Auction Problem Research Articles

Threshold Policies with Tight Guarantees for Online Selection with Convex Costs

This article provides threshold policies with tight guarantees for online selection with convex cost (OSCC). In OSCC, a seller wants to sell some asset to a sequence of buyers with the goal of maximizing her profit. The seller can produce additional units of the asset, but at non-decreasing marginal costs. Each time, a buyer arrives and offers a price. The seller must make an immediate and irrevocable decision in terms of whether to accept the offer and produce/sell one unit of the asset to this buyer. The goal is to develop an online algorithm that selects a subset of buyers to maximize the seller’s profit, namely, the total selling revenue minus the total production cost. Our main result is the development of a class of simple threshold policies that are logistically simple and easy to implement but have provable optimality guarantees among all deterministic algorithms. We also derive a lower bound on competitive ratios of randomized algorithms and prove that the competitive ratio of our threshold policy asymptotically converges to this lower bound when the total production output is sufficiently large. Our results generalize and unify various online search, pricing, and auction problems, and provide a new perspective on the impact of non-decreasing marginal costs on real-world online resource allocation problems.

A Double Auction for Charging Scheduling among Vehicles Using DAG-Blockchains

Electric Vehicles (EVs) are becoming more and more popular in our daily life, which replaces traditional fuel vehicles to reduce carbon emissions and protect the environment. EVs need to be charged, but the number of charging piles in a Charging Station (CS) is limited and charging is usually more time-consuming than fueling. According to this scenario, we propose a secure and efficient charging scheduling system based on a Directed Acyclic Graph (DAG)-blockchain and double auction mechanism. In a smart area, it attempts to assign EVs to the available CSs in the light of their submitted charging requests and status information. First, we design a lightweight charging scheduling framework that integrates DAG-blockchain and modern cryptography technology to ensure security and scalability during performing scheduling and completing tradings. In this process, a constrained multi-item double auction problem is formulated because of the limited charging resources in a CS, which motivates EVs and CSs in this area to participate in the market based on their preferences and statuses. Due to this constraint, our problem is more complicated and harder to achieve truthfulness as well as system efficiency compared to the existing double auction model. To adapt to it, we propose two algorithms, namely Truthful Mechanism for Charging (TMC) and Efficient Mechanism for Charging (EMC), to determine an assignment between EVs and CSs and pricing strategies. Then, both theoretical analysis and numerical simulations show the correctness and effectiveness of our proposed algorithms.

MODEL ALOKASI SUBSIDI DANA APBD DAN CSR UNTUK OPTIMASI PENGADAAN MESIN KOMODITAS LELANG: STUDY KASUS

Procurement of machinery is a facilitation to overcome auction problems in accordance with the strategic plan of the Dinas TPHPKP to maintain and improve the quality or quality of commodities so as to increase the selling value. To carry out this facilitation with limited funds, other sources of subsidized funds are needed, the government needs tools to determine the nominal funding decision, the decision to place the machine, and the feasibility study of the model. Based on surveys, interviews, and previous research, the research data was processed using goal programming with Excel and ILOG CPLEX. This study chooses scenario three as the optimal scenario because the nominal subsidy of funds is smaller than scenarios one and two, but results in machine option decisions on each quality improvement function with a positive benefit deviation value of Rp. 20,014,000. This study succeeded in formulating a fund allocation model, determining five locations for placing machines and stating the feasibility of a fund allocation model with a Benefit Cost Ratio value of 1.49. Future research is expected to be able to consider the cost of energy consumption in the next use of the machine, consider the form of village assets as a candidate for placing the machine, and calculate other feasibility study parameters.

Low complexity joint spectrum resource and power allocation for ultra dense networks

In this paper, we propose a low complexity spectrum resource allocation scheme cross the access points (APs) for the ultra dense networks (UDNs), in which all the APs are divided into several AP groups (APGs) and the total bandwidth is divided into several narrow band spectrum resources and each spectrum resource is allocated to APGs independently to decrease the interference among the cells. Furthermore, we investigate the joint spectrum and power allocation problem in UDNs to maximize the overall throughput. The problem is formulated as a mixed-integer nonconvex optimization (MINCP) problem which is difficult to solve in general. The joint optimization problem is decomposed into two subproblems in terms of the spectrum allocation and power allocation respectively. For the spectrum allocation, we model it as a auction problem and a combinatorial auction approach is proposed to tackle it. In addition, the DC programming method is adopted to optimize the power allocation subproblem. To decrease the signaling and computational overhead, we propose a distributed algorithm based on the Lagrangian dual method. Simulation results illustrate that the proposed algorithm can effectively improve the system throughput.

A Semi-supervised Sensing Rate Learning based CMAB scheme to combat COVID-19 by trustful data collection in the crowd

A Semi-supervised Sensing Rate Learning based CMAB scheme to combat COVID-19 by trustful data collection in the crowd

Intelligent EV Charging for Urban Prosumer Communities: An Auction and Multi-Agent Deep Reinforcement Learning Approach

Recently, the deployment of electric vehicles supply equipment (EVSE) and its market is expanding rapidly to support the massive penetration of electric vehicles (EVs). However, to accomplish an effective EV charging mechanism for urban prosumer communities, it is imperative to tackle the challenges of distinct energy generation among the communities, dependency of the total purchasable energy price of each EV based on the distance between EV and EVSE, and extreme uncertainty among the energy demand and generation. Therefore, in this paper, the problem of EV charging of urban prosumer communities is studied. In particular, a joint optimization problem is proposed to maximize both the social welfare and EV charging achieved rate of the considered urban prosumer communities. Consequently, the formulated problem is decomposed into 1) truthful double auction problem for determining the unit price and winners by maximizing social welfare, and 2) EV auction losers charging problem for improving EVs charging achieved rate by purchasing energy from the power grid. Then the breakeven-based double auction (BDA) mechanism is proposed to find the unit price and EV winners’ for charging. Sequentially, a multi-agent deep reinforcement learning-based asynchronous advantage actor-critic algorithm with a long short-term memory layer (A3C-LSTM) is adopted to achieve the optimal grid energy buying decision for ensuring the charging of the losers. Finally, the experimental results demonstrate the efficacy of the proposed model that can increase the number of EV charging up to 57.31%, and prosumer communities have gained 86.04% of their income compared to baseline methods.

Diffusive Limit Approximation of Pure-Jump Optimal Stochastic Control Problems

We consider the diffusive limit of a typical pure-jump Markovian control problem as the intensity of the driving Poisson process tends to infinity. We show that the convergence speed is provided by the Hölder exponent of the Hessian of the limit problem, and explain how correction terms can be constructed. This provides an alternative efficient method for the numerical approximation of the optimal control of a pure-jump problem in situations with very high intensity of jumps. We illustrate this approach in the context of a display advertising auction problem.

Uncommon Knowledge in Multiparty Auctions

The pure strategy Nash equilibrium (PSNE) solution to multiparty auctions makes the strong but unrealistic assumption that all participants share the same beliefs about the type distributions of the others, and that all know that this information is mutually known. This paper proposes two alternative analyses of such auction problems that do not make that presupposition. The first is based on a solution concept similar to the PSNE. The second is employs the level k thinking solution concept.

An evidential reasoning-based stochastic multi-attribute acceptability analysis method for uncertain and heterogeneous multi-attribute reverse auction

Multi-attribute reverse auction has been frequently adopted by manufacturers or governments to purchase goods or services. In order to address the multi-attribute reverse auction problem with imprecise and heterogeneous information, this study introduces an evidential reasoning-based stochastic multi-attribute acceptability analysis (ER-SMAA) method. Firstly, quantitative evaluations are transformed to belief degrees on a pre-defined set of evaluation grades using the imprecise Simos-Roy Figueira (SRF) method. The SRF method is also adopted to sample different sets of attribute weights compatible with the preferences of experts. Then, the evidential reasoning approach is used to fuse evaluations. Regarding the plurality of rankings obtianed by possible transformed performances and possible sets of attribute weights, the stochastic multi-attribute acceptability analysis (SMAA) is applied to draw robust conclusions about the ranking of providers. A numerical example concerning the winner determination for clean energy device procurement is given to illustrate the effectiveness and robustness of the proposed ER-SMAA method.

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.

A Price-Incentive Resource Auction Mechanism Balancing the Interests Between Users and Cloud Service Provider

For a cloud service provider, it necessitates an emerging cloud ecosystem to consolidate the existing users and attract more potential users, further gaining its market share. Therefore, in this article, we design a price-incentive resource auction mechanism in cloud environment. In response to the cloud resource price, each user synthesizes her bidding budget and QoS requirement, and purchases cloud resources according to her resource demand in a strategic manner. The cloud service provider, meanwhile, can regulate the resource demands of users through conducting a market-based pricing strategy, against too low prices to cover the operational costs (i.e., energy costs) or too high prices resulting in user churn. In virtue of an elaborate market-based pricing strategy, the interests of users and the cloud service provider are balanced. Our price-incentive resource auction mechanism targets to stimulate maximum users willing to purchase resources and perform their applications at the cloud, on the premise of a minimum profit rate guaranteed for the cloud service provider. It is also able to provide budge balance and truthfulness guarantee, and satisfy the envy-freeness. In order to carry out the above objectives, we carefully design the user utility function reflecting the complicated user interest, and formulate our resource pricing and auction problem as a bin packing problem, which has non-polynomial computational complexity. Regarding the NP-hardness of optimization problem and the concavity of user utility, we present a computational-efficient ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1+\epsilon $ </tex-math></inline-formula> )-approximate algorithm namely PIRA. Finally, we conduct simulations based on the real-world dataset to validate the effectiveness of our proposed approach.

A Hybrid Spectrum Combinational Auction Mechanism Based on a Weighted Bipartite Graph for Energy Internet in Smart Cities

Energy Internet (EI) is aimed at sustainable computing by integrating various energy forms into a highly flexible grid similar to the Internet. The network subsystems of EI connect different components to enable real-time monitoring, controlling, and management. In this paper, the spectrum allocation problem of the cognitive radio network for EI in a smart city is investigated. The network spectrum allocation with both heterogeneous primary operators and secondary users is formulated as the combinatorial auction problem and then is converted to a subset selection problem on a weighted bipartite graph. We propose a hybrid algorithm to solve the problem. Firstly, the proposed algorithm uses a constructive procedure based on the Kuhn-Munkres algorithm to obtain an initial solution. Then, a local search is used to improve the solution quality. In addition, the truthfulness of the auction is guaranteed by adopting a “Vickrey-like” mechanism. Simulation results show that the performance of the proposed algorithm is better than existing greedy algorithms in terms of the social welfare, seller revenue, buyer satisfaction ratio, and winning buyer ratio.

Revenue-Optimal Auction For Resource Allocation in Wireless Virtualization: A Deep Learning Approach

Wireless virtualization has become a key concept in future cellular networks which can provide multiple virtualized wireless networks for different mobile virtual network operators (MVNOs) over the same physical infrastructure. Resource allocation is a main challenging issue in wireless virtualization for which auction approaches have been widely used. However, for most existing auction-based allocation schemes, the objective is to maximize the social welfare (i.e., the sum of all valuations of winning bidders) due to its simplicity. While in reality, MVNOs are more interested in maximizing their own revenues (i.e., received payments from auction winners). However, the revenue-optimal auction problem is much more complex since the payment price is unknown before calculation. In this paper, we aim to design a revenue-optimal auction mechanism for resource allocation in wireless virtualization. Considering the complexity, deep learning techniques are applied. Specifically, we construct a multi-layer feed-forward neural network based on the analysis of optimal auction design. The neural network adopts users’ bids as the input and the allocation rule and conditional payment rule for the users as the output. The proposed auction mechanism possesses several desirable properties, e.g., individual rationality, incentive compatibility and budget constraint. Finally, simulation results demonstrate the effectiveness of the proposed scheme. Comparing with second-price auction and optimization-based schemes, the proposed scheme can increase the revenue by 10 and 30 percent on average, for single MVNO and multi-MVNO cases, respectively.

Optimal Design of Online Sequential Buy-Price Auctions with Consumer Valuation Learning

Buy-price auction has been successfully used as a new channel of online sales. This paper studies an online sequential buy-price auction problem, where a seller has an inventory of identical products and needs to clear them through a sequence of online buy-price auctions such that the total profit is maximized by optimizing the buy price in each auction. We propose a methodology by dynamic programming approach to solve this optimization problem. Since the consumers’ behavior affects the seller’s revenue, the consumers’ strategy used in this auction is first investigated. Then, two different dynamic programming models are developed to optimize the seller’s decision-making: one is the clairvoyant model corresponding to a situation where the seller has complete information about consumer valuations, and the other is the Bayesian learning model where the seller makes optimal decisions by continuously recording and utilizing auction data during the sales process. Numerical experiments are employed to demonstrate the impacts of several key factors on the optimal solutions, including the size of inventory, the number of potential consumers, and the rate at which the seller discounts early incomes. It is shown that when the consumers’ valuations are uniformly distributed, the Bayesian learning model is of great efficiency if the demand is adequate.

Online Second Price Auction with Semi-Bandit Feedback under the Non-Stationary Setting

In this paper, we study the non-stationary online second price auction problem. We assume that the seller is selling the same type of items in T rounds by the second price auction, and she can set the reserve price in each round. In each round, the bidders draw their private values from a joint distribution unknown to the seller. Then, the seller announced the reserve price in this round. Next, bidders with private values higher than the announced reserve price in that round will report their values to the seller as their bids. The bidder with the highest bid larger than the reserved price would win the item and she will pay to the seller the price equal to the second-highest bid or the reserve price, whichever is larger. The seller wants to maximize her total revenue during the time horizon T while learning the distribution of private values over time. The problem is more challenging than the standard online learning scenario since the private value distribution is non-stationary, meaning that the distribution of bidders' private values may change over time, and we need to use the non-stationary regret to measure the performance of our algorithm. To our knowledge, this paper is the first to study the repeated auction in the non-stationary setting theoretically. Our algorithm achieves the non-stationary regret upper bound Õ(min{√S T, V¯⅓T⅔), where S is the number of switches in the distribution, and V¯ is the sum of total variation, and S and V¯ are not needed to be known by the algorithm. We also prove regret lower bounds Ω(√S T) in the switching case and Ω(V¯⅓T⅔) in the dynamic case, showing that our algorithm has nearly optimal non-stationary regret.

Online Combinatorial Auctions for Resource Allocation With Supply Costs and Capacity Limits

We study a general online combinatorial auction problem in algorithmic mechanism design. A provider allocates multiple types of capacity-limited resources to customers that arrive in a sequential and arbitrary manner. Each customer has a private valuation function on bundles of resources that she can purchase (e.g., a combination of different resources such as CPU and RAM in cloud computing). The provider charges payment from customers who purchase a bundle of resources and incurs an increasing supply cost with respect to the totality of resources allocated. The goal is to maximize the social welfare, namely, the total valuation of customers for their purchased bundles, minus the total supply cost of the provider for all the resources that have been allocated. We adopt the competitive analysis framework and provide posted-price mechanisms with optimal competitive ratios. Our pricing mechanism is optimal in the sense that no other online algorithms can achieve a better competitive ratio. We validate the theoretic results via empirical studies of online resource allocation in cloud computing. Our numerical results demonstrate that the proposed pricing mechanism is competitive and robust against system uncertainties and outperforms existing benchmarks.

Matching algorithm of the auctions on Ebay

This paper explores eBay auction properties that match buyers and sellers and generates millions of sales every month. eBay’s auction is now a well known mechanism designed to make buyers and sellers feel comfortable doing business without meeting each other. In a theoretical point of view, the current matching algorithm has not solved the online auction problems because the main conditions of agents’ preferences do not satisfy when bidders are unobservable and a set of bidders is not identified. Therefore, we construct a new simplified model of matching with a given object for sale to form a seller-bidder pair to overcome the online auction issues. Specially, our model may extend for the matching mechanism of the job market.

A discrete cooperatively coevolving particle swarm optimization algorithm for combinatorial double auctions

A combinatorial double auction is a type of double-side auction which makes buyers and sellers trade goods more conveniently than multiple combinatorial auctions. In this paper, we consider the combinatorial double auction problem in which there are transaction costs, supply constraints and surplus constraints. We formulate the WDP of combinatorial double auction problem as an integer programming problem formulation. The winner determination problem (WDP) in combinatorial double auctions poses a challenge due to computational complexity. Particle swarm optimization (PSO) is a well-known approach to deal with complex optimization problems. In the existing literature, different variants of PSO algorithms have been proposed. However, there still lacks a comparative study on effectiveness of applying different variants of PSO algorithms in combinatorial double auctions. As standard discrete PSO (DPSO) algorithm suffers from premature convergence problem, we adopt a coevolution approach to develop a discrete cooperatively coevolving particle swarm optimization (DCCPSO) algorithm that can scale with the problem. The effectiveness of the proposed algorithm is verified by comparing the results with several variants of PSO algorithms and Differential Evolution algorithms through simulation. Simulation results indicate that the proposed DCCPSO algorithm significantly outperforms these variants of PSO algorithms and Differential Evolution algorithms in most test cases of combinatorial double auctions.

Preserving Geo-Indistinguishability of the Primary User in Dynamic Spectrum Sharing

Dynamic spectrum sharing (DSS) has been taken as an encouraging method to address the increasing demand for wireless spectrum resources. Without privacy protection in location, however, the primary user will hesitate to share spectrum with secondary users. In this paper, we present LpriDSS, the first scheme for a spectrum administrator to select spectrum-sharing secondary users while implementing the geo-indistinguishability of primary user. First, we formulate the secondary users selection without privacy in DSS system as an auction problem and demonstrate the location inference attacks based on the winner sets in detail. Then, a ranking metric to characterize the administrators’ preference for secondary users is defined. Moreover, a probability of each secondary user being selected as a winner is calculated and used during the process of secondary user selection. Finally, a truthful payment computation is designed according to that probability. Thorough theoretical analysis and simulation studies show that LpriDSS can simultaneously achieve geo-indistinguishability, approximate social welfare maximization, and truthfulness.