Bidding Language Research Articles

An Iterative Procurement Combinatorial Auction Mechanism for the Multi-Item, Multi-Sourcing Supplier-Selection and Order-Allocation Problem under a Flexible Bidding Language and Price-Sensitive Demand

This study addresses the multi-item, multi-sourcing supplier-selection and order-allocation problem. We propose an iterative procurement combinatorial auction mechanism that aims to reveal the suppliers’ minimum acceptable selling prices and assign orders optimally. Suppliers use a flexible bidding language to submit procurement bids. The buyer solves a Mixed Integer Non-linear Programming (MINLP) model to determine the winning bids for the current auction iteration. We introduce a buyer’s profit-improvement factor that constrains the suppliers to reduce their selling prices in subsequent bids. Moreover, this factor enables the buyer to strike a balance between computational effort and optimality gap. We develop a separate MINLP model for updating the suppliers’ bids while satisfying the buyer’s profit-improvement constraint. If none of the suppliers can find a feasible solution, the buyer reduces the profit-improvement factor until a pre-determined threshold is reached. A randomly generated numerical example is used to illustrate the proposed mechanism. In this example, the buyer’s profit improved by as much as 118% compared to a single-round auction. The experimental results show that the proposed mechanism is most effective in competitive environments with several suppliers and comparable costs. These results reinforce the importance of fostering competition and diversification in a supply chain.

A flexible combinatorial auction bidding language for supplier selection and order allocation in a supply chain with price sensitive demand

This study addresses the multi-item multi-sourcing supplier selection and order allocation problem in a Combinatorial Auction (CA) framework. First, we propose a new flexible procurement CA bidding language, then prove that it can convey the same information as existing bidding languages while allowing more efficient auction outcomes and reduced computational complexity. Suppliers submit combinatorial bids to a single manufacturer. Each bid carries information about the supplier’s cost structure and potential discounts. The manufacturer purchases the items and assembles one or more product types that experience price-sensitive demand rates by end consumers. We use the realistic logit function to represent the price-sensitive demand rates of finished products. A Mixed Integer Non-Linear Programming (MINLP) model is developed to help the manufacturer make optimal supplier selection, order allocation, and pricing decisions under the proposed bidding language. The MINLP model considers purchasing, transportation, ordering, administrative, holding, and manufacturing costs. These considerations make the results of this study realistic with the potential to be used in practical applications. Also, we derive a set of necessary conditions that must exist in at least one optimal solution to the problem. These conditions can be utilized to design efficient solution mechanisms for this difficult problem in the future. Finally, an extensive numerical analysis is performed to illustrate the bidding language and the key results.

Solving Strong-Substitutes Product-Mix Auctions

This paper develops algorithms to solve strong-substitutes product-mix auctions: it finds competitive equilibrium prices and quantities for agents who use this auction’s bidding language to truthfully express their strong-substitutes preferences over an arbitrary number of goods, each of which is available in multiple discrete units. Our use of the bidding language and the information it provides contrasts with existing algorithms that rely on access to a valuation or demand oracle. We compute market-clearing prices using algorithms that apply existing submodular minimization methods. Allocating the supply among the bidders at these prices then requires solving a novel constrained matching problem. Our algorithm iteratively simplifies the allocation problem, perturbing bids and prices in a way that resolves tie-breaking choices created by bids that can be accepted on more than one good. We provide practical running time bounds on both price finding and allocation and illustrate experimentally that our allocation mechanism is practical. Funding: E. Baldwin and P. Klemperer were supported by the Economic and Social Research Council [Grant ES/L003058/1]. P. W. Goldberg and E. Lock were supported by a JP Morgan faculty fellowship during the work on the final version of the paper. Supplemental Material: The online companion is available at https://doi.org/10.1287/moor.2019.0248 .

An energy-aware combinatorial auction-based virtual machine scheduling model and heuristics for green cloud computing

Considering the increasing demand for cloud computing, and the financial and environmental impact of the increasing energy consumption trend of data centers, improving energy efficiency is vital for cloud service providers. In this study, an energy-aware virtual machine scheduling model is proposed which is based on the multi-unit nondiscriminatory combinatorial auction. The model includes a powerful bidding language that allows users to declare their complicated virtual machine requests using logical AND and OR relations along with the time constraints. The study also presents the formal definition of the model and the associated optimization problem for determining the optimum schedule and energy-efficient placement of VMs on physical servers. The optimization problem is formulated using integer linear programming and several heuristic solution methods including the Genetic Algorithm are proposed for this problem. The performances of the model and the proposed heuristics are assessed on a comprehensive test suite. The proposed model is estimated to provide approximately a 37% improvement in revenues, and the solution methods are estimated to provide high-quality solutions within only 5% of the optimum which enable the model to be deployed in large-scale clouds.

Learning Strong Substitutes Demand via Queries

This article addresses the computational challenges of learning strong substitutes demand when given access to a demand (or valuation) oracle. Strong substitutes demand generalises the well-studied gross substitutes demand to a multi-unit setting. Recent work by Baldwin and Klemperer shows that any such demand can be expressed in a natural way as a finite list of weighted bid vectors. A simplified version of this bidding language has been used by the Bank of England. Assuming access to a demand oracle, we provide an algorithm that computes the unique list of weighted bid vectors corresponding to a bidder’s demand preferences. In the special case where their demand can be expressed using positive bids only, we have an efficient algorithm that learns this list in linear time. We also show super-polynomial lower bounds on the query complexity of computing the list of bids in the general case where bids may be positive and negative. Our algorithms constitute the first systematic approach for bidders to construct a bid list corresponding to non-trivial demand, allowing them to participate in “product-mix” auctions.

Strong substitutes: structural properties, and a new algorithm for competitive equilibrium prices

We show the strong substitutes product-mix auction bidding language provides an intuitive and geometric interpretation of strong substitutes as Minkowski differences between sets that are easy to identify. We prove that competitive equilibrium prices for agents with strong substitutes preferences can be computed by minimizing the difference between two linear programs for the positive and the negative bids with suitably relaxed resource constraints. This also leads to a new algorithm for computing competitive equilibrium prices which is competitive with standard steepest descent algorithms in extensive experiments.

Bidder Support in Multi-item Multi-unit Continuous Combinatorial Auctions: A Unifying Theoretical Framework

Combinatorial auctions have seen limited applications in large-scale consumer-oriented marketplaces, partly due to the substantial complexity to keep track of auction status and formulate informed bidding strategies. We study the bidder support problem for the general multi-item multi-unit (MIMU) combinatorial auctions, where multiple heterogeneous items are being auctioned and multiple homogeneous units are available for each item. Under two prevalent bidding languages (OR bidding and XOR bidding), we derive theoretical results and design efficient algorithmic procedures to calculate important bidder support information, such as the winning bids of an auction and the minimum bidding value for a bid to win an auction either immediately or potentially in the future. Our results unify the theoretical insights on bidder support problem for different bidding languages as well as different special cases of general MIMU auctions, namely the single-item multi-unit (SIMU) auctions and the multi-item single-unit (MISU) auctions. We also consider auctions with additional bidding constraints, including batch-based combinatorial auctions and hierarchical combinatorial auctions, as well as the combinatorial reverse auctions, all of which have relevant practical applications (e.g., industrial procurements). Our results can be readily extended to solve the bidder support problems in these auction mechanisms.

An Energy-Aware Combinatorial Virtual Machine Allocation and Placement Model for Green Cloud Computing

Resource allocation is an important problem for cloud environments. This paper introduces an energy-aware combinatorial auction-based model for the resource allocation problem in clouds. The proposed model allows users of a cloud to submit their virtual resource requests as bids using the provided bidding language which allows complementarities and substitutabilities among those resources to be declared. The model finds the most profitable mutually satisfiable set of winning bids, and the corresponding allocation of virtual resources to the users while considering the placement of virtual resources to the available physical resources in the cloud by executing an optimization problem. During the optimization, the model also takes account of the non-linear energy requirements of the physical resources based on their utilization levels to find a placement with the lowest energy cost, thus, providing an energy-aware solution to the resource allocation problem. The associated optimization problem is formally defined and formulated using integer programming. Since the optimization problem is intractable, four heuristic methods are also proposed. To evaluate the performance of the model and the proposed heuristic methods, several experiments are conducted on a comprehensive test suite. The results demonstrate the benefits of the proposed model, and the high-quality solutions provided by the proposed methods.

What are the US Spectrum Auctions for 5G Teaching Us About Auction Efficiency?

This paper seeks to assess the efficiency of the first 5G spectrum auctions held in the United States. In 2018 and 2019, the Federal Communications Commission (FCC) administered auctions 101 and 102 to assign spectrum in the 28 GHz and 24 GHz bands, respectively. Auction 101 sold spectrum on the 28 GHz band for Upper Microwave Flexible Use Service licenses and raised a total of about $700 million. Auction 102 assigned spectrum on the 24 GHz band for Upper Microwave Flexible Use Services. It raised a total of close to $2 billion. In July 2020, the FCC auctioned the 3.5 GHz band for Priority Access Licensees, raising over $4 billion. I implement an assessment of the efficiency of an auction based on its observed bidding data during the clock rounds of the auctions, while relying on revealed preference theory. Data are available at the FCC’s Auctions website. Bidding data are organised by geographical area and for each geographical area, demand point sets for each round, for each bidder. I rely on the application of the well-known Generalised Axiom of Revealed Preference or GARP, and less well-known Homothetic Axiom of Revealed Preference or HARP, to construct two indexes, Afriat Efficiency Index (AEI) and Homothetic Efficiency Index (HEI) to calculate measurements of rational bidding associated with each bidder. The US relied on an auction format, which uses demand revelation but allows the bidders to state the price at which they would demand a number of units of the same item (that is, blocks or licenses). In essence, the auction format for auctions 102 and 105 followed a multiple round format with an ascending clock not entirely driven by the auctioneer, whereby a bid is best described as a stepwise (ascending or descending) demand function revealed on the price range set by the auctioneer for the round. The difficulty in dealing with the data is that the bidding language of these auctions allows a bidder to express its demand for the items being sold in a service area by means of a stepwise function (either ascending or descending). The challenge at this stage is to suitably adapt the data to the usual data set format assumed by GARP or HARP. Using an efficiency approach, I assess each auction at two levels: assessment of efficiency through utility maximisation via AEI and an assessment of efficiency through homotheticity via HEI. Auctioneers, in particular, and spectrum authorities, in general, are concerned with the economic aspects of their spectrum assignment processes. The most important issue that pertains the results of the auction is the answer to the question, was the spectrum assigned to those bidders who can make the best use of it? Answering the question puts us on the grounds of auction efficiency. Devising methods to use the auction bidding data to answer such question has been a long-standing question. GARP and HARP are two revealed preference approaches that do not require us to adopt a parametrized utility function to represent bidder’s preferences. Those methods use the observed data and define a rigorous consistency test on the data.

Optimal pricing in iterative flexible combinatorial procurement auctions

Abstract In a combinatorial procurement auction with large demand volumes, bidders can find it challenging to carefully combine, evaluate and price different units of items in a package while at the same time considering their internal capacity and production costs. As opposed to static combinatorial procurement auctions, flexible procurement combinatorial auctions provide the bidders with the ability to reveal their price functions and therefore more efficiently communicate numerous variations of pricing for multiple units of items via concise bids. In this paper we propose a fully expressive bidding language for flexible combinatorial auctions. We define its associated winner determination problem, show that it is NP-hard and propose a Lagrangian-based approach to solve it. Optimal Lagrangian multipliers are used as proxies for auction item prices. The multipliers are also used in formulating the suppliers’ profit maximization problem to find their optimal bid quantities and prices while taking into account various levels of suppliers’ risk-taking attitudes. We analytically show the convergence of the iterative flexible auction. Our numerical experiments show that on average flexible iterative auctions generate lower market prices, require less computational effort and converge faster than their static counterpart. At termination, while the auctioneer secures lower procurement costs in a flexible auction, the total winning-suppliers’ profit slightly reduces due to price reduction in the auction.

How to Bid Effectively in Multi-Unit Multi-Item Combinatorial Auctions

When a bid is placed on a package in a combinatorial auction (CA), the bid value must be large enough to ensure that the package remains in contention for inclusion in winning combinations in future. The Deadness Level (DL) of a package can serve as an ask price on a fresh bid that can be meaningfully placed on it. Package DL values in single-unit CAs are readily determined. In recent years, however, interest in multi-unit CAs has grown rapidly. The number of packages can be very large in this case, and bidders need greater guidance in estimating valuations. But the DL value of a package tends to creep upwards unsteadily as more bids are placed, and no closed form expression or computational method has been found for it as yet. Here we present for the first time an exact method for determining package DLs in the multi-unit case, assuming that an OR bidding language is being used. A dynamic programming implementation is described that enables fast incremental computations of ask prices after each bid. Experimental runs on simulated data and live data from a recent U.K. multi-unit spectrum auction show that the memory requirement is not excessive. Thus the proposed method could help to promote bidder participation in online multi-unit eBay-like CAs in the procurement and sale of commodities.

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.

A Study of Compact Reserve Pricing Languages

Online advertising allows advertisers to implement fine-tuned targeting of users. While such precise targeting leads to more effective advertising, it introduces challenging multidimensional pricing and bidding problems for publishers and advertisers. In this context, advertisers and publishers need to deal with an exponential number of possibilities. As a result, designing efficient and compact multidimensional bidding and pricing systems and algorithms are practically important for online advertisement. Compact bidding languages have already been studied in the context of multiplicative bidding. In this paper, we study the compact pricing problem.

Coordination of Inventions and Innovations Through Patent Markets with Prices

This article examines the coordination of inventor, trader, and innovator decisions through a market in contracts on patents with prices, focusing on the willingness to search (WTS) for new and uncertain patentable technology, using a controlled laboratory experiment. Typically an implicit hierarchical approach, i.e., coordinating inventor and innovator decisions in a single firm, is assumed or used in analyzing these relationships, in particular in Arrow (1962) where allocation of resources for invention is discussed under neoclassical conditions of perfect information and competitive commodity (not technology) markets. Schumpeter also assumes a hierarchy as coordinating mechanism, as entrepreneurial firms disrupt incumbents (1934) or intrapreneurs create disruptive product and service innovations within firms ( 1942) treating technology as an exogenous force. In this analysis, coordination takes place between specialized agents through a design market based on the principles and practices of real world patent systems. WTS is compared between three institutional designs with different demand side bidding language, in environments with “weak” and “strong” patents in a 3 × 2 design. Technology “tastes” is here a learning process through prices (“price signals”) and can be altered (discovered) by the inventor agent within a searchable area. The results indicate that WTS appears more sensitive to mechanisms (institutional design) than patent validity (environment) in this dynamic economic system. This main finding thus suggests that policy efforts ought to be placed on institutional mechanisms together with environment such as enforcement, where the mechanisms with richer demand-side bidding language appear to matter more than enforcement in explaining WTS, i.e., risk taking. Regarding economic performance, patent validity was (naturally) of major importance, but (surprisingly) no significant effect of institutions (at least long run). These results may provide elements to expand economic theory of the patent system when it comes to treatment of risk.

Joint Resource Bidding and Tipping Strategies in Multi-Hop Cognitive Networks

In multi-hop secondary networks, bidding strategies for spectrum auction, route selection and relaying incentives should be jointly considered to establish multi-hop communication. In this paper, a framework for joint resource bidding and tipping is developed where users iteratively revise their strategies, which include bidding and incentivizing relays, to achieve their Quality of Service (QoS) requirements. A bidding language is designed to generalize secondary users' heterogeneous demands for multiple resources and willingness to pay. Then, group partitioning-based auction mechanisms are presented to exploit the heterogeneity of SU demands in multi-hop secondary networks. These mechanisms include primary operator (PO) strategies based on static and dynamic partition schemes combined with new payment mechanisms to obtain high revenue and fairly allocate the resources. The proposed auction schemes stimulate the participation of SUs and provide high revenue for the PO while maximizing the social welfare. Besides, they satisfy the properties of truthfulness, individual rationality and computational tractability. Simulation results have shown that for highly demanding users the static group scheme achieves 150% more winners and 3 times higher revenue for the PO compared to a scheme without grouping. For lowly demanding users, the PO may keep similar revenue with the dynamic scheme by lowering 50% the price per channel as the number of winners will increase proportionally.

A Framework for Truthful Online Auctions in Cloud Computing with Heterogeneous User Demands

Auction-style pricing policies can effectively reflect the underlying trends in demand and supply for the cloud resources, and thereby attracted a research interest recently. In particular, a desirable cloud auction design should be (1) online to timely reflect the fluctuation of supply-demand relations, (2) expressive to support the heterogeneous user demands, and (3) truthful to discourage users from cheating behaviors. Meeting these requirements simultaneously is non-trivial, and most existing auction mechanism designs do not directly apply. To meet these goals, this paper conducts the first work on a framework for truthful online cloud auctions where users with heterogeneous demands could come and leave on the fly. Concretely speaking, we first design a novel bidding language, wherein users’ heterogeneous requirement on their desired allocation time, application type, and even how they value among different possible allocations can be flexibly and concisely expressed. Besides, building on top of our bidding language we propose COCA, an incentive-Compatible (truthful) Online Cloud Auction mechanism. To ensure truthfulness with heterogenous and online user demand, the design of COCA is driven by a monotonic payment rule and a utility-maximizing allocation rule. Moreover, our theoretical analysis shows that the worst-case performance of COCA can be well-bounded, and our further discussion shows that COCA performs well when some other important factors in online auction design are taken into consideration. Finally, in simulations the performance of COCA is seen to be comparable to the well-known off-line Vickrey-Clarke-Groves (VCG) mechanism [19] .

Compact Bid Languages and Core Pricing in Large Multi-item Auctions

We introduce an auction design framework for large markets with hundreds of items and complex bidder preferences. Such markets typically lead to computationally hard allocation problems. Our new framework consists of compact bid languages for sealed-bid auctions and methods to compute second-price rules such as the Vickrey–Clarke–Groves or bidder-optimal, core-selecting payment rules when the optimality of the allocation problem cannot be guaranteed. To demonstrate the efficacy of the approach for a specific, complex market, we introduce a compact bidding language for TV advertising markets and investigate the resulting winner-determination problem and the computation of core payments. For realistic instances of the respective winner-determination problems, very good solutions with a small integrality gap can be found quickly, although closing the integrality gap to find marginally better solutions or prove optimality can take a prohibitively large amount of time. Our subsequent adaptation of a constraint-generation technique for the computation of bidder-optimal core payments to this environment is a practically viable paradigm by which core-selecting auction designs can be applied to large markets with potentially hundreds of items. Such auction designs allow bidders to express their preferences with a low number of parameters, while at the same time providing incentives for truthful bidding. We complement our computational experiments in the context of TV advertising markets with additional results for volume discount auctions in procurement to illustrate the applicability of the approach in different types of large markets. Data, as supplemental material, are available at http://dx.doi.org/10.1287/mnsc.2014.2076 . This paper was accepted by Lorin Hitt, information systems.

Sponsored Search Auctions

Sponsored search has been proven to be a successful business model, and sponsored search auctions have become a hot research direction. There have been many exciting advances in this field, especially in recent years, while at the same time, there are also many open problems waiting for us to resolve. In this article, we provide a comprehensive review of sponsored search auctions in hopes of helping both industry practitioners and academic researchers to become familiar with this field, to know the state of the art, and to identify future research topics. Specifically, we organize the article into two parts. In the first part, we review research works on sponsored search auctions with basic settings, where fully rational advertisers without budget constraints, preknown click-through rates (CTRs) without interdependence, and exact match between queries and keywords are assumed. Under these assumptions, we first introduce the generalized second price (GSP) auction, which is the most popularly used auction mechanism in the industry. Then we give the definitions of several well-studied equilibria and review the latest results on GSP’s efficiency and revenue in these equilibria. In the second part, we introduce some advanced topics on sponsored search auctions. In these advanced topics, one or more assumptions made in the basic settings are relaxed. For example, the CTR of an ad could be unknown and dependent on other ads; keywords could be broadly matched to queries before auctions are executed; and advertisers are not necessarily fully rational, could have budget constraints, and may prefer rich bidding languages. Given that the research on these advanced topics is still immature, in each section of the second part, we provide our opinions on how to make further advances, in addition to describing what has been done by researchers in the corresponding direction.

Combinatorial auctions of railway track capacity in vertically separated freight transport markets

This paper addresses the problem of allocating residual track capacity among multiple competing carriers where infrastructure ownership and train operations are vertically separated to facilitate delivery by train. Two bid set construction techniques are proposed that allow carriers to fully express their preferences for track usage. Both techniques enable the expression of complementary or substitutable relationships among the train slots constructed along predetermined train routes and permit quick configuration of routes from residual track capacity along which new trains can be operated. A winner determination problem that simultaneously accommodates bidding languages of both bid set construction techniques is used to generate an optimal capacity allocation among bidders based on different bidding strategies. Results of computational experiments designed to illustrate the efficiency of the proposed bid construction technique and effectiveness of the framework are presented.

Ascending Combinatorial Auctions with Allocation Constraints: On Game Theoretical and Computational Properties of Generic Pricing Rules

Combinatorial auctions are used in a variety of application domains, such as transportation or industrial procurement, using a variety of bidding languages and different allocation constraints. This flexibility in the bidding languages and the allocation constraints is essential in these domains but has not been considered in the theoretical literature so far. In this paper, we analyze different pricing rules for ascending combinatorial auctions that allow for such flexibility: winning levels and deadness levels. We determine the computational complexity of these pricing rules and show that deadness levels actually satisfy an ex post equilibrium, whereas winning levels do not allow for a strong game theoretical solution concept. We investigate the relationship of deadness levels and the simple price update rules used in efficient ascending combinatorial auction formats. We show that ascending combinatorial auctions with deadness level pricing rules maintain a strong game theoretical solution concept and reduce the number of bids and rounds required at the expense of higher computational effort. The calculation of exact deadness levels is a [Formula: see text]-complete problem. Nevertheless, numerical experiments show that for mid-sized auctions this is a feasible approach. The paper provides a foundation for allocation constraints in combinatorial auctions and a theoretical framework for recent Information Systems contributions in this field.