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20 pages, 888 KB  
Article
How to Sell Debt (But Not Money)
by Arup Daripa
Games 2026, 17(2), 13; https://doi.org/10.3390/g17020013 (registering DOI) - 9 Mar 2026
Abstract
Multi-unit common value auctions in which bidders submit demand functions are used for a variety of purposes, including selling government debt (Treasury auctions) and allocating liquidity (repo auctions). Typically, either a discriminatory or a uniform-price format is used. In this paper, we consider [...] Read more.
Multi-unit common value auctions in which bidders submit demand functions are used for a variety of purposes, including selling government debt (Treasury auctions) and allocating liquidity (repo auctions). Typically, either a discriminatory or a uniform-price format is used. In this paper, we consider the incentive for participation by relatively uninformed bidders in the presence of more informed bidders under these formats. We characterize the equilibrium under a discriminatory auction and show that discriminatory pricing inhibits uninformed participation. In contrast, the equilibria we construct under a uniform pricing rule show that profitable uninformed participation can occur. The usefulness of widening participation in Treasury auctions makes the latter format a natural choice in these auctions, providing an explanation for the switch to the uniform-price format in US Treasury auctions. We also apply our results to repo auctions and show that a uniform-price format can reduce the ability of a central bank to steer interest rates. This sheds light on the reason for the switch away from the uniform-price format by several central banks in conducting repo auctions. We also consider the question of information aggregation and show that uniform-price auctions might fail to do so. The results also offer an explanation for the fact that the ECB, as well as several other central banks, prefer to allocate liquidity through a fixed-rate tender rather than either uniform-price or discriminatory auctions. Full article
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37 pages, 20396 KB  
Article
Comparative Analysis of Peer-to-Peer Energy Trading with Multi-Objective Optimization in Rooftop Photovoltaics-Powered Residential Community
by Mohammad Zeyad, Berk Celik, Timothy M. Hansen, Fabrice Locment and Manuela Sechilariu
Energies 2026, 19(5), 1231; https://doi.org/10.3390/en19051231 - 1 Mar 2026
Viewed by 228
Abstract
The rapid growth of distributed solar energy, such as rooftop photovoltaics (PVs), has revolutionized conventional power systems into more distributed networks, enabling end-users to engage in and trade within the energy market. Maximizing the benefits of rooftop PV panels for residential end-users, including [...] Read more.
The rapid growth of distributed solar energy, such as rooftop photovoltaics (PVs), has revolutionized conventional power systems into more distributed networks, enabling end-users to engage in and trade within the energy market. Maximizing the benefits of rooftop PV panels for residential end-users, including increased renewable energy use and reduced reliance on the utility grid, remains an essential challenge in conventional centralized markets. Moreover, reducing energy consumption may lead to increased peak demand, decreased self-consumption, reduced system flexibility, and reduced grid stability. Therefore, this study presents a transactive energy market framework that integrates home energy management systems (HEMSs) with multi-objective optimization and an aggregator-based, distributed peer-to-peer (P2P) trading strategy to increase rooftop PV utilization and reduce grid dependency within an intra-residential community. The HEMS is structured to integrate rooftop PV production, battery energy storage systems, and smart appliances to offer flexibility through demand response programs in balancing supply and demand by scheduling appliances during periods of rooftop PV production and lower grid prices. Multi-objective (i.e., minimizing energy consumption cost and peak load) optimization problems are solved using the Non-Dominated Sorting Genetic Algorithm-II (NSGA-II) by achieving a Pareto-optimal solution. To validate the reliability and optimality of the NSGA-II results, the same problem formulation is solved using a mixed-integer linear programming approach. Moreover, a Strategic Double Auction with Dynamic Pricing (SDA-DP) strategy is proposed to support P2P trading among consumers and prosumers and thereafter compared with a rule-based zero-intelligence strategy with market-matching rules to analyze the trading performance of the proposed SDA-DP. The results of this comparative analysis (for 10 households, year-long simulation with 15 min time resolution) demonstrate that compared to the baseline case, integrating NSGA-II optimization with SDA-DP trading significantly enhances rooftop PV utilization by 35.11%, reduces grid dependency by 34.04%, and reduces electricity consumption costs by 30.53%, with savings of €1.93 to €6.67 for a single day after participating in the proposed P2P market. Full article
(This article belongs to the Special Issue New Trends in Photovoltaic Power System)
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17 pages, 402 KB  
Article
Determinants of Market Choices Among Beef Cattle Farmers in uMgungundlovu District of Kwa-Zulu Natal, South Africa
by Rachel S. Mkhize, Gloria Mokolopi, Unity Chipfupa and Olwethu Loki
Agriculture 2026, 16(4), 414; https://doi.org/10.3390/agriculture16040414 - 11 Feb 2026
Viewed by 383
Abstract
Globally, the demand for beef and beef-related products has significantly escalated over the past decade. This study aimed to evaluate the factors influencing the market participation of smallholder beef cattle farmers in uMgungundlovu, South Africa. The study employed a cross-sectional research design, which [...] Read more.
Globally, the demand for beef and beef-related products has significantly escalated over the past decade. This study aimed to evaluate the factors influencing the market participation of smallholder beef cattle farmers in uMgungundlovu, South Africa. The study employed a cross-sectional research design, which followed a mixed-methods approach to collect data. Survey data were collected from smallholder cattle farmers from the uMgungundlovu District in KwaZulu-Natal using a semi-structured questionnaire. Purposive sampling was employed to select four local municipalities from the uMgungundlovu District out of a total of seven, whereas a simple random sampling was used to recruit farmers. The sampling was conducted using Microsoft Excel, whereby each farmer was allocated a random number, and then the required sample was generated from those numbers. To determine factors that influence farmers’ market choice, a multinomial logit regression model was used. A significant proportion of the farmers (43.1%) were aged between 51 and 70, followed by 35.5% aged 31 to 50. Just under half (48.2%) of farmers had received formal training in livestock production. This finding (p < 0.001) reinforces the central role of education in income determination. Better-educated individuals tend to earn more and diversify their income sources. This study underpinned that the livestock farming population is dominated by primarily middle-aged, male, semi-educated, and resource-poor individuals, and they rely significantly on traditional farming methods and government assistance. The multinomial logit regression revealed that farmers’ market choices are influenced by education level, extension service quality, access to quality bulls, and breeding knowledge significantly influenced farmers’ market choices. Specifically, secondary and tertiary education reduced the likelihood of participating in auction markets relative to informal markets, while limited breeding knowledge and poor extension services further constrained participation in formal channels. Full article
(This article belongs to the Section Agricultural Economics, Policies and Rural Management)
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23 pages, 2298 KB  
Article
Optimal Market Share in Automobile Insurance Auction Markets
by Manuel Rodriguez, Rolando Rubilar-Torrealba, Cristóbal Fernandez-Robin, Diego Yáñez and Bernardo Pincheira
Mathematics 2026, 14(4), 628; https://doi.org/10.3390/math14040628 - 11 Feb 2026
Viewed by 293
Abstract
The automobile insurance industry plays a pivotal role in the financial system, fostering economic stability through effective risk management and consumer confidence. Continuous enhancement in price optimisation not only ensures the sustainability of insurers but also fosters a more competitive, fair, and balanced [...] Read more.
The automobile insurance industry plays a pivotal role in the financial system, fostering economic stability through effective risk management and consumer confidence. Continuous enhancement in price optimisation not only ensures the sustainability of insurers but also fosters a more competitive, fair, and balanced market, which is vital for a country’s economic development. The objective of this research is to develop a methodology for determining the optimal price offered by insurance firms for automobile policies in an industry where a First Price Sealed Bid auction system operates. A statistical methodology is employed to ascertain the expected value and standard deviation of the policies on offer in the public domain, whereby these values are calculated using a heteroskedastic linear regression estimation methodology. Furthermore, the aforementioned expected values and standard deviation enable the calculation of the value of the cumulative distribution for an optimal price set within the public offer. This study demonstrates that identifying the optimal price that maximizes profits is analogous to establishing an expected market share for each niche automobile policy market. Moreover, the market share can be calculated through a straightforward heteroskedastic linear regression estimation for instances where market shares are below 50%. Full article
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31 pages, 646 KB  
Article
On Model Improvement Algorithms—Generalised Linear Models and Neural Networks
by Manuel L. Esquível, Nadezhda P. Krasii and Raquel M. Gaspar
Mathematics 2026, 14(3), 561; https://doi.org/10.3390/math14030561 - 4 Feb 2026
Viewed by 217
Abstract
We propose a generic approach to stochastic model improvement by first introducing an archetypal algorithm based on error minimisation and establishing two results on the weak convergence of the probability laws associated with the models under improvement. We then present two concrete instances [...] Read more.
We propose a generic approach to stochastic model improvement by first introducing an archetypal algorithm based on error minimisation and establishing two results on the weak convergence of the probability laws associated with the models under improvement. We then present two concrete instances of this approach: Generalised Linear Models and classical multivariate models assessed using a neural network. In both cases, we illustrate the methodology using economic, financial, and social data related to the determination of government bond coupon rates prior to primary market auctions. For each application, we derive weak convergence results that specify conditions under which model improvement occurs, in the sense of convergence in law of the probability distributions associated with successive models. These results ensure the convergence of the proposed archetypal algorithm and provide a probabilistic foundation for systematic model improvement. Full article
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40 pages, 3962 KB  
Article
Energy Recovery of Gases from Charcoal Production: Potential, Available Technologies, Costs, Sustainability, and Its Contribution to the Energy Transition in Brazil
by Guilherme Mandelo Oliveira, Alisson Aparecido Vitoriano Julio, Osvaldo José Venturini, Márcio Montagnana Vicente Leme, Túlio Tito Godinho de Rezende, José Carlos Escobar Palacio and Electo Eduardo Silva Lora
Processes 2026, 14(3), 511; https://doi.org/10.3390/pr14030511 - 1 Feb 2026
Viewed by 427
Abstract
Minas Gerais is Brazil’s largest charcoal producer, relying on carbonization kilns that release effluent gases and waste energy while generating environmental impacts. This work evaluates the electricity generation potential from these gases using different conversion technologies. A database-based assessment of charcoal production units, [...] Read more.
Minas Gerais is Brazil’s largest charcoal producer, relying on carbonization kilns that release effluent gases and waste energy while generating environmental impacts. This work evaluates the electricity generation potential from these gases using different conversion technologies. A database-based assessment of charcoal production units, based on official institutional records, enabled estimating the energy potential for 2020 and projecting it to 2030. Three technologies were assessed: Steam Rankine Cycle, Organic Rankine Cycle, and Externally Fired Gas Turbine. For each one, efficiencies were calculated and applied to the surveyed producers, ranging from 5% to 24% for power capacities between 100 kW and 2000 kW. The highest energy generation potential, 1348 GWh/year, was obtained using the regenerative and superheated ORC with n-decane as the working fluid. In addition, an economic analysis was performed based on Brazilian electricity auction prices, together with a sensitivity analysis of key variables, including installed power, electricity price, minimum attractiveness rate, taxes, operating hours, and capital expenditure. The results demonstrate that current technical and economic conditions are unfavorable for implementing waste-heat-based power plants in Minas Gerais. Plants below 10 MW are especially unfeasible. A Life Cycle Assessment estimated emissions of 2437.7 kg CO2eq per ton of charcoal. Sustainable measures such as eliminating native wood use, increasing Gravimetric Yield, and adding afterburners could reduce emissions by over 57%. Full article
(This article belongs to the Section Energy Systems)
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16 pages, 588 KB  
Article
Market Price Determination for Ready-to-Cook Catfish Products: Insights from Experimental Auctions
by Saroj Adhikari, Uttam Kumar Deb, Nabin B. Khanal, Madan M. Dey and Lin Xie
Gastronomy 2026, 4(1), 3; https://doi.org/10.3390/gastronomy4010003 - 15 Jan 2026
Viewed by 314
Abstract
Determination of the right price is vital for the success of newly developed food products. This study examined the market prices and their determinants for five ready-to-cook catfish products: Panko-Breaded Standard Strips (PBSS), Panko-Breaded Standard Fillet (PBSF), Panko-Breaded Delacata Fillet (PBDF), Sriracha-Marinated Delacata [...] Read more.
Determination of the right price is vital for the success of newly developed food products. This study examined the market prices and their determinants for five ready-to-cook catfish products: Panko-Breaded Standard Strips (PBSS), Panko-Breaded Standard Fillet (PBSF), Panko-Breaded Delacata Fillet (PBDF), Sriracha-Marinated Delacata Fillet (SMDF), and Sesame-Ginger-Marinated Delacata Fillet (SGMDF). Market prices were derived using Vickrey’s second-price auction, where the second-highest bid represents the market price. We analyzed experimental auction data from 121 consumers using a logit model to estimate the probability of offering the market price based on product sensory attributes, socio-demographic characteristics of the participants, and the level of competition (panel size). Consumers’ willingness-to-pay (WTP) was elicited in two rounds: before tasting (visual evaluation) and after tasting (organoleptic evaluation) the products. Breaded products received higher market prices than marinated products, with PBDF ranked highest. Sensory traits, especially taste, along with income, education, and grocery shopping involvement, significantly influenced the formation of market price. Increased competition elevated the market prices. Both product features and consumer characteristics significantly affect market price outcomes, and experimental auctions provide a robust tool for understanding consumer behavior toward newly developed food products. Full article
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10 pages, 648 KB  
Communication
How Dairy Cows Are Culled from Freestall-Housed Dairy Herds in Wisconsin
by Kaitlin I. Buterbaugh, Thomas B. Naze and Nigel B. Cook
Animals 2026, 16(2), 238; https://doi.org/10.3390/ani16020238 - 13 Jan 2026
Viewed by 367
Abstract
Efforts to improve efficiency and profitability on dairy farms have renewed focus on how culling practices affect herd sustainability and economic outcomes. This study surveyed decision-makers on 60 high-producing, freestall-housed dairy farms in Wisconsin, with a mean (SD) turnover rate of 36.0 (8.0)%. [...] Read more.
Efforts to improve efficiency and profitability on dairy farms have renewed focus on how culling practices affect herd sustainability and economic outcomes. This study surveyed decision-makers on 60 high-producing, freestall-housed dairy farms in Wisconsin, with a mean (SD) turnover rate of 36.0 (8.0)%. Using a structured questionnaire, we examined herd management, culling criteria, and motivations. Most farms (93%) used on-farm management systems to guide culling, yet only 48% used designated reports, relying instead on individual cow records. Milk production, infertility, and somatic cell count were the top culling criteria, with high milk yield cited as the most difficult factor in removal decisions. While 54% recorded the most obvious reason for culling, only 7% documented multiple causes. Cull cows were typically transported by third parties; 80% farms sent cows directly to slaughter, while 52% sent them to auction. One-third of farms sold cows for continued dairy use. Euthanasia was performed on 93% of farms, mostly by employees, with minimal veterinary input. The study aimed to investigate producer perspectives on the culling decision-making process on commercial dairy farms. The findings highlight opportunities for improved veterinary involvement and the use of structured herd-level reports to support more strategic culling decisions. Full article
(This article belongs to the Section Animal System and Management)
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28 pages, 6456 KB  
Article
IB-DARP: An Algorithm for Multi-Vessel Collaborative Task and Path Planning
by Yuhao Wang and Liang Luo
J. Mar. Sci. Eng. 2026, 14(2), 165; https://doi.org/10.3390/jmse14020165 - 12 Jan 2026
Cited by 1 | Viewed by 242
Abstract
This paper presents IB-DARP (Iteration Balancing—Divide Areas Routing Problem), an enhanced multi-vessel cooperative mission and path planning method designed to address the limitations of traditional approaches, including uneven task allocation, workload imbalance, and path conflicts. The proposed method integrates four key mechanisms to [...] Read more.
This paper presents IB-DARP (Iteration Balancing—Divide Areas Routing Problem), an enhanced multi-vessel cooperative mission and path planning method designed to address the limitations of traditional approaches, including uneven task allocation, workload imbalance, and path conflicts. The proposed method integrates four key mechanisms to improve planning robustness and computational efficiency. A historical data mining mechanism is first employed to extract stable navigation patterns from accumulated vessel trajectories and construct a high-confidence maritime route network. Based on this network, a precomputation mechanism significantly reduces planning-stage computational complexity by calculating essential inter-node distances in advance. A heading-aware partitioning mechanism further decomposes the multi-vessel planning problem into tractable single-vessel subproblems, while an iterative auction–equilibrium mechanism dynamically adjusts task assignments to enhance global load balance and suppress conflicts. To evaluate the effectiveness of IB-DARP, comprehensive ablation studies and large-scale scenario experiments were conducted, demonstrating its advantages in mission allocation, conflict mitigation, and cooperative path optimization. The results confirm that IB-DARP provides a scalable and efficient solution for multi-vessel cooperative mission planning in complex maritime environments. Full article
(This article belongs to the Section Ocean Engineering)
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14 pages, 305 KB  
Article
All-Pay Auctions with Different Forfeits
by Benjamin Kang and James Unwin
Games 2026, 17(1), 2; https://doi.org/10.3390/g17010002 - 9 Jan 2026
Viewed by 373
Abstract
In an auction, each party bids a certain amount, and the one who bids the highest is the winner. Interestingly, auctions can also be used as models for other real-world systems. In an all-pay auction all parties must pay a forfeit for bidding. [...] Read more.
In an auction, each party bids a certain amount, and the one who bids the highest is the winner. Interestingly, auctions can also be used as models for other real-world systems. In an all-pay auction all parties must pay a forfeit for bidding. In the most commonly studied all-pay auction, parties forfeit their entire bid, and this has been considered as a model for expenditure on political campaigns. Here, we consider a number of alternative forfeits that might be used as models for different real-world competitions, such as preparing bids for defense or infrastructure contracts. Full article
(This article belongs to the Special Issue Game-Theoretical Analysis of the Division of Labor and Trade Conflict)
21 pages, 876 KB  
Article
Multi-Party Semi-Quantum Simultaneous Ascending Auction Protocol Based on Single-Particle States
by Xiuqi Wu, Yu Yang, Baichang Wang, Yue Zhang and Yunguang Han
Entropy 2026, 28(1), 39; https://doi.org/10.3390/e28010039 - 28 Dec 2025
Viewed by 351
Abstract
Simultaneous ascending auctions find extensive applications in spectrum licensing and advertising space allocation. However, existing quantum sealed-bid auction protocols suffer from dual limitations: they cannot support multi-item simultaneous bidding scenarios, and their reliance on complex quantum resources along with requiring full quantum operational [...] Read more.
Simultaneous ascending auctions find extensive applications in spectrum licensing and advertising space allocation. However, existing quantum sealed-bid auction protocols suffer from dual limitations: they cannot support multi-item simultaneous bidding scenarios, and their reliance on complex quantum resources along with requiring full quantum operational capabilities from bidders fails to accommodate practical constraints of quantum resource-limited users. To address these challenges, this paper proposes a multi-party semi-quantum simultaneous ascending auction protocol based on single-particle states. The protocol employs a trusted honest third party (HTP) responsible for quantum state generation, distribution, and security verification. Bidders determine their groups through quantum measurements and privately encode their bid vectors. Upon successful HTP authentication, each bidder obtains a unique identity code. During the bidding phase, HTP dynamically updates quantum sequences, allowing bidders to submit bids for multiple items by performing only simple unitary operations. HTP announces the highest bid for each item in real time and iteratively generates auction sequences until no new highest bid emerges, thereby achieving simultaneous ascending auctions for multiple items. It acts as a quantum-secured signaling layer, ensuring unconditional security for bid transmission and identity verification while maintaining classical auction logic. Quantum circuit simulations validate the protocol’s feasibility with current technology while satisfying critical security requirements, including anonymity, verifiability, non-repudiation, and privacy preservation. It provides a scalable semi-quantum auction solution for resource-constrained scenarios. Full article
(This article belongs to the Special Issue Quantum Information Security)
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29 pages, 10515 KB  
Article
A Chimpanzee Troop-Inspired Algorithm for Multiple Unmanned Aerial Vehicles on Patrolling Missions
by Ebtesam Aloboud and Heba Kurdi
Drones 2026, 10(1), 10; https://doi.org/10.3390/drones10010010 - 25 Dec 2025
Viewed by 679
Abstract
Persistent patrolling with multiple Unmanned Aerial Vehicles (UAVs) remains challenging due to dynamic surveillance priorities, heterogeneous node importance, and evolving operational constraints. We present the novel Chimpanzee Troop Algorithm for Patrolling (CTAP), a decentralized policy inspired by chimpanzees fission–fusion dynamics and territorial behavior. [...] Read more.
Persistent patrolling with multiple Unmanned Aerial Vehicles (UAVs) remains challenging due to dynamic surveillance priorities, heterogeneous node importance, and evolving operational constraints. We present the novel Chimpanzee Troop Algorithm for Patrolling (CTAP), a decentralized policy inspired by chimpanzees fission–fusion dynamics and territorial behavior. CTAP provides three capabilities: (i) on-the-fly patrol-group instantiation, (ii) importance-aware territorial partitioning of the patrol graph, and (iii) adaptive boundary expansion via a lightweight shared-memory overlay that coordinates neighboring groups without centralization. Unlike the Ant Colony Optimization (ACO), Heuristic Pathfinder Conscientious Cognitive (HPCC), Recurrent LSTM Path-Maker (RLPM), State-Exchange Bayesian Strategy (SEBS), and Dynamic Task Assignment via Auctions (DTAP) baselines, CTAP couples local-idleness reduction with controlled edge-exploration, yielding stable coverage under shifting demand. We evaluate these approaches across multiple maps and fleet sizes using the average weighted idleness, global worst-weighted idleness, and Time-Normalized Idleness metrics. CTAP reduces the average weighted idleness by 7% to 22% and the global worst-weighted idleness by 30–65% relative to the strongest competitor and attains the lowest Time-Normalized Idleness in every configuration. These results show that a simple, communication-limited, partition-based policy enables robust, scalable patrolling suitable for resource-constrained UAV teams in smart-city environments. Full article
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18 pages, 3635 KB  
Article
Multi-Agent Reinforcement Learning for Sustainable Integration of Heterogeneous Resources in a Double-Sided Auction Market with Power Balance Incentive Mechanism
by Jian Huang, Ming Yang, Li Wang, Mingxing Mei, Jianfang Ye, Kejia Liu and Yaolong Bo
Sustainability 2026, 18(1), 141; https://doi.org/10.3390/su18010141 - 22 Dec 2025
Viewed by 531
Abstract
Traditional electricity market bidding typically focuses on unilateral structures, where independent energy storage units and flexible loads act merely as price takers. This reduces bidding motivation and weakens the balancing capability of regional power systems, thereby limiting the large-scale utilization of renewable energy. [...] Read more.
Traditional electricity market bidding typically focuses on unilateral structures, where independent energy storage units and flexible loads act merely as price takers. This reduces bidding motivation and weakens the balancing capability of regional power systems, thereby limiting the large-scale utilization of renewable energy. To address these challenges and support sustainable power system operation, this paper proposes a double-sided auction market strategy for heterogeneous multi-resource (HMR) participation based on multi-agent reinforcement learning (MARL). The framework explicitly considers the heterogeneous bidding and quantity reporting behaviors of renewable generation, flexible demand, and energy storage. An improved incentive mechanism is introduced to enhance real-time system power balance, thereby enabling higher renewable energy integration and reducing curtailment. To efficiently solve the market-clearing problem, an improved Multi-Agent Twin Delayed Deep Deterministic Policy Gradient (MATD3) algorithm is employed, along with a temporal-difference (TD) error-based prioritized experience replay mechanism to strengthen exploration. Case studies validate the effectiveness of the proposed approach in guiding heterogeneous resources toward cooperative bidding behaviors, improving market efficiency, and reinforcing the sustainable and resilient operation of future power systems. Full article
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23 pages, 4486 KB  
Article
A Fast Distributed Algorithm for Uniform Price Auction with Bidding Information Protection
by John Sum, Chi-Sing Leung and Janet C. C. Chang
Computation 2025, 13(12), 294; https://doi.org/10.3390/computation13120294 - 17 Dec 2025
Viewed by 416
Abstract
In this paper, a fast distributed algorithm is proposed for solving the winners and price determination problems in a uniform price auction in which each bidder bids for multiple units out of a lot of k identical items with a per-unit price. In [...] Read more.
In this paper, a fast distributed algorithm is proposed for solving the winners and price determination problems in a uniform price auction in which each bidder bids for multiple units out of a lot of k identical items with a per-unit price. In a conventional setting, all bidders disclose their bidding information to an auctioneer and let the auctioneer allocate the items and determine the uniform price, i.e., the least winning price. In our setting, all bidders do not need to disclose their bidding information to the auctioneer. The bidders and the auctioneer collaboratively compute by the distributed algorithm to determine in a small number of steps the units allocated and the uniform price. The number of steps is independent of the number of bidders. At the end of the computing process, each bidder can only know the units allocated to him/her and the uniform price. The auctioneer can only know the units being allocated to the bidders and the uniform price. Therefore, neither the bidders nor the auctioneer are able to know the per-unit bidding prices of the bidders except the uniform price. Moreover, the auctioneer is not able to know the bidding units of the losing bidders. Bidders’ per-unit bidding prices are protected, and the bidding units of the losing bidders are protected. Bidding information privacy is preserved. Full article
(This article belongs to the Section Computational Social Science)
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28 pages, 2278 KB  
Article
A Flexible Combinatorial Auction Algorithm (FCAA) for Multi-Task Collaborative Scheduling of Heterogeneous UAVs
by Leiming He, Xudong Gong, Jiangan Zheng, Yue Wang and Yunsen Cui
Drones 2025, 9(12), 870; https://doi.org/10.3390/drones9120870 - 16 Dec 2025
Cited by 1 | Viewed by 447
Abstract
To address the inefficiency of collaborative scheduling of heterogeneous Unmanned Aerial Vehicles under resource constraints, particularly in large-scale multi-tasking scenarios, an improved Flexible Combinatorial Auction Algorithm is proposed, leveraging the bidding mechanism of simultaneous ascending auctions. This algorithm is designed with a candidate [...] Read more.
To address the inefficiency of collaborative scheduling of heterogeneous Unmanned Aerial Vehicles under resource constraints, particularly in large-scale multi-tasking scenarios, an improved Flexible Combinatorial Auction Algorithm is proposed, leveraging the bidding mechanism of simultaneous ascending auctions. This algorithm is designed with a candidate solution generation mechanism and an addition mechanism, which collectively reduce the number of candidate solutions generated prior to combinatorial auctions. It allows tasks to flexibly combine resources and submit bids. By calculating each candidate solution’s benefit based on real-time resource prices, it dynamically adjusts their priorities to search for the overall optimal multi-task scheduling scheme. It effectively addresses the inability of traditional auction algorithms to dynamically form resource clusters via flexible resource combination to collaboratively complete tasks. Meanwhile, it overcomes the technical bottleneck that existing heuristic algorithms struggle to handle highly complex heterogeneous resource scheduling cases. Simulation experiments show that in small-scale multi-tasking scenarios, the FCAA achieves a scheduling success rate of over 88%, with the maximum solution benefit proportion reaching 83.9%; in multi-tasking scenarios, it achieves a scheduling success rate of 98%, with the maximum solution benefit proportion reaching 93%. Its time efficiency and solution quality are significantly superior to those of traditional algorithms, providing an efficient and stable solution for heterogeneous resource scheduling problems in complex operational environments. Full article
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