auction 65, for example, bids were proportionally higher for large blocks of bandwidth for air-to-ground communications; a block with 3 times as much bandwidth as a smaller block sold for about 4.5 times as much.

Introduction

The continued growth of wireless networks and services depends on the availability of adequate spectrum resources. Accelerating demand for those resources, due to the popularity of portable data-intensive wireless devices, are testing the limits of current commercial wireless networks, underscoring the need for changes in current spectrum allocations. This has prompted the Federal Communications Commission (FCC) in the United States to consider ways to increase the supply of spectrum allocated to broadband access and to introduce techniques for improving the utilization of existing allocations [1, Ch. 5].

Spectrum allocations generally fall into one of two categories: a licensed allocation gives exclusive use rights to the licensee, whereas an unlicensed allocation corresponds to the commons model in which the band can be shared by different applications and service providers [2]. Licensed spectrum typically carries restrictions on how it can be used, and is generally not transferable. Although these restrictions have been alleviated to some extent by the introduction of secondary spectrum markets [3], existing rules still inhibit the reallocation of spectrum to more efficient uses.

In contrast to the current “command and control” method for licensing spectrum, a spectrum market is based on a notion of spectrum property rights, which can be traded among buyers and sellers. The potential benefits of spectrum markets for increasing the efficiency of spectrum allocations is widely acknowledged. Thus far related discussions have focused on secondary markets, which allow service providers with licensed spectrum to lease their spectrum to other service providers. Transactions must be filed with the FCC for approval (which are automatic in some scenarios), introducing delays that increase transaction costs [3].

Here we reconsider the spectrum allocation problem without existing regulatory constraints. We start by providing general motivations for introducing spectrum markets. That is, a basic policy choice is whether to define and enforce spectrum property rights. From a social welfare point of view, this choice ultimately depends on whether spectrum is scarce, that is, if demand for it exceeds supply when it is free.

Introduction

There has been a long discussion on appropriate auction mechanisms for the sale of spectrum rights (Porter and Smith, 2006). Since 1994, the Simultaneous Multi-Round Auction (SMRA) has been used worldwide (Milgrom, 2000). The SMRA design was very successful, but also led to a number of strategic problems for bidders (Cramton, 2013). The exposure problem is central and refers to the risk for a bidder to make a loss due to winning only a fraction of the bundle of items (or blocks of spectrum) he has bid on at a price which exceeds his valuation of the won subset.

Combinatorial auctions (CAs) allow for bids on indivisible bundles avoiding the exposure problem. The design of such auctions, however, led to a number of fundamental problems, and many theoretical and experimental contributions during the past ten years (Cramton et al., 2006b). The existing experimental literature comparing SMRAs and CAs suggests that in the presence of significant complementarities in bidders’ valuations and a setting with independent private and quasi-linear valuations, combinatorial auctions achieve higher efficiency than simultaneous auctions (Banks et al., 1989; Ledyard et al., 1997; Porter et al., 2003; Kwasnica et al., 2005; Brunner et al., 2010; Goeree and Holt, 2010). Since 2008 several countries such as the U.K., Ireland, the Netherlands, Denmark, Austria, Switzerland, and the U.S. have adopted combinatorial auctions for selling spectrum rights (Cramton, 2013). While the U.S. used an auction format called Hierarchical Package Bidding (HPB) (Goeree and Holt, 2010), which accounts for the large number of regional licenses, the other countries used a Combinatorial Clock Auction (CCA) (Maldoom, 2007; Cramton, 2009), a two-phase auction format with primary bid rounds (aka. clock phase) for price discovery, which is extended by a supplementary bids round (aka. supplementary phase). The CCA design used in those countries has a number of similarities to the Clock-Proxy auction, which was proposed by Ausubel et al. (2006). It was used for the sale of blocks in a single spectrum band (i.e., paired and unpaired blocks in the 2.6 GHz band) and for the sale of multiple bands in Switzerland.

Although, spectrum auction design might appear specific, the application is a representative of a much broader class of multi-object markets as they can be found in logistics and industrial procurement. Spectrum auctions are very visible in public and successful designs are a likely role model for other domains as well.

Introduction

Combinatorial Clock Auctions (CCAs) are multi-object auctions where bidders make package bids in a clock phase followed by a supplementary round. CCAs have been recently used around the world to allocate spectrum frequencies for mobile telecommunication purposes. CCAs were introduced by Ausubel et al. (2006) and are the subject of quite a few recent investigations (see, e.g., Ausubel and Baranov, 2014; Bichler et al., 2013; Janssen and Karamychev, 2016; Knapek and Wambach, 2012; Levin and Skrzypacz, 2016; and papers in this volume).

One of the issues that is under-explored in the literature on CCAs is the impact of budget constraints on the bidding behavior of participating bidders and, consequently, on the efficiency properties of the auction. It is difficult to obtain direct evidence of the fact that budget constraints play an important role in real-life CCAs. It is also difficult to believe, however, that bidders in recent spectrum auctions have not been financially constrained. The amount of money typically paid is in the billions of euros, and even though a firm may think it will earn that money back in the years after the auction, it is likely to have to borrow the money in one way or another. Also, casual empiricism suggests that share prices of companies participating in a long-lasting auction decline during and after the auction (cf. the share prices of KPN in the Netherlands in 2012 and A1 in Austria in 2013).

It can be useful to distinguish between hard and soft budget constraints. On one hand, a hard budget constraint implies that bidders cannot pay more than a certain exogenously determined amount of money. On the other hand, senior management can set a soft budget constraint and inform the company's bidding team that it is not allowed to spend more than a certain amount of money. That is, under soft budget constraints, senior management may set aside a certain amount of money to be invested in acquiring spectrum.

Since its proposal in a 2006 academic paper, 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 2015, the CCA has been used for more than ten 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.

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 with quantities demanded at these prices. If aggregate demand exceeds available supply for any items, the auctioneer announces higher prices for these items in the next round. 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 process 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 entire 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 packages are determined by finding an allocation that maximizes the total value (as reflected in bids) subject to feasibility constraints: each item can be sold only once and only one bid from each bidder can be selected as part of the winning allocation.

Introduction

Theory, experiment and practice suggest that, when bidder valuations for multiple objects are super-additive, combinatorial auctions are needed to increase efficiency, seller revenue, and bidder willingness to participate (Bykowsky et al. 2000, Rassenti et al. 1982, Ledyard et al. 2002). A combinatorial auction is an auction in which bidders are allowed to express bids in terms of packages of objects. The now famous FCC spectrum auctions are a good example of the relevance of these issues. In 41 auction events from 1994 to 2003, the FCC used what is known as a Simultaneous Multiple Round (SMR) auction to allocate spectrum and raise over $40 billion in revenue. This auction format does not allow package bidding. The FCC auctions also divide the spectrum by geographic location. It is reasonable to expect that some bidders might receive extra benefits by obtaining larger, more contiguous portions of the spectrum. A firm might enjoy cost savings if they could purchase two adjacent locations. However, without package bidding, a bidder cannot express that preference, potentially lowering the efficiency and revenue of the auction. If the bidder attempts to acquire both licenses through bidding on the licenses individually, they might be forced to expose themselves to potential losses. The high number of bidder defaults on payments might, in part, be evidence of losses caused by the lack of package bidding. In response to these difficulties, the FCC plans to allow package bidding in future auctions (Federal Communications Commission 2002, Dunford et al. 2001). In particular, the FCC in its auction #31 for the upper 700 MHz band, affords bidders the ability to submit bids for packages of licenses. The particular design presented in this paper was developed prior to the FCC package auction design. Indeed one of the major features of the FCC design was clearly influenced by the pricing rules we developed herein.

Introduction

Since being pioneered by the U.S. in 1994, simultaneous ascending auctions have become a common mechanism to allocate spectrum rights. Spectrum auctions can involve billions of dollars and companies bidding in these auctions regularly create specialized bidding teams and hire experts in auction theory to develop bidding strategies. Nevertheless, the results can be surprising. In the FCC's auction of Advanced Wireless Service spectrum, price arbitrage failed so dramatically that one new entrant was able to purchase essentially nationwide coverage for about a third (more than a billion dollars) less than what incumbent carriers paid for equivalent spectrum in the same auction. At the same time, the other prospective nationwide entrant exited the auction early and filed a letter with the FCC claiming that the auction rules disadvantaged new entrants!

Results of this sort raise questions for economists. Does the apparent failure of the Law of One Price indicate a fundamental flaw in auction design? If not, why must such auctions be complicated? What are the issues that create strategic complexity for bidders? And to what extent can the tools of economic theory provide insights that facilitate effective bidding in highly complex environments?

We start by explaining some of the reasons why large spectrum auctions are necessarily complicated, and why the Law of One Price can fail so dramatically in a spectrum auction.We emphasize two difficulties facing bidders: exposure problems, which are essentially the problems of bidders wishing to acquire complementary licenses, and budget constraints, which we argue are ubiquitous.We explain why these difficulties make bidding in simultaneous ascending auctions complicated, and also why they would complicate bidding in other auction designs.

Exposure problems create fundamental difficulties for a new entrant seeking to compete head-to-head with incumbent nationwide wireless carriers in the US. Such an entrant needs to acquire adequate bandwidth in every major metropolitan area, but because licenses covering cities or regions are sold individually, the entrant could commit to spending billions of dollars winning spectrum licenses before discovering that the total price for the bundle of licenses it seeks makes the whole entry unaffordable or unprofitable. It could then be left to dispose of extensive holdings at fire-sale prices.

Make things as simple as possible, but not simpler (Albert Einstein)

Introduction

From 1994 to 2008, spectrum was sold almost exclusively using the Simultaneous Multiple Round Auction (SMRA). The SMRA is based on simple rules, which make it easy to explain and implement, yet they create considerable strategic complexity. Since items have to be won one-by-one, bidders who compete aggressively for combinations of items risk paying too much if they ultimately win an inferior subset. This exposure risk suppresses bidding with adverse consequences for the auction's efficiency and revenue.

Since 2008, regulators worldwide have adopted the Combinatorial Clock Auction (CCA) to avoid exposure problems. The CCA is based on very complex rules, but the premise was that bidding would be “straightforward,” i.e. bids would truthfully reflect valuations. Unfortunately, it is now well known that the CCA admits many other behaviors, including demand reduction, demand expansion, and predatory bidding (see Chapters 15–17). In particular, the CCA's supplementary stage may provide bidders with an opportunity to raise rivals’ costs, which has led to some hard-to-defend outcomes.

In light of recent experiences with the CCA, regulators should be reassured about the advantages of combinatorial formats when synergies for adjacent geographic regions or contiguous blocks of spectrum are important. Market designers should beware of Einstein's advice and not regress to offering solutions that are too simplistic. Instead, they should take stock of two decades of field experience to pinpoint features essential to participating bidders and regulators. After all, spectrum auction design will only be truly successful if we are able to model their preferences correctly.

The standard paradigm in mechanism design assumes bidders with independent and private valuations, quasi-linear utility functions, and unlimited budgets, and regulators who aim to maximize efficiency or revenue of an auction in isolation, i.e. ignoring its effect on the downstream market. While these assumptions result in models that are elegant, they are not necessarily relevant. In what follows, we discuss objectives of regulators and bidders in spectrum auctions and how they differ from these “textbook” assumptions. These differences have an impact on the choice of the auction format. Furthermore, we discuss challenges for future auction designs and requirements for new models.

Introduction

The “simultaneous ascending auction” was first introduced in 1994 to sell licenses to use bands of radio spectrum in the United States. Much of the attention devoted to the auction came from its role in reducing federal regulation of the radio spectrum and allowing market values, rather than administrative fiat, to determine who would use the spectrum resource. Many observers were also fascinated by the then-novel use of weblike interfaces for bidders. The large amounts of money involved were yet another source of interest. The very first use of the auction rules was a $617 million sale of 10 paging licenses in July 1994. In the broadband personal communications services (PCS) auction, which began in December 1994, 99 licenses were sold for a total price of approximately $7 billion. Once the auctions had been conducted, it became much harder to ignore the tremendous value of the large amounts of spectrum allocated to uses such as high-definition television, for which Congress had demanded no compensation at all. Moreover, the perceived successes with the new rules inspired imitators to conduct similar spectrum auctions in various countries around the world and to recommend similar auctions for other applications.

Among academic economists, attention was also piqued because the auction design made detailed use of the ideas of economic theory and the recommendations of economic theorists. Indeed, the U.S. communications regulator adopted nearly all its important rules from two detailed proposals for a simultaneous ascending auction: one by Preston McAfee and the other by Robert Wilson and me. Economic analysis dictated nearly all the rule choices in the first few auctions. Various reviews suggest that the new auction design realized at least some of the theoretical advantages that had been claimed for it.

Several parts of economic theory proved helpful in designing the rules for the simultaneous ascending auction and in thinking about how the design might be improved and adapted for new applications. After briefly reviewing the major rules of the auction in Section II, I turn in Section III to an analysis based on tatonnement theory, which regards the auction as a mechanism for discovering an efficient allocation and its supporting prices. The analysis reveals a fundamental difference between situations in which the licenses are mutual substitutes and others in which the same licenses are sometimes substitutes and sometimes complements.

Introduction

The design of auction protocols and systems has received considerable academic attention in the recent years and found application in industrial procurement, logistics, and in public tenders (Airiau and Sen, 2003; Bellantuono et al., 2013). Spectrum auction design is one of the most challenging and visible applications. It is often seen as a pivotal example for the design of multi-object markets and successful auction designs are likely role-models for other markets in areas such as procurement and logistics.

Efficiency, revenue, and strategic simplicity for bidders are typical design goals that a regulator has in mind. In theory, theVickrey-Clarke-Groves (VCG) auction is the only strategy-proof and efficient auction but for practical reasons, it has rarely been used so far (Rothkopf, 2007). Several other auction formats have been designed and used for selling spectrum. The most prominent example is the Simultaneous Multi-Round Auction (SMRA) which has been used since the mid-90s to sell spectrum licenses world-wide. The more recent Combinatorial Clock Auction (CCA) is a two-phase auction format with an initial ascending clock auction and a sealed-bid supplementary bid phase afterward. It has lately been used to sell spectrum in countries such as Australia, Austria, Canada, Denmark, Ireland, the Netherlands, Slovenia, and the UK.

The CCA draws on a number of elegant ideas inspired by economic theory. A revealed preference activity rule should provide incentives for bidders to bid straightforward or consistent, i.e., to bid truthfully on one of the payoff-maximizing packages in each round of the clock phase. If bidders fail to maximize utility and bid on a package with a less than optimal payoff, we will also refer to this as inconsistent bidding behavior, i.e., bids which are not consistent with the assumption of utility maximization. A second-price rule should set incentives to bid all valuations truthfully in the second sealed-bid phase. It can be shown that if bidders respond to these incentives in both phases of the CCA, then the outcome is efficient and in the core (Ausubel et al., 2006). However, bidders might not have incentives to bid truthful in both phases, and this can lead to inefficiencies.

Introduction

Fred Kahn recognized the important role of market design in improving how markets work. He believed that prices should be set in an open competitive process, rather than administratively. I had the pleasure of working with Fred on a project to evaluate the pricing rule in California's electricity market.We examined whether the electricity market should use uniform pricing or pay-as-bid pricing (Kahn et al. 2001). In this tribute to Fred Kahn, I also focus on auction design, but in the communications industry.

Spectrum auctions have been used by governments to assign and price spectrum for about 20 years. Over those years, the simultaneous ascending auction, first introduced in the US in 1994, has been the predominant method of auctioning spectrum. The auctions have proved far superior to the prior methods of beauty contests and lotteries (Cramton 1997; Milgrom 2004).

Despite the generally positive experience with the simultaneous ascending auction, several design issues have surfaced. Some were addressed with minor rule changes. For example, bidders’ use of trailing digits to signal other bidders and support tacit collusion was eliminated by limiting bids to integer multiples of the minimum increment (Cramton and Schwartz 2002). However, many other design problems remain. In this paper, I identify these problems, and describe a new approach—the combinatorial clock auction—which is based primarily on the clock-proxy auction (Ausubel et al. 2006), which addresses the main limitations of the simultaneous ascending auction.

My focus here is on spectrum auction design, rather than spectrum policy more generally. Certainly, communications regulators face many other critical challenges, such as how best to free up new spectrum for auction (Cramton et al. 1998), or whether an auction is needed at all (FCC 2002). For some allocations, it is better to set aside the spectrum for common property use, as is done with unlicensed spectrum. In particular, for applications that do not create additional scarcity, the commons model is better than the auction model.

Introduction

In a series of auctions starting in 1994, the Federal Communications Commission (FCC) sold the rights to provide personal communications services (PCS) using the electromagnetic spectrum. The rights are defined by both wavelength and geographic coverage. The largest of these auctions, for ninety-nine 30-MHz licenses in 51 major trading areas (MTAs) in the United States and its territories (two per MTA, except one each in New York, Los Angeles, and Washington, DC) began on December 5, 1994. Thirty bidders registered and qualified for the auction and spent over $7 billion acquiring licenses. This report describes how our team (for GTE) answered the following question: Given the information we had about GTE's valuations, budgets and objectives, the valuations, budgets and objectives of rival bidders, and the rules, how should we bid to achieve the best attainable outcome?

In developing our auction strategy we relied on (1) our knowledge of the other bidders and market opportunities, (2) our understanding of GTE's senior management's objectives, and (3) the ability to adapt game theory to model the behavior of bidders in the auction. Going into the auction, GTE's senior management gave our bidding team an outline of the company's objectives. Because we had limited information about our rivals, we needed to make some guesses about their interests, valuations, and budgets, as well as about the auction's duration and the price threshold.

The FCC used a novel simultaneous, multiple-round ascending-bid SMR format for this auction (see Cramton (1995a) or McAfee and McMillan (1995) for a more detailed description). In summary, 30 firms simultaneously bid on 99 PCS licenses in a sequence of rounds. At the end of each round, the FCC posted all the bids from that round, and the bidders then had the chance to place new bids in the next round (subject to constraints imposed by the activity rules). The auction rules specified that the auction would close on all 99 properties at the same time.