Combinatorial Clock Auction Research Articles

Machine Learning-Powered Combinatorial Clock Auction

We study the design of iterative combinatorial auctions (ICAs). The main challenge in this domain is that the bundle space grows exponentially in the number of items. To address this, several papers have recently proposed machine learning (ML)-based preference elicitation algorithms that aim to elicit only the most important information from bidders. However, from a practical point of view, the main shortcoming of this prior work is that those designs elicit bidders' preferences via value queries (i.e., “What is your value for the bundle {A, B}?''). In most real-world ICA domains, value queries are considered impractical, since they impose an unrealistically high cognitive burden on bidders, which is why they are not used in practice. In this paper, we address this shortcoming by designing an ML-powered combinatorial clock auction that elicits information from the bidders only via demand queries (i.e., “At prices p, what is your most preferred bundle of items?''). We make two key technical contributions: First, we present a novel method for training an ML model on demand queries. Second, based on those trained ML models, we introduce an efficient method for determining the demand query with the highest clearing potential, for which we also provide a theoretical foundation. We experimentally evaluate our ML-based demand query mechanism in several spectrum auction domains and compare it against the most established real-world ICA: the combinatorial clock auction (CCA). Our mechanism significantly outperforms the CCA in terms of efficiency in all domains, it achieves higher efficiency in a significantly reduced number of rounds, and, using linear prices, it exhibits vastly higher clearing potential. Thus, with this paper we bridge the gap between research and practice and propose the first practical ML-powered ICA.

Selling spectrum in the presence of shared networks: The case of the Israeli 5G auction

The Israeli 5G auction that took place in August 2020 used the Combinatorial Clock Auction mechanism adapted to the Israeli market. We review the challenges that the Israeli Ministry of Communication faced while designing the auction and discuss the strategic consequences of the design. We highlight the special characteristics of the Israeli telecommunication market and, in particular, the fact that most operators share their antenna networks and their spectrum assets with other auction participants, but spectrum licenses need to be purchased by each operator individually. The Israeli Ministry of Communication required operators sharing the same networks to submit joint bids in the auction. We discuss the implications of this decision on the efficiency of the auction, and the difficulties it caused the bidders. We discuss the effect of further incentive schemes that accompanied the auction, and we also describe some signaling opportunities that emerged during the auction process.

An iterative combinatorial auction design for fractional ownership of autonomous vehicles

AbstractThis study designs a new market for fractional ownership of autonomous vehicles (AVs), in which an AV is co‐leased by a group of individuals. We present a practical iterative auction based on the combinatorial clock auction to match the interested customers together and determine their payments. In designing such an auction, we consider continuous‐time items (time slots) that are defined by bidders and naturally exploit driverless mobility of AVs to form co‐leasing groups. To relieve the computational burdens of both bidders and the auctioneer, we devise user agents who generate packages and bid on behalf of bidders. Through numerical experiments using the California 2010–2012 travel survey, we test the performance of the auction design. We also compare various bidding strategies and study the effect of activity rules on the bidders' payoffs. We find that the designed activity rules successfully remove the strategic behavior of bidders. We also find that core‐selecting payment rule brings the largest revenue to the auctioneer in most cases.

Optimizing Social Welfare of Live Video Streaming Services in Mobile Edge Computing

The live video streaming services have been suffered from the limited backhaul capacity of the cellular core network and occasional congestions due to the cloud-based architecture. Mobile Edge Computing (MEC) brings the services from the centralized cloud to nearby network edge to improve the Quality of Experience (QoE) of cloud services, such as live video streaming services. Nevertheless, the resource at edge devices is still limited and should be allocated economically efficiently. In this paper, we propose Edge Combinatorial Clock Auction (ECCA) and Combinatorial Clock Auction in Stream (CCAS), two auction frameworks to improve the QoE of live video streaming services in the Edge-enabled cellular system. The edge system is the auctioneer who decides the backhaul capacity and caching space allocation and streamers are the bidders who request for the backhaul capacity and caching space to improve the video quality their audiences can watch. There are two key subproblems: the caching space value evaluations and allocations. We show that both problems can be solved by the proposed dynamic programming algorithms. The truth-telling property is guaranteed in both ECCA and CCAS. The simulation results show that the overall system utility can be significantly improved through the proposed system.

An Analysis of Allocation Phase Pricing and Clock Round Price Increases in the Canadian 600 MHz Auction

The 600 MHz auction conducted by Innovation, Science, and Economic Development (ISED) in Canada was a Combinatorial Clock Auction (CCA) that used a spectrum set-aside to prevent three large national wireless providers—specifically, Bell, Rogers, and Telus—from winning the entirety of the spectrum at auction. The product space was divided into 16 geographic areas, and seven 2x5 MHz block were available in each area. Within the context of the ISED consultation regarding auction design for the 3500 MHz tender, respondents have commented on certain aspects of the 600 MHz auction design as it relates to the set-aside and to price determination in the 600 MHz auction. The purpose of this paper is to provide interested parties with an accurate understanding of pricing in the Canadian 600 MHz auction of 2019. This paper does not take a position on any proposed design elements of the 3500 MHz auction in Canada. We find that set-aside eligible bidders in the 600 MHz auction did not significantly affect the base prices that Rogers or Telus paid for 600 MHz spectrum. In addition, an examination of clock round bidding behavior shows that open prices did not increase significantly due to bidding from set-aside eligible bidders.

T-Tree: The Tokyo toolbox for large-scale combinatorial auction experiments

This paper provides a brief introduction to t-Tree, a general auction software package that implements single-unit auctions, Vickrey–Clarke–Groves auctions (“VCG auctions”), Simultaneous Multiple Round Auctions (“SMRA”), and Combinatorial Clock Auctions (“CCA”) used in transportation, logistics, procurements, and spectrum allocation. The critical contribution of t-Tree is that it can handle computational complexities of the winner determination problem in large-scale combinatorial auctions by natively implementing Zhong et al. (2004)’s combinatorial optimization algorithms. Thus researchers can study large-scale combinatorial auction mechanisms off the shelf using t-Tree.

Combinatorial clock auctions: Price direction and performance

The lack of price guidance towards efficiency relevant packages in ascending combinatorial clock auctions (ACCA) can lead to a low-efficiency allocation of goods. We propose a descending price combinatorial clock auction (DCCA) with a newly devised pricing strategy to improve on this problem. Using agent-based simulations we document that the DCCA provides significant improvements over the ACCA and we are able to understand in which environments these improvements are likely to be the strongest. We test these predictions in the laboratory with human subjects and find evidence that the DCCA generates improvements in auction efficiency and revenue.

On the clock of the combinatorial clock auction

The combinatorial clock auction (CCA) has frequently been used in recent spectrum auctions. It combines a dynamic clock phase and a one‐off supplementary round. The winning allocation and the corresponding prices are determined by the Vickrey–Clarke–Groves rules. These rules should encourage truthful bidding, whereas the clock phase is intended to reveal information. We inquire into the role of the clock when bidders have lexicographic preferences for raising rivals' costs. We show that in an efficient equilibrium, the clock cannot fully reveal bidders' types. In the spirit of the ratchet effect, in the supplementary round competitors extract surplus from strong bidders whose type is revealed. We also show that if there is substantial room for information revelation, that is, if the uncertainty about the final allocation is large, all equilibria of the CCA are inefficient. Qualitative features of our equilibria are in line with evidence concerning bidding behavior in some recent CCAs.

On the Clock of the Combinatorial Clock Auction

The Combinatorial Clock Auction (CCA) has been frequently used in recent spectrum auctions. It combines a dynamic clock phase with subsequent VCG pricing in order to maximize price discovery and efficiency. We inquire into the role of the clock when bidders have lexicographic preferences for raising rivals' costs. All equilibria of the CCA are inefficient if there is substantial room for price discovery, that is, if there is large uncertainty concerning the competitor's type. Conversely, in all efficient equilibria price discovery is limited. Qualitative features of our equilibria are in line with evidence concerning bidding behavior in some recent CCAs.

A Bayesian Clearing Mechanism for Combinatorial Auctions

We cast the problem of combinatorial auction design in a Bayesian framework in order to incorporate prior information into the auction process and minimize the number of rounds to convergence. We first develop a generative model of agent valuations and market prices such that clearing prices become maximum a posteriori estimates given observed agent valuations. This generative model then forms the basis of an auction process which alternates between refining estimates of agent valuations and computing candidate clearing prices. We provide an implementation of the auction using assumed density filtering to estimate valuations and expectation maximization to compute prices. An empirical evaluation over a range of valuation domains demonstrates that our Bayesian auction mechanism is highly competitive against the combinatorial clock auction in terms of rounds to convergence, even under the most favorable choices of price increment for this baseline.

A Practical Guide to the Combinatorial Clock Auction

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 neglected. In this article, we examine some of the most critical practical decisions for a regulator implementing the CCA. Topics include: implementation of reserve prices; endogenous band plans; supplementary round activity rules; competition policy; bidding languages; and allocation of the core burden. We illustrate our discussion with examples from recent spectrum auctions that used the CCA format.

Synergistic valuations and efficiency in spectrum auctions

In spectrum auctions, bidders typically have synergistic values for combinations of licenses. This has been the key argument for the use of combinatorial auctions in the recent years. Considering synergistic valuations turns the allocation problem into a computationally hard optimization problem that generally cannot be approximated to a constant factor in polynomial time. Ascending auction designs such as the Simultaneous Multiple Round Auction (SMRA) and the single-stage or two-stage Combinatorial Clock Auction (CCA) can be seen as simple heuristic algorithms to solve this problem. Such heuristics do not necessarily compute the optimal solution, even if bidders are truthful. We study the average efficiency loss that can be attributed to the simplicity of the auction algorithm with different levels of synergies. Our simulations are based on realistic instances of bidder valuations we inferred from bid data from the 2014 Canadian 700 MHz auction. The goal of the paper is not to reproduce the results of the Canadian auction but rather to perform “out-of-sample” counterfactuals comparing SMRA and CCA under different synergy conditions when bidders maximize payoff in each round. With “linear” synergies, a bidder's marginal value for a license grows linearly with the total number of licenses won, while with the “extreme national” synergies, this marginal value is independent of the number of licenses won unless the bidder wins all licenses in a national package. We find that with the extreme national synergy model, the CCA is indeed more efficient than SMRA. However, for the more realistic case of linear synergies, SMRA outperforms various versions of CCA that have been implemented in the field including the one used in the Canadian 700 MHz auction. Overall, the efficiency loss of all ascending auction algorithms is small even with high synergies, which is remarkable given the simplicity of the algorithms.

A review of radio spectrum combinatorial clock auctions

This paper surveys a decade of Combinatorial Clock Auctions (CCAs) to allocate radio spectrum licenses from their inception to 2016. Although all CCAs share a common structure (first an allocation stage and then, an assignment stage), regulators have tailored key variables depending on their spectrum policies and market structures. We identify these variables, such as: spectrum packaging policy, reserve price, demand limit, activity rule, transparency and pricing rule. We also analyze the different ways in which regulators can design them along with their implications. This theoretical work is accompanied by a review of the practical implementation decisions in each actual auction and final outcomes. Although all the information is public, it is not easy to find because it is highly disaggregated. Finally, after having identified advantages and disadvantages in this auction model, we present some proposals to improve the actual mechanism.

Spiteful bidding and gaming in combinatorial clock auctions

Combinatorial Clock Auctions (CCAs) have recently been used around the world to allocate mobile telecom spectrum. CCAs are claimed to significantly reduce the scope for strategic bidding. This paper shows, however, that bidding truthfully does not constitute an equilibrium if bidders also have an incentive to engage in spiteful bidding to raise rivals' cost. The restrictions on further bids imposed by the clock phase of a CCA give certainty to bidders that certain bids above value cannot be winning bids, assisting bidders to engage in spiteful bidding.

Properties of the Combinatorial Clock Auction

The combinatorial clock auction has become popular for large-scale spectrum awards and other uses, replacing more traditional ascending or clock auctions. We describe some surprising properties of the auction, including a wide range of ex post equilibria with demand expansion, demand reduction, and predation. Our results obtain in a standard homogeneous good setting where bidders have well-behaved linear demand curves, and suggest some practical difficulties with dynamic implementations of the Vickrey auction. (JEL D44, D47, H82, L13)

Strategic Bidding in a Combinatorial Clock Auction: The 700 Mhz Canadian Auction

Using data provided by Industry Canada this paper seeks to understand what strategic bidding is in the 2014 700-MHz Canadian auction. The auction format is known as Combinatorial Clock. Its design seeks to induce truthful bidding, that is, a bidder is expected to bid in a way that at each round of the Clock Rounds stage her utility is maximised, and expected to reveal her true valuation for each bundle that make up her final bid in the Combinatorial stage.The Combinatorial Clock auction is an innovative auction design which aims to overcome some of the problems evidenced in the application of the Simultaneous Ascending auction, a format that has been widely popular for assigning radio spectrum to commercial providers of mobile communications services over the last 20 years.The paper uses publicly available data from the auction by Industry Canada. By focusing on the longest of the three auction stages, the Clock Rounds, it examines the evolution of several auction indexes as a means to devise an approach to understand bidders’ strategic behaviour. It also uses a Revealed Preference theory framework to test whether bidders bidding was consistent with utility maximisation. When it is not, the paper analyses evidence to support claims of strategic behaviour.

Frontiers in spectrum auction design

Spectrum auction design has seen number innovations in the recent years. Regulators have used various types of combinatorial auction formats including simple ascending combinatorial clock auctions and first-price sealed-bid combinatorial auctions. The Simultaneous Multi-Round Auction (SMRA) and the two-stage Combinatorial Clock Auction (CCA) are the most wide-spread auction formats for spectrum sales to date. We provide an accessible overview of strategic problems in these auction formats and summarize research challenges in this field for a broader audience of readers in industrial organization.

Raising rivals’ cost in multi-unit auctions

The objective many telecom regulators want to achieve when they decide to auction spectrum is that acquiring firms pay a market price (based on the opportunity cost principle). The simultaneous ascending auction may fail in this respect, as it provides bidders with an opportunity to engage in strategic demand reduction. This paper asks whether the combinatorial clock auction (CCA) fares better in this respect. We show that the answer to this question depends on the objectives bidders have. If bidders have only the slightest preference to raise rivals’ cost, they will use the opportunities the CCA provides them to engage in strategic demand expansion. This is even the case when the clock phase ends with excess demand.

Canada's 700 Mhz Spectrum Auction: A Case Study

The purpose of this paper is to present a case study of Canada’s 700 MHz spectrum auction, which took place at the beginning of 2014. The auction format adopted by the Canadian regulator was the Combinatorial Clock Auction (CCA). In Section 1, we review the band plan for Canada’s 700 MHz spectrum auction. We discuss the reasons and benefits from the band plan that Industry Canada applied. Section 2 presents the background information about selected, qualified bidders in this auction. Further in Section 3 the main stage of the auction, the Clock Rounds, is described; two conditions designed to induce bidders to truthfully reveal their preferences are explained as their understanding is key to understanding the novelties of the CCA; in this section results from the Canadian auction are presented. In Section 4 we analyse the Clock Rounds stage in search for behavioural patterns observed from the auction history and data that can help us characterise the bidding strategies employed in the auction.

Strategic Complexities in the Combinatorial Clock Auction

In recent years, regulatory bodies in Europe and around the world implemented Combinatorial Clock Auctions (CCA) to allocate scarce and valuable spectrum frequencies usage rights. Although the auction design is complex, the promise is that bidding becomes simple. More precisely, bidders may bid on the profit-maximizing package (truthful bidding) during the clock phase and submit bids that are equal to their valuations on only a handful of relevant packages (truncated bidding) in the supplementary phase. While this might be correct with the ideal implementation of the CCA for perfectly rational, profit-maximizing bidders with private values, our experience with consulting bidders shows that practical implementations of the CCA and the concerns of the bidders lead to severe complexities in determining the right bidding behavior. We provide simple examples that illustrate how “truthful and truncated“ bidding may be harmful to bidders and thereby illustrate the complexities bidders face in preparing for a CCA.