Search Results (57)

This paper investigates the problem of contract coordination in a two-tier multi-unit auction supply chain consisting of a seller and an auction house. We theoretically show that the conventional commission-based mechanism distorts the transmission of demand information from the demand side to the supply side, thereby preventing effective supply chain coordination. In contrast, guaranteed auction contracts can achieve coordination under both cooperative and non-cooperative game frameworks. Under the cooperative game setting, profits are allocated according to a Nash bargaining solution, in which each party receives its disagreement payoff and a bargaining-power-weighted share of the surplus, with risks and returns being allocated symmetrically. Under the non-cooperative game setting, the supply chain leader can appropriate a larger share of the total profit while bearing relatively lower risk. These results indicate that, as the supply chain leader, the auction house can select different cooperation modes under guaranteed auction contracts according to its bargaining position, but profit allocation should be benchmarked against the cooperative game outcome in order to enhance the long-term competitiveness and stability of the supply chain. Full article

Vehicular Edge Computing (VEC) can effectively guarantee the service experience of user vehicles, but resource-limited Roadside Units (RSUs) may face insufficient computing capacity during task peak periods. Utilizing Assisting Vehicles (AVs) with idle resources to share computing power can alleviate the pressure on RSUs. However, existing studies often fail to adequately incentivize selfish assisting vehicles to contribute resources and frequently lack a global optimization perspective from the overall system welfare. To address these challenges, this paper proposes an incentive-driven utility-balanced task offloading framework that aims to maximize social welfare while jointly optimizing resource allocation and profit pricing. Specifically, we first formulate the resource allocation as a Mixed-Integer Nonlinear Programming (MINLP) problem. To solve this problem, we introduce hybrid action representation learning to VEC for the first time and propose the HyAR-PPO algorithm to jointly optimize discrete offloading decisions and continuous resource allocation. This algorithm maps heterogeneous hybrid actions to a unified latent representation space through a Variational Autoencoder for the solution. Subsequently, equilibrium prices among user vehicles, Computation Service Providers (CSPs), and assisting vehicles are determined through Nash bargaining games, satisfying individual rationality constraints and achieving Pareto-optimal fair profit distribution. Experimental results demonstrate that the proposed framework can effectively coordinate multi-party interests. Compared with mainstream methods, the approach based on hybrid action representation learning achieves a significant improvement in social welfare, with its advantages being more pronounced in medium-to-large-scale scenarios. Full article

For interconnected multi-microgrids, it is crucial to improve operational economy and renewable energy utilization while ensuring system security. However, existing studies still face limitations in handling multi-time-scale uncertainties and enhancing the incentive for energy trading. Therefore, this paper proposes a cooperative distributed energy management strategy for interconnected microgrids based on model predictive control. First, a multi-time-scale framework is introduced into the multi-microgrid model, where rolling optimization and adaptive prediction/control horizons are used to cope with stochastic fluctuations of sources and loads. Then, a cooperative game model for the multi-microgrid coalition is formulated, and the asymmetric Nash bargaining problem is equivalently decomposed into a two-stage procedure of “coalition operation cost minimization–transaction bargaining”. Next, an algorithm for a distributed alternating-direction method of multipliers is employed for solution. Finally, multi-scenario simulations are carried out to compare three operation modes: independent operation, cooperation only, and model predictive control-based cooperation. The results show that compared with the independent operation mode, the total operation cost of the system is reduced by 22.8% using the proposed method and by 6.3% compared with the mode only adopting the cooperation mechanism, which demonstrates the effectiveness of the proposed strategy. The proposed strategy also enhances sustainability by improving local renewable energy accommodation, reducing reliance on upstream grid electricity, and supporting more resilient operation of interconnected microgrids under uncertainty. Full article

Shared energy storage provides a promising solution for the operation of microgrid clusters. This paper explores a hybrid electric–hydrogen shared energy storage model within microgrid clusters, aiming for clean energy generation and economical energy supply despite renewable energy’s unpredictability and complex stakeholder interactions. First, the proposed method features a shared energy storage operator that hosts electric storage and power-to-gas, enabling multi-microgrids energy sharing. To address market dynamics, a hybrid game theory approach using Nash bargaining and Stackelberg games is employed to manage interactions among the shared energy storage operator, microgrid operators, and internal end-users, while accounting for their differing interests. Second, to address uncertainty in renewable energy output, a distributionally robust optimization model is implemented with conditional value at risk, focusing on risk in extreme scenarios. The Adaptive Alternating Direction Method of Multipliers algorithm and Karush–Kuhn–Tucker conditions are used to solve the optimal decision scheme for each entity. Finally, a case study is used to verify the model’s effectiveness. Simulation results show that hybrid electric–hydrogen energy sharing improves resource utilization, leading to significant revenue increases for microgrids and higher profitability for shared energy storage operator. The game-theory-based approach ensures equitable revenue distribution and a 9.86% increase in coalition revenue. It provides a flexible approach to balance economic efficiency and system robustness by allowing decision-makers to adjust risk preference parameters and use historical sample data for informed decision-making. Full article

Wireless Body Area Network (WBAN) is an emerging medical health monitoring technology. However, WBANs encounter critical challenges in balancing reliability, energy efficiency, and Quality of Service (QoS) requirements for life-critical medical data. The design of its Medium Access Control (MAC) protocol has challenges since dynamic body-shadowing effects and heterogeneous traffic patterns. In this paper, we propose the Nash Bargaining Rate-optimization MAC (NBR-MAC), a hybrid MAC protocol that integrates TDMA-based Guaranteed Time Slots (GTS) with CSMA/CA-based contention access. Unlike traditional schemes, we model the rate allocation as an Asymmetric Nash Bargaining Game, introducing a rigorous disagreement point to guarantee minimum service for critical nodes. The utility function is normalized to resolve dimensional inconsistencies, incorporating sensor priority, buffer status, and channel quality. The Nash Bargaining solution is derived after proving convexity and verifying the axioms. Superframe time slots are allocated based on sensor data priority. Simulation results demonstrate that the proposed protocol enhances transmission success ratio and throughput while reducing packet age and energy consumption under different load conditions. Full article

To address the challenges of renewable energy curtailment under normal conditions and severe power outages under extreme scenarios, this paper proposes a hydrogen-integrated comprehensive energy system (H-IES) configuration method aimed at enhancing the resilience of distribution networks. The proposed method improves energy utilization efficiency while achieving a balance between economic performance and resilience. First, an operational model of the H-IES is established considering the operating characteristics of distribution networks under extreme conditions. On this basis, a Nash bargaining-based equilibrium model is developed, where economic performance and resilience act as game participants negotiating toward equilibrium. By applying the particle swarm optimization algorithm, the Nash equilibrium solution is obtained, realizing a Pareto-optimal trade-off between the two objectives. Finally, case studies demonstrate that the proposed configuration improves the resilience index by 3.13% and reduces total cost by 10.86% compared with mobile battery energy storage. Under the Nash bargaining framework, the equilibrium configuration increases renewable energy utilization and provides up to 21.6% higher resilience compared with an economy-only optimization scheme. Full article

Against the backdrop of the full market integration of renewable energy, determining a reasonable proportion between medium- and long-term (MLT) contracts and spot trading has become a core issue in power market reform. Current Chinese policy requires that the share of MLT contracts should not be less than 90%, which helps ensure system security but may suppress the price discovery function of the spot market and limit renewable energy integration. This paper constructs a three-layer model: the first layer describes spot market clearing through Direct Current Optimal Power Flow (DC-OPF), yielding system energy prices and nodal prices; the second layer models bilateral contract decisions between generators and users based on Nash bargaining, incorporating risk preferences via a mean–variance framework; and the third layer introduces two evaluation indicators—contract penetration rate and economic proportion—and applies outer-layer optimization to search for the optimal contract ratio. Parameters are calibrated using coal prices, wind speed, solar irradiance, and load data, with numerical solutions obtained through Monte Carlo simulation and convex optimization. Results show that increasing the share of spot trading enhances overall system efficiency, primarily because renewable energy has low marginal costs and high supply potential, thereby reducing average market prices and mitigating volatility. Simulations indicate that the optimal contract coverage rate may exceed the current policy lower bound, which would expand spot market space and promote renewable energy integration. Sensitivity analysis further reveals that fuel price fluctuations, renewable output, load structure, and risk preferences all affect the optimal proportion, though the overall conclusions remain robust. Policy implications suggest moderately relaxing the constraints on MLT contract proportions, improving contract design, and combining this with transmission expansion and demand response, in order to establish a more efficient and flexible market structure. Full article

With the rapid expansion of digital knowledge platforms and intelligent information systems, organizations and communities are producing a vast number of unstructured knowledge data, including annotated corpora, technical diagrams, collaborative whiteboard content, and domain-specific multimedia archives. However, knowledge sharing across institutions is hindered by privacy risks, high communication overhead, and fragmented ownership of data. Federated learning promises to overcome these barriers by enabling collaborative model training without exchanging raw knowledge artifacts, but its success depends on motivating data holders to undertake the additional computational and communication costs. Most existing incentive schemes, which are based on non-cooperative game formulations, neglect unstructured interactions and communication efficiency, thereby limiting their applicability in knowledge-driven scenarios. To address these challenges, we introduce SC-NBTI, a smart contract and Nash bargaining-based incentive framework for federated learning in knowledge collaboration environments. We cast the reward allocation problem as a cooperative game, devise a heuristic algorithm to approximate the NP-hard Nash bargaining solution, and integrate a probabilistic gradient sparsification method to trim communication costs while safeguarding privacy. Experiments on the FMNIST image classification task show that SC-NBTI requires fewer training rounds while achieving 5.89% higher accuracy than the DRL-Incentive baseline. Full article

In the context of the coordinated operation of microgrids and community energy storage systems, achieving optimal resource allocation under complex and uncertain conditions has emerged as a prominent research focus. This study proposes a robust collaborative optimization model for microgrids and community energy storage systems under a game-theoretic environment where potential fraudulent behavior is considered. A multi-energy collaborative system model is first constructed, integrating multiple uncertainties in source-load pricing, and a max-min robust optimization strategy is employed to improve scheduling resilience. Secondly, a game-theoretic model is introduced to identify and suppress manipulative behaviors by dishonest microgrids in energy transactions, based on a Nash bargaining mechanism. Finally, a distributed collaborative solution framework is developed using the Alternating Direction Method of Multipliers and Column-and-Constraint Generation to enable efficient parallel computation. Simulation results indicate that the framework reduces the alliance’s total cost from CNY 66,319.37 to CNY 57,924.89, saving CNY 8394.48. Specifically, the operational costs of MG1, MG2, and MG3 were reduced by CNY 742.60, CNY 1069.92, and CNY 1451.40, respectively, while CES achieved an additional revenue of CNY 5130.56 through peak shaving and valley filling operations. Furthermore, this distributed algorithm converges within 6–15 iterations and demonstrates high computational efficiency and robustness across various uncertain scenarios. Full article

Under carbon emission constraints, to promote low-carbon transformation and achieve the aim of carbon peaking and carbon neutrality in the energy sector, this paper constructs an operational optimization model for the coordinated operation of a virtual power plant cluster (VPPC). Considering the resource characteristics of different virtual power plants (VPPs) within a cooperative alliance, we propose a multi-VPP interaction and sharing architecture accounting for electricity–carbon interaction. An optimization model for VPPC is developed based on the asymmetric Nash bargaining theory. Finally, the proposed model is solved using an alternating-direction method of multipliers (ADMM) algorithm featuring an improved penalty factor. The research results show that P2P trading within the VPPC achieves resource optimization and allocation at a larger scale. The proposed distributed ADMM solution algorithm requires only the exchange of traded electricity volume and price among VPPs, thus preserving user privacy. Compared with independent operation, the total operation cost of the VPPC is reduced by 20.37%, and the overall proportion of new energy consumption is increased by 16.83%. The operation costs of the three VPPs are reduced by 1.12%, 20.51%, and 6.42%, respectively, while their carbon emissions are decreased by 4.47%, 5.80%, and 5.47%, respectively. In addition, the bargaining index incorporated in the proposed (point-to-point) P2P trading mechanism motivates each VPP to enhance its contribution to the alliance to achieve higher bargaining power, thereby improving the resource allocation efficiency of the entire alliance. The ADMM algorithm based on the improved penalty factor demonstrates good computational performance and achieves a solution speed increase of 15.8% compared to the unimproved version. Full article

Establishing a partnership necessitates agreeing on how to divide future profits or losses. We consider parties who wish to contract on the division of uncertain future profits. We propose to divide profits according to the Raiffa–Kalai–Smorodinsky (K-S) solution, which is the intersection point of the feasible region’s boundary and the line connecting the disagreement and ideal points. It is the only function which satisfies invariance to linear transformations, symmetry, strong Pareto optimality, and monotonicity. We formulate the general problem of designing a contract which divides uncertain future profit between the partners and determines shares of each partner. We first focus on linear and, later, non-linear contracts between two partners, providing analytical and numerical solutions for various special cases in terms of the utility functions of the partners, their beliefs, and the disagreement point. We then generalize the analysis to any number of partners. We also consider a contract which is partially based on the parties’ financial contribution to the partnership, which have a positive impact on profit. Finally, we address asymmetric K-S solutions. K-S solutions are seen to be a useful predictor of the outcome of negotiations, similar to Nash’s bargaining solution. Full article

Under the goal of “dual carbon”, the power market and carbon market are developing synergistically, which is strongly promoting the transformation of the power system in a clean and low-carbon direction. In order to realise the synergistic optimisation of multi-virtual power plants, economic and low-carbon operation, and the reasonable distribution of revenues, this paper proposes a multi-VPP power–carbon sharing operation optimisation strategy considering multiple uncertainties. Firstly, a cost model for each VPP power–carbon sharing considering the uncertainties of market electricity price and new energy output is established. Secondly, a multi-VPP power–carbon sharing operation optimisation model is established based on the Nash negotiation theory, which is then decomposed into a multi-VPP coalition cost minimisation subproblem and a revenue allocation subproblem based on asymmetric bargaining. Thirdly, the variable penalty parameter alternating directional multiplier method is used for the solution. Finally, an asymmetric bargaining method is proposed to quantify the contribution size of each participant with a nonlinear energy mapping function, and the VPPs negotiate with each other regarding the bargaining power of their electricity–carbon contribution size in the co-operation, so as to ensure a fair distribution of co-operation benefits and thus to motivate and maintain a long-term and stable co-operative relationship among the subjects. Example analyses show that the method proposed in this paper can significantly increase the revenue level of each VPP and reduce carbon emissions and, at the same time, improve the ability of VPPs to cope with uncertain risks and achieve a fair and reasonable distribution of the benefits of VPPs. Full article

In the vigorous development of the power system, to address the economic challenges of multi-microgrid systems, this paper proposes a Nash bargaining model for collaboration between microgrid operators (MGs) and a distribution system operator (DSO) under conditions of multiple uncertainties. Firstly, a model for energy transactions between multiple complementary microgrid systems and a distribution system is established. Secondly, the chance-constrained method and robust optimization method are applied to model the multiple uncertainties in renewable energy generation and electricity trading prices. Moreover, using Nash bargaining theory, a cooperative operation model between MGs and a DSO is established, which is then transformed into two subproblems: cost minimization in cooperation and revenue maximization from power trading. To protect the privacy of each participant, a distributed solution approach using the alternating direction method of multipliers (ADMM) is applied to solve these subproblems. Finally, the simulation results indicate that the benefit values of all entities have improved after cooperative operation through the proposed model. Specifically, the benefit value of MG 1 is CNY 919,974.3, MG 2 is CNY 1,420,363.2, MG 3 is CNY 790,288.3, and the DSO is CNY 26,257.2. These results demonstrate that the proposed model has favorable economic performance. Full article

The intensifying overexploitation of water resources and the increasing pollution discharge have exacerbated conflicts in water resource utilization, making it urgent to effectively reconcile the contradiction between water resource utilization and environmental protection. This study developed a Cost-Inclusive Multi-Objective Bargaining Methodology (CIMB), coupled with a Compromise Programming (CP) method, to address conflicts between water use and pollution discharge, considering the economic benefits and the sustainable development of water resources. A deterministic multi-objective bargaining approach was employed, with two players representing the maximization of water use benefits and the minimization of total pollution discharge. This study takes the middle and lower reaches of the Han River region as an example to optimize water resource allocation in ten cities in this area. Using the CIMB-CP model, the water use and pollution discharge for different cities were obtained, and the impact of various factors on the game outcomes was analyzed. The model results indicate that negotiation cost have a significant impact on the Nash equilibrium solution. Compared to the Cost-Exclusive Multi-Objective Bargaining Methodology (CEMB) model, the Nash equilibrium solution of the CIMB-CP model shows an approximately 0.1% decrease in economic benefits and an approximately 0.3% decrease in pollution discharge. The risk attitudes of the participants have a significant impact on the game outcomes, and decision-makers need to formulate corresponding negotiation strategies based on their own risk preferences. Full article

This paper proposes a two-stage, three-layer stochastic robust model and its solution method for a multi-energy access system (MEAS) considering different weather scenarios which are described through scenario probabilities and output uncertainties. In the first stage, based on the principle of the master–slave game, the master–slave relationship between the grid dispatch department (GDD) and the MEAS is constructed and the master–slave game transaction mechanism is analyzed. The GDD establishes a stochastic pricing model that takes into account the uncertainty of wind power scenario probabilities. In the second stage, considering the impacts of wind power and photovoltaic scenario probability uncertainties and output uncertainties, a max–max–min three-layer structured stochastic robust model for the MEAS is established and its cooperation model is constructed based on the Nash bargaining principle. A variable alternating iteration algorithm combining Karush–Kuhn–Tucker conditions (KKT) is proposed to solve the stochastic robust model of the MEAS. The alternating direction method of multipliers (ADMM) is used to solve the cooperation model of the MEAS and a particle swarm algorithm (PSO) is employed to solve the non-convex two-stage model. Finally, the effectiveness of the proposed model and method is verified through case studies. Full article