Combinatorial Auctions Research Articles

A hybrid binary harmony search algorithm for solving the winner determination problem

The winner determination problem (WDP) in combinatorial auctions is to determine an allocation of items to bidders such that each item is allocated to at most one bidder, and the auctioneer's revenue is maximised. This paper proposes a hybrid binary harmony search algorithm for the WDP. Firstly, to enhance the global search ability of the proposed algorithm, a modified harmony improvisation mechanism is developed with a modified memory consideration rule and an adaptive pitch adjustment scheme. Next, a repair operator is employed to guarantee the feasibility of the new candidate harmonies. Finally, a tabu search procedure is presented to improve the local search ability. These strategies make a good balance between intensification and diversification. In the experiments, the performance of the proposed algorithm is validated on five groups of 500 instances. Experimental results and comparisons show that the proposed algorithm is very efficient, and the tabu search procedure significantly improves the performance of the proposed algorithm.

Demand relaxation in supplier selection processes

Abstract Supplier selection processes generally evaluate several criteria in order to fulfill a demand. But, what if the demand itself could be rethought, spreading the possibilities of acquisition? What are the impacts in cost and utility of buying objectives instead of pre-determined materials? This work tries to expand this discussion with a mathematical programming approach to selecting suppliers with demand relaxation. The requirements for the framework development and application in purchasing departments are also pointed out. Its adoption in association with combinatorial auctions concepts in a hypothetical but realistic context suggests a high potential to cost reduction with no significant utility decrease.

Delay-Optimal Joint Processing in Computation-Constrained Fog Radio Access Networks

With fog radio access networks (F-RANs), the computation capability is provided in the physical proximity of the users, which can significantly lower the delay and mitigate the heavy traffic over backhaul links. As the number of remote radio head (RRH) increases, the computational complexity becomes a severe issue and it is necessary to group the RRHs into multiple clusters. In this paper, we optimize the joint processing strategy, including the RRH clustering and the RRH-server matching to minimize the delay for F-RANs. We model the delay-optimal joint processing problem in computation-constrained F-RANs as a Markov decision process (MDP) problem. By deriving the optimality condition of this MDP, we obtain a per-slot weighted sum rate maximization problem, in which the RRH clustering and the RRH-server matching are solved jointly. Specifically, we transform the weighted sum rate maximization problem into a combinatorial auction problem (CAP). Since the CAP is NP-hard, we greedily obtain an initial solution of CAP and gradually improve the performance by adopting local α-good improvement algorithm based on the weighted independent set problem (WISP). Furthermore, we theoretically derive the bound of the performance of the proposed algorithm.

The Potential of Flexible Reservations in a Car Sharing System With an Auction Scheme

In the last 20 years car sharing has been a growing trend in personal mobility. Multiple aspects of these systems have been already discussed: different forms of car sharing, user's preferences and behavior, or benefits estimation. Nevertheless, the management of these systems needs to be continuously improved to remain a competitive alternative. In this work, we propose a reservation scheme to manage rental reservations of a two-way station-based car sharing system. It allows the operator to better plan the necessary vehicles at each station, and encourages the drivers to make better use of the existing vehicles, by showing flexibility in the starting rental time. The reservation scheme is organized with an auction, where drivers bet for their preferred rental start time. Drivers participating in the auction are offered a reduced rental fare, which is then complemented with the reservation fee that results from the auction. The auction is solved under Vickrey-Clarke-Groves (VCG) mechanism for combinatorial auctions, which guarantees the desired properties for the operator and a fair assignment for the drivers. The proposed scheme is tested on instances inspired by the Mobility car sharing system in Zurich, Switzerland. The results show that operators could decrease their fleets with low to no impacts on the overall rental revenues, especially when drivers show flexibility in their rental start times. For certain levels of demand price elasticity, even positive impacts on the overall rental revenues can be expected. Moreover, reservation fees are proven to partially compensate for the decrease in rental revenues provided to the auction users.

Trust-based quality awareness using combinatorial auction web service selection in service-based systems

With the immense growth and development of the computing exemplar in service-based systems (SBS), the establishment of the engineering architectures has taken new standards. The computation of trus...

Geometry of gross substitutes valuations

We consider the set of gross substitutes valuations which is one of the most important classes of valuation functions in combinatorial auctions. This is due the fact that the existence of a Walrasian equilibrium is guaranteed if all bidders have gross substitutes valuations. We interpret normalized valuation functions v:2N→R with v(0̸)=0 on N≔{1,…,n} as points of R2n−1. The set of gross substitutes valuations turns out to be the union of finitely many polyhedral cones. It has been proved that the set of gross substitutes valuations has Lebesgue-measure zero in R2n−1, but the question whether the dimension of each of these cones is polynomial in the number of items n is open. We answer this question negatively by showing that the dimension of each cone is actually exponential in n and provide a lower bound of ⌈1n+1⋅(2n−n−2)⌉+2n−1 for their dimension. By explicit calculation we verify that our lower bound matches the dimension in the case of n≤3, but becomes loose for larger n.

A bi-level programming for transportation services procurement based on combinatorial auction with fuzzy random parameters

Purpose The purpose of this paper is to study a transportation service procurement bid construction problem from a less than a full truckload perspective. It seeks to establish stochastic mixed integer programming to allow for the proper bundle of loads to be chosen based on price, which could improve the likelihood that carrier can earn its maximum utility. Design/methodology/approach The authors proposes a bi-level programming that integrates the bid selection and winner determination and a discrete particle swarm optimization (PSO) solution algorithm is then developed, and a numerical simulation is used to make model and algorithm analysis. Findings The algorithm comparison shows that although GA could find a little more Pareto solutions than PSO, it takes a longer time and the quality of these solutions is not dominant. The model analysis shows that compared with traditional approach, our model could promote the likelihood of winning bids and the decision effectiveness of the whole system because it considers the reaction of the shipper. Originality/value The highlights of this paper are considering the likelihood of winning the business and describing the conflicting and cooperative relationship between the carrier and the shipper by using a stochastic mixed integer programming, which has been rarely examined in previous research.

A Combinatorial Auction Mechanism for Multiple Resource Procurement in Cloud Computing

In hybrid cloud computing, cloud users have the ability to procure resources from multiple cloud vendors, and furthermore also the option of selecting different combinations of resources. The problem of procuring a single resource from one of many cloud vendors can be modeled as a standard winner determination problem, and there are mechanisms for single item resource procurement given different QoS and pricing parameters. There however is no compatible approach that would allow cloud users to procure arbitrary bundles of resources from cloud vendors. We design the CLOUD-CABOB algorithm to solve the multiple resource procurement problem in hybrid clouds. Cloud users submit their requirements, and in turn vendors submit bids containing price, QoS and their offered sets of resources. The approach is scalable, which is necessary given that there are a large number of cloud vendors, with more continually appearing. We perform experiments for procurement cost and scalability efficacy on the CLOUD-CABOB algorithm using various standard distribution benchmarks like random, uniform, decay and CATS. Simulations using our approach with prices procured from several cloud vendors' datasets show its effectiveness at multiple resource procurement.

Nash Equilibria in Combinatorial Auctions with Item Bidding and Subadditive Symmetric Valuations

Nash Equilibria in Combinatorial Auctions with Item Bidding and Subadditive Symmetric Valuations

Combinatorial auctions for energy storage sharing amongst the households

Abstract This paper presents a business model for energy storage trading in a small neighborhood. A region composed of multiple households with a common energy storage system is considered, the capacity of which is shared amongst the households. The households submit bids to an auctioneer to get storage capacity in the shared energy storage system. This paper introduces a combinatorial auction mechanism for such trades to happen. The participants are allowed to bid in single bid format or with combinations of bids called packages. It also presents a novel winner determination solution for combinatorial auctions that uses an evolutionary algorithm by combining the genetic algorithm with particle swarm optimization. Furthermore, the price determination of each trade is also explained. Using MATLAB, performance evaluation and stability tests of the proposed auction technique are performed and presented in this paper.

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.

The Generalized Random Priority Mechanism with Budgets

This paper studies allocation problems with and without monetary transfers, such as combinatorial auctions, school choice, and course allocation. Interdependent values and multidimensional signals are allowed. Despite known negative results, a mechanism exists that is feasible, ex post individually rational, ex post incentive compatible, and asymptotically both efficient and envy-free. This mechanism is a special case of the generalized random priority mechanism (GRP), which always satisfies the first three properties. The asymptotic properties follow as a corollary of the main theorem: GRP approximates virtually any infinite-market mechanism in large finite markets.

The generalized random priority mechanism with budgets

This paper studies allocation problems with and without monetary transfers, such as combinatorial auctions, school choice, and course allocation. Interdependent values and multidimensional signals are allowed. Despite known negative results, a mechanism exists that is feasible, ex post individually rational, ex post incentive compatible, and asymptotically both efficient and envy-free. This mechanism is a special case of the generalized random priority mechanism (GRP), which always satisfies the first three properties. The asymptotic properties follow as a corollary of the main theorem: GRP approximates virtually any infinite-market mechanism in large finite markets.

A Graph Based Ant Algorithm for the Winner Determination Problem in Combinatorial Auctions

Combinatorial auctions are increasingly being used to allocate bundles of items among interested bidders. However, as the number of bundles increases, it takes exponentially longer to solve for the winners in the auction. In such situations, regular solvers such as IBM CPLEX or AMPL fail to produce the optimal solution either completely due to computational limitations or in reasonable time. We propose an Ant Colony-based algorithm (TrACA) that produces optimal or near-optimal results within specified time. Experiments are performed on 90 instances to show and compare the performance of TrACA to the current state-of-the-art memetic algorithm (MA). Results indicate that in a given run-time, the median of results from TrACA statistically significantly outperforms MA results in 85% of the cases. Further, the best value from TrACA is at least as good as MA values in 100% of the cases. Additionally, to better understand the why deterministic algorithms fail or take too long for approximating winners in such auctions, we analyze empirical hardness of tested instances and use a standard supervised learning method to build a predictive model of TrACA run-times. Using the predictive model, we highlight factors that make winner determination in combinatorial auctions computationally hard to estimate and show why TrACA is better suited to handle such hard instances.

The Power of Verification for Greedy Mechanism Design


 
 
 
 Greedy algorithms are known to provide, in polynomial time, near optimal approximation guarantees for Combinatorial Auctions (CAs) with multidimensional bidders. It is known that truthful greedy-like mechanisms for CAs with multi-minded bidders do not achieve good approximation guarantees.
 In this work, we seek a deeper understanding of greedy mechanism design and investigate under which general assumptions, we can have efficient and truthful greedy mechanisms for CAs. Towards this goal, we use the framework of priority algorithms and weak and strong verification, where the bidders are not allowed to overbid on their winning set or on any subset of this set, respectively. We provide a complete characterization of the power of weak verification showing that it is sufficient and necessary for any greedy fixed priority algorithm to become truthful with the use of money or not, depending on the ordering of the bids. Moreover, we show that strong verification is sufficient and necessary to obtain a 2-approximate truthful mechanism with money, based on a known greedy algorithm, for the problem of submodular CAs in finite bidding domains. Our proof is based on an interesting structural analysis of the strongly connected components of the declaration graph.
 
 
 

The cost of incentive compatibility in auction-based mechanisms for carrier collaboration.

Collaboration has been one of the important trends in vehicle routing. A typical mechanism to enable carrier collaboration is to use combinatorial auctions, where requests are not traded individually but are combined into bundles. Previous literature on carrier collaboration has focused on issues such as bundle formation or winner determination, typically assuming truthfulness of all agents and absence of any strategic behavior. This article considers the interdependencies and problems that arise from bidders acting as buyers and sellers of requests at the same time. From standard auction theory, desirable properties of exchange mechanisms are identified as efficiency, incentive compatibility, individual rationality, and budget balance. It is shown that these desirable properties cannot be fulfilled at the same time. In particular, the properties efficiency and incentive compatibility induce that budget balance is violated, that is, an outside subsidy is required. We propose two incentive compatible exchange mechanisms. One is more closely related to the classical VCG approach, while the other one uses a more complicated concept for computing payments to participants. A numerical study investigates how frequently desired properties are violated. We show that both mechanisms can be acceptable in practical situations, but none of them can satisfy all desired properties.

Valuation Compressions in VCG-Based Combinatorial Auctions

The focus of classic mechanism design has been on truthful direct-revelation mechanisms. In the context of combinatorial auctions, the truthful direct-revelation mechanism that maximizes social welfare is the Vickrey-Clarke-Groves mechanism. For many valuation spaces, computing the allocation and payments of the VCG mechanism, however, is a computationally hard problem. We thus study the performance of the VCG mechanism when bidders are forced to choose bids from a subspace of the valuation space for which the VCG outcome can be computed efficiently. We prove improved upper bounds on the welfare loss for restrictions to additive bids and upper and lower bounds for restrictions to non-additive bids. These bounds show that increased expressiveness can give rise to additional equilibria of poorer efficiency.

Adaptive-Price Combinatorial Auctions

This work introduces a novel iterative combinatorial auction that aims to achieve both high efficiency and fast convergence across a wide range of valuation domains. We design the first fully adaptive-price combinatorial auction that gradually extends price expressivity as the rounds progress. We implement our auction design using polynomial prices and show how to detect when the current price structure is insufficient to clear the market, and how to correctly expand the polynomial structure to guarantee progress. An experimental evaluation confirms that our auction is competitive with bundle-price auctions in regimes where these excel, namely multi-minded valuations, but also performs well in regimes favorable to linear prices, such as valuations with pairwise synergy.

Combinatorial auctions: theory, experiments, and practice

This doctoral dissertation contributes to theory, experiments, and practice in combinatorial auctions. Combinatorial auctions are multi-object auctions, that enable bidders to bid on packages of items. In Chapter 2, we theoretically investigate the classical winner determination problem in geometrical settings. Specifically, we consider combinatorial auctions of items that can be arranged in rows, and the objective is, given bids on subsets of items, to find a subset of bids that maximizes auction revenue. Possible practical applications include allocating pieces of land for real estate development, or seats in a theater or stadium. We investigate several geometrical structures and bid shapes, and provide either a polynomial dynamic programming algorithm or an NP-hardness proof, filling in several gaps in academic literature. In Chapter 3, we combine theory with experiments, investigating coordination and threshold problems in combinatorial auctions. Bidders on small packages of items are unable to outbid provisionally winning bids on large packages alone; despite free-rider incentives, both coordination and cooperation are required. Coordination because smaller bidders need to bid on disjoint packages, and cooperation because more than one bidder is required to outbid a larger package bid. We propose indices quantifying both the coordination and the threshold problem, that can be used in providing feedback or generating valuations for laboratory experiments. Additionally, we develop coalitional feedback that is specifically aimed at helping bidders to overcome coordination and threshold problems. We test this in an experimental setting using human bidders, varying feedback from provisionally winning bids and prices, to winning and deadness levels, and coalitional feedback. We find that in situations where threshold problems are severe, coalitional feedback increases economic efficiency, but in easy or insurmountable threshold problems that is not always the case. Finally, in Chapter 4, we combine theory with practice. Scheduling a conference, based on preferences expressed by conference participants, can be seen as a combinatorial auction with public goods. In a situation with public goods, the utility of the final selected goods (presentations scheduled in parallel) are consumed by all bidders (conference participants). Constructing a good conference schedule is important: they are an essential part of academic research and require significant investments (e.g. time and money) from their participants. We provide computational complexity results, along with a combined approach of assigning talks to rooms and time slots, grouping talks into sessions, and deciding on an optimal itinerary for each participant. Our goal is to maximize attendance, considering the common practice of session hopping. On a secondary level, we accommodate presenters’ availabilities. This personalized conference scheduling approach has been applied to construct the schedule of the MathSport (2013), MAPSP (2015 and 2017) and ORBEL (2017) conferences.

Pareto optimal budgeted combinatorial auctions

This paper studies the possibility of implementing Pareto optimal outcomes in the combinatorial auction setting where bidders may have budget constraints. I show that when the setting involves a single good, or multiple goods but with single-minded bidders, there is a unique mechanism, called truncation VCG, that is individually rational, incentive compatible and Pareto optimal. Truncation VCG works by first truncating valuations at budgets, and then implementing standard VCG on the truncated valuations. I also provide maximal domain results, characterizing when it is possible to implement Pareto optimal outcomes and, if so, providing an implementing mechanism. Whenever there is at least one multi-minded constrained bidder and another multi-minded bidder, implementation is impossible. For any other domain, however, implementation is possible.