Winner Determination Research Articles

Constraint-guided evolutionary algorithm for solving the winner determination problem

Constraint-guided evolutionary algorithm for solving the winner determination problem

The Price of Neutrality for the Ranked Pairs Method

The complexity of the winner determination problem has been studied for almost all common voting rules. A notable exception, possibly caused by some confusion regarding its exact definition, is the method of ranked pairs. The original version of the method, due to Tideman, yields a social preference function that is irresolute and neutral. A variant introduced subsequently uses an exogenously given tie-breaking rule and therefore fails neutrality. The latter variant is the one most commonly studied in the area of computational social choice, and it is easy to see that its winner determination problem is computationally tractable. We show that by contrast, computing the set of winners selected by Tideman's original ranked pairs method is NP-complete, thus revealing a trade-off between tractability and neutrality. In addition, several known results concerning the hardness of manipulation and the complexity of computing possible and necessary winners are shown to follow as corollaries from our findings.

Sustainable–responsive winner determination for transportation service procurement auctions under accidental disruptions

This paper investigates a new winner determination problem with sustainable and responsive concerns under disruption risks for transportation service procurement auctions. In such an auction, a fourth party logistics (4PL) provider purchases transportation services from multiple third party logistics (3PL) providers. We develop a two-stage stochastic mixed-integer programming model that incorporates two features, including (i) a sustainable–responsive constraint to quantitatively describe the sustainability and responsiveness performance, and (ii) an effective hybrid mitigation strategy that combines the fortification policy with the temporary outsourcing service policy to mitigate disruptions. To determine winning 3PLs, a reduced scenario-based approximation approach is developed to solve the model and obtain a nearly optimal solution very quickly. Numerical experiments are conducted to illustrate the effectiveness and applicability of our model and method by using randomly generated instances as well as real data of a Chinese 4PL firm. Compared with existing studies, sensitivity analysis indicates that our proposed model can significantly reduce the 4PL’s expected cost and improve the long-term competitive advantages. Managerial implications are also drawn for 4PLs to run a sustainable–responsive logistics system under disruptions in a cost-effective way.

Winner determination for logistics service procurement auctions under disruption risks and quantity discounts

Disruption risks and quantity discounts have not been explicitly studied in traditional winner determination problems. This paper investigates an innovative winner determination problem with accidental disruptions and quantity discounts for a fourth party logistics provider in a logistics service procurement auction. An effective hybrid strategy that integrates a fortification policy with an outside option policy is developed to mitigate possible disruptions. Integrating the hybrid strategy with a piecewise-linear discount function, a stochastic nonlinear winner determination model is constructed. Utilizing a linearization technique, such a nonlinear winner determination model can be reformulated as a mixed integer linear program. To obtain nearly optimal solutions, a scenario-based approximation method is developed, including a reduced scenario technique and a dual decomposition Lagrangian relaxation technique. Numerical experiments are conducted to illustrate the effectiveness and applicability of the proposed model and method. When the discount parameter decreases or the disruption probability increases, the fortification policy becomes more important for the logistics system. An interesting result indicates that both the auctioneer and bidders may benefit from considering the discount policy. Managerial implications are drawn for fourth party logistics providers to run a reliable logistics system in a cost-effective way.

A Social Network-Based Examination on Bid Riggers’ Relationships in the Construction Industry: A Case Study of China

Collusive bidding has been an insidious issue in the construction industry. Bidders initiate collusive networks of various sizes to win market shares. The popularity of collusive bidding networks affects market fairness and erodes the interests of market players. Although considerable research efforts were made to diagnose collusive bidding networks, there remains a gap in knowledge regarding the relationships bid riggers use to engage in the networks. Therefore, this study used the social network method, where two hundred sixteen collusion cases were collected from China to test these relationships. The results show that collusive bidding networks were characterized by sparseness, a small scale, a high concentration, and strong randomness. Three types of collusive bidding networks were also detected: contractual, spontaneous, and shadow. Furthermore, these collusive bidding networks had discrepancies regarding participants’ identities, forms of collusive bids, and the determination of bid winners. It was found that the proposed social network model of deliberating bid riggers’ relationships lays a solid foundation for the detection of collusive bidding in the construction sector.

Iterative Multi-Attribute Procurement Auction with Decision Support for Bid Formulation

Iterative multi-attribute reverse auctions in practice create certain difficulties for both the buyer and participating bidders. While the buyer faces the problem of creating the right attribute weights, the bidders have difficulty in adjusting the attribute values in each round. In this paper, we present an iterative multi-attribute reverse auction mechanism based on integrated data envelopment analysis (DEA) and best–worst method (BWM) with an objective of reducing the intervention of the buyer in the determination of the winner and also easing up the preference elicitation process. Unlike the typical scoring auctions, the proposed mechanism does not require the buyer to estimate the characteristics of the participating sellers in order to determine the optimal scoring function. As there will be no other intervention from the buyer during the winner determination process, the proposed method makes the procurement process impartial and corruption-free. Besides solving the buyer’s problem, the proposed mechanism is also associated with an optimal bid determination method (OBDM) to assist the sellers in formulating improvised bids in iterative rounds of the auction. Simulation experiments show that the proposed OBDM benefits both the buyer and sellers. For the buyer, it provides higher expected utility and attribute values as per his preferences; for the seller, it gives a better expected profit and a higher probability of winning.

An optimization approach for winner determination problem considering transportation cost discounts

An optimization approach for winner determination problem considering transportation cost discounts

The Smoothed Complexity of Computing Kemeny and Slater Rankings

The computational complexity of winner determination under common voting rules is a classical and fundamental topic in the field of computational social choice. Previous work has established the NP-hardness of winner determination under some commonly-studied voting rules, such as the Kemeny rule and the Slater rule. In a recent position paper, Baumeister, Hogrebe, and Rothe (2020) questioned the relevance of the worst-case nature of NP-hardness in social choice and proposed to conduct smoothed complexity analysis (Spielman and Teng 2009) under Blaser and Manthey’s (2015) framework. In this paper, we develop the first smoothed complexity results for winner determination in voting. We prove the smoothed hardness of Kemeny and Slater using the classical smoothed runtime analysis, and prove a parameterized typical-case smoothed easiness result for Kemeny. We also make an attempt of applying Blaser and Manthey’s (2015) smoothed complexity framework in social choice contexts by proving that the framework categorizes an always-exponential-time brute force search algorithm as being smoothed poly-time, under a natural noise model based on the well-studied Mallows model in social choice and statistics. Overall, our results show that smoothed complexity analysis in computational social choice is a challenging and fruitful topic.

Solving the winner determination problem for online B2B transportation matching platforms

We consider the problem of matching multiple shippers and transporters participating in an online B2B last-mile logistics platform in an emerging market. Each shipper places a bid that is made up of multiple jobs, where each job comprises key information like the weight, volume, pickup and delivery locations, and time windows. Each transporter specifies its vehicle capacity, available time periods, and a cost structure. We formulate the mathematical model and provide a Branch-and-Cut approach to solve small-scale problem instances exactly and larger scale instances heuristically using an Adaptive Large Neighbourhood Search approach. To increase the win percentage of both shippers and transporters, we propose an extension of the single round auction to a second-round for failed bids. Using our models and the results obtained, we present interesting managerial insights that are helpful to platform participants. For example, due to the cost structure, there is little impact on profitability with time varying speeds, but time windows play a significant role in the profitability of the system. And there are tangible benefits that all platform participants (shippers, transporters and operator) can gain by extending single-round auction to two rounds.

Using combinatorial auctions for the procurement of occasional drivers in the freight transportation: A case-study

The logistics companies should continuously invent novel solutions to oppose fierce competition. Introducing occasional drivers in the context of freight transportation can represent a valuable option. This paper is concerned with reinforcing the distribution capability of a real-life company by using the novel paradigm of crowdshipping, besides employing its fleet of vehicles. Crowdshipping consists involving occasional drivers, which are to be selected from the public through the use of the combinatorial auction paradigm. We propose a mathematical model that integrates the decisions related to the vehicle routing with the winner determination problem for the occasional drivers’ selection. The objective is to minimize the overall transportation cost of using the company’s available fleet plus the cost of employing external drivers. We also propose two heuristic methods to solve real-life distribution instances; one is based on the decomposition method and the other on a cost-comparison greedy approach. The validity of the model, as well as the heuristic methods, has been verified by solving a real case study related to an online bookstore with door-to-door delivery in Oman. Our computational results show savings that reach 30% with respect to the solution implemented by the company.

Incentive Based Load Shedding Management in a Microgrid Using Combinatorial Auction with IoT Infrastructure.

This paper presents a novel incentive-based load shedding management scheme within a microgrid environment equipped with the required IoT infrastructure. The proposed mechanism works on the principles of reverse combinatorial auction. We consider a region of multiple consumers who are willing to curtail their load in the peak hours in order to gain some incentives later. Using the properties of combinatorial auctions, the participants can bid in packages or combinations in order to maximize their and overall social welfare of the system. The winner determination problem of the proposed combinatorial auction, determined using particle swarm optimization algorithm and hybrid genetic algorithm, is also presented in this paper. The performance evaluation and stability test of the proposed scheme are simulated using MATLAB and presented in this paper. The results indicate that combinatorial auctions are an excellent choice for load shedding management where a maximum of 50 users participate.

Predicting winner and estimating margin of victory in elections using sampling

Predicting the winner of an election and estimating the margin of victory of that election are favorite problems both for news media pundits and computational social choice theorists. Since it is often infeasible to elicit the preferences of all the voters in a typical prediction scenario, a common algorithm used for predicting the winner and estimating the margin of victory is to run the election on a small sample of randomly chosen votes and predict accordingly. We analyze the performance of this algorithm for many commonly used voting rules.More formally, for predicting the winner of an election, we introduce the (ε,δ)-Winner Determination problem, where given an election E on n voters and m candidates in which the margin of victory is at least εn votes, the goal is to determine the winner with probability at least 1−δ where ε and δ are parameters with 0<ε,δ<1. The margin of victory of an election is the smallest number of votes that need to be modified in order to change the election winner. We show interesting lower and upper bounds on the number of samples needed to solve the (ε,δ)-Winner Determination problem for many common voting rules, including all scoring rules, approval, maximin, Copeland, Bucklin, plurality with runoff, and single transferable vote. Moreover, the lower and upper bounds match for many common voting rules up to constant factors.For estimating the margin of victory of an election, we introduce the (c,ε,δ)–Margin of Victory problem, where given an election E on n voters, the goal is to estimate the margin of victory M(E) of E within an additive error of cM(E)+εn with probability of error at most δ where ε,δ, and c are the parameters with 0<ε,δ<1 and c>0. We exhibit interesting bounds on the sample complexity of the (c,ε,δ)–Margin of Victory problem for many commonly used voting rules including all scoring rules, approval, Bucklin, maximin, and Copelandα. We observe that even for the voting rules for which computing the margin of victory is NP-hard, there may exist efficient sampling based algorithms for estimating the margin of victory, as observed in the cases of maximin and Copelandα voting rules.

A Double Auction Framework for Multi-Channel Multi-Winner Heterogeneous Spectrum Allocation in Cognitive Radio Networks

Opportunistic availability of licensed frequency bands enables the secondary users (SUs) to avail the radio spectrum dynamically. Cognitive radio (CR) paradigm extends the dynamic spectrum access techniques to sense for free channels (called spectrum holes) which can be efficiently redistributed amongst SUs. Motivated by the adaptive technology in CR, this paper introduces a sealed-bid double auction mechanism which aims to obtain an effective allocation of the unused radio spectrum. The proposed auction model adopts multi-channel allocation where one SU can access more than one available channel, while imposing the constraints for dynamics in spectrum opportunities and varying channel availability time amongst SUs. Previously designed double auctions miss out the CR constraints which can further degrade the network performance. Also, multi-winner allocation is induced in the model which encourages spectrum reuse by allowing a common channel to be assigned to multiple non-interfering SUs. A preference list of channels is maintained at each SU using which SUs offer their bid values for the heterogeneous channels which the primary owners are competing to lease. To organize channel specific groups of non-interfering SUs, a bidder group formation algorithm is developed such that members of a winner group get access to a common channel. The auctioneer formulates a winner determination strategy and a pricing strategy which achieves truthfulness while assigning the idle spectrum. Effectiveness of the proposed model is studied by comparing it with an existing work which shows that channel allocation gets significantly improved on deploying the proposed model.

A Comprehensive Survey on Auction Mechanism Design for Cloud/Edge Resource Management and Pricing

Driven by the vision of cloud and edge computing as the 5th utility, a major challenge is the efficient resource management and pricing taking into account incentives and preferences of cloud/edge providers, users, and the system. In recent years, auction mechanism design has gained wide attention as a tool for addressing this challenge. Here existing surveys lack detailed studies in this area, hence this work presents a comprehensive survey on the state-of-the-art auction-based mechanisms in the field of cloud/edge computing. First, the problem statements and background are presented for cloud/edge computing and auction theory. This is followed by a collaboration model on the benefits of auction mechanism designs to cloud/edge computing. Next, various auction mechanisms in cloud computing are reviewed based upon the following aspects: (1) direction of bids—forward, reverse, and two-sided auctions, (2) the heterogeneity of resources—combinatorial auctions, (3) the number and types of adopted attributes in winner determination—multi-attribute auctions, (4) the setting of auction—offline, online, or sequential auctions, and (5) the interoperability among cloud providers—inter-clouds. For each aspect, existing studies are summarized along with their saliencies and drawbacks. Moreover, existing auction mechanisms in the context of edge computing are also presented. Our comprehensive survey shows that although significant progress has been achieved in this field, there still exist key challenges that need to be investigated, as discussed here to provide future research directions.

A Fast Graph Neural Network-Based Method for Winner Determination in Multi-Unit Combinatorial Auctions

The combinatorial auction (CA) is an efficient mechanism for resource allocation in different fields, including cloud computing. It can obtain high economic efficiency and user flexibility by allowing bidders to submit bids for combinations of different items instead of only for individual items. However, the problem of allocating items among the bidders to maximize the auctioneers’ revenue, i.e., the winner determination problem (WDP), is NP-complete to solve and inapproximable. Existing works for WDPs are generally based on mathematical optimization techniques and most of them focus on the single-unit WDP, where each item only has one unit. On the contrary, few works consider the multi-unit WDP in which each item may have multiple units. Given that the multi-unit WDP is more complicated but prevalent in cloud computing, we propose leveraging machine learning (ML) techniques to develop a novel low-complexity algorithm for solving this problem with negligible revenue loss. Specifically, we model the multi-unit WDP as an augmented bipartite bid-item graph and use a graph neural network (GNN) with half-convolution operations to learn the probability of each bid belonging to the optimal allocation. To improve the sample generation efficiency and decrease the number of needed labeled instances, we propose two different sample generation processes. We also develop two novel graph-based post-processing algorithms to transform the outputs of the GNN into feasible solutions. Through simulations on both synthetic instances and a specific virtual machine (VM) allocation problem in a cloud computing platform, we validate that our proposed method can approach optimal performance with low complexity and has good generalization ability in terms of problem size and user-type distribution.

A Tabu Search Method for the Multi-objective Winner Determination Problem of Combinatorial Auctions

We are interested by the problem of combinatorial auctions in which multiple items are sold and bidders submit bids on packages. First, we present a multi-objective formulation for a combinatorial auctions problem extending the existing single-objective models. Indeed, the bids may concern several specifications of the item, involving not only its price, but also its quality, delivery conditions, delivery deadlines, the risk of not being paid after a bid has been accepted and so on. The seller expresses his preferences upon the suggested items and the buyers are in competition with all the specified attributes done by the seller. Second, we develop and implement a metaheuristic algorithm based on a tabu search method.

An Exact Method for the Multi-objective Winner Determination Problem of Combinatorial Auctions

We are interested by the problem of combinatorial auctions in which multiple items are sold and bidders submit bids on packages. First, we present a multi-objective formulation for a combinatorial auctions problem extending the existing single-objective models. Indeed, the bids may concern several specifications of the item, involving not only its price, but also its quality, delivery conditions, delivery deadlines, the risk of not being paid after a bid has been accepted and so on. The seller expresses his preferences upon the suggested items and the buyers are in competition with all the specified attributes done by the seller. Second, we develop and implement an exact algorithm based on a multi-objective branch-and-bound method.

Walrasian equilibria from an optimization perspective: A guide to the literature

AbstractAn ideal market mechanism allocates resources efficiently such that welfare is maximized and sets prices in a way so that the outcome is in a competitive equilibrium and no participant wants to deviate. An important part of the literature discusses Walrasian equilibria and conditions for their existence. We use duality theory to investigate existence of Walrasian equilibria and optimization algorithms to describe auction designs for different market environments in a consistent mathematical framework that allows us to classify the key contributions in the literature and open problems. We focus on auctions with indivisible goods and prove that the relaxed dual winner determination problem is equivalent to the minimization of the Lyapunov function. This allows us to describe central auction designs from the literature in the framework of primal‐dual algorithms. We cover important properties for existence of Walrasian equilibria derived from discrete convex analysis, and provide open research questions.

Auction-Based Multichannel Cooperative Spectrum Sharing in Hybrid Satellite-Terrestrial IoT Networks

In this article, we investigate the multichannel cooperative spectrum sharing in hybrid satellite-terrestrial Internet of Things (IoT) networks with the auction mechanism, which is designed to reduce the operational expenditure of the satellite-based IoT (S-IoT) network while alleviating the spectrum scarcity issues of terrestrial-based IoT (T-IoT) network. The cluster heads of selected T-IoT networks assist the primary satellite users transmission through cooperative relaying techniques in exchange for spectrum access. We propose an auction-based optimization problem to maximize the sum transmission rate of all primary S-IoT receivers with the appropriate secondary network selection and corresponding radio resource allocation profile by the distributed implementation while meeting the minimum transmission rate of secondary receivers of each T-IoT network. Specifically, the one-shot Vickrey-Clarke-Groves (VCG) auction is introduced to obtain the maximum social welfare, where the winner determination problem is transformed into an assignment problem and solved by the Hungarian algorithm. To further reduce the primary satellite network decision complexity, the sequential Vickrey auction is implemented by sequential fashion until all channels are auctioned. Due to incentive compatibility with those two auction mechanisms, the secondary T-IoT cluster yields the true bids of each channel, where both the nonorthogonal multiple access (NOMA) and time division multiple access (TDMA) schemes are implemented in cooperative communication. Finally, simulation results validate the effectiveness and fairness of the proposed auction-based approach as well as the superiority of the NOMA scheme in secondary relays selection. Moreover, the influence of key factors on the performance of the proposed scheme is analyzed in detail.

PP-VCA: A Privacy-Preserving and Verifiable Combinatorial Auction Mechanism

Combinatorial auctions can be employed in the fields such as spectrum auction, network routing, railroad segment, and energy auction, which allow multiple goods to be sold simultaneously and any combination of goods to be bid and the maximum sum of combinations of bidding prices to be calculated. However, in traditional combinatorial auction mechanisms, data concerning bidders’ price and bundle might reveal sensitive information, such as personal preference and competitive relation since the winner determination problem needs to be resolved in terms of sensitive data as above. In order to solve this issue, this paper exploits a privacy-preserving and verifiable combinatorial auction protocol (PP-VCA) to protect bidders’ privacy and ensure the correct auction price in a secure manner, in which we design a one-way and monotonically increasing function to protect a bidder’s bid to enable the auctioneer to pick out the largest bid without revealing any information about bids. Moreover, we design and employ three subprotocols, namely, privacy-preserving winner determination protocol, privacy-preserving scalar protocol, and privacy-preserving verifiable payment determination protocol, to implement the combinatorial auction with bidder privacy and payment verifiability. The results of comprehensive experimental evaluations indicate that our proposed scheme provides a better efficiency and flexibility to meet different types of data volume in terms of the number of goods and bidders.