Nash Bargaining Game Model Research Articles

Capacity and operation joint optimization for integrated energy system based on Nash bargaining game

Integrated energy systems (IESs) can uniformly coordinate different locations and diversified forms of energy systems, which is critical for ensuring low-carbon and sustainable energy usage. This paper proposed a capacity and operation joint optimization method for an IES with multiple interconnected energy hubs (EHs) based on the Nash bargaining game. Firstly, considering the uncertainty of the EH, robust optimization was carried out for both long-term capacity planning and short-term operational strategies at the same stage. Furthermore, the optimization of the single EH is embedded in the cooperative framework of the IES, and it is formulated as an asymmetrical Nash bargaining game model, in which the players bargain over the transaction energy. Finally, this game model is solved by the alternating direction method of multipliers algorithm. Case studies with a typical IES including three EHs are conducted to verify the effectiveness of the proposed methods. It was found that the proposed joint optimization method has better computational ability than traditional two-stage method. The asymmetrical bargaining solution can not only effectively reduce the cost of the IES, but also help achieve a fair benefit balance among EHs.

Nash Bargaining Game Enhanced Global Malmquist Productivity Index for Cross-Productivity Index

The Global Malmquist Productivity Index (GMPI) stands as an evolution of the Malmquist Productivity Index (MPI), emphasizing global technology to incorporate all-time versions of Decision-Making Units (DMUs). This paper introduces a novel approach, integrating the Nash Bargaining Game model with GMPI to establish a Cross-Productivity Index. Our primary objective is to develop a comprehensive framework utilizing the Nash Bargaining Game model to derive equitable common weights for different time versions of DMUs. These weights serve as a fundamental component for cross-evaluation based on GMPI, facilitating a holistic assessment of DMU performance over varying time periods. The proposed index is designed with essential properties: feasibility, non-arbitrariness concerning the base time period, technological consistency across periods, and weight uniformity for GMPI calculations between two-time versions of a unit. This research amalgamates cross-evaluation and global technology while employing geometric averages to derive a conclusive cross-productivity index. The core motivation behind this methodology is to establish a reliable and fair means of evaluating DMU performance, integrating insights from Nash Bargaining Game principles and GMPI. This paper elucidates the rationale behind merging the Nash Bargaining Game model with GMPI and outlines the objectives to provide a comprehensive Cross-Productivity Index, aiming to enhance the robustness and reliability of productivity assessments across varied time frames.

A Nash bargaining model for energy sharing between micro-energy grids and energy storage

Micro-energy grids (MEGs) play a crucial role in achieving diverse energy utilization and promoting low-carbon economies. However, the intermittent nature of distributed generation and the inter-coupling of multiple energy types pose challenges to efficient energy management in MEGs. In this paper, we propose a novel Nash bargaining game-based electricity-gas energy-sharing model for MEGs. Our model incorporates bus structure-based energy storage combined with power-to-gas technology, which enables MEGs to establish an integrated electricity-gas energy-sharing network. This network facilitates both direct sharing and buffered sharing of energy, addressing the limitations of intermittent generation and enhancing overall energy management. To address the issue of computational complexity, the proposed Nash bargaining game model is decomposed into two sub-problems: social energy cost minimization and benefits sharing. Through optimization, we obtain optimal energy-sharing profiles and energy-sharing payments. Moreover, we consider the investment payback period of energy storage and adjust the initial benefit-sharing results accordingly. Case studies demonstrate that our model significantly improves economic performance, increasing the self-sufficiency ratio of MEGs to 64% and energy storage efficiency to 63% compared to operating independently. Additionally, the multiplayer Nash bargaining game model facilitates Pareto optimal benefits for MEGs and energy storage by capturing their interactive dynamics.

Energy trading and scheduling in networked microgrids using fuzzy bargaining game theory and distributionally robust optimization

To ensure the robust performance of networked microgrids (MGs) against uncertainty and provide a fair energy trading scheme, this paper proposes a decentralized bi-level energy trading and scheduling framework equipped with an innovative incentive mechanism. The upper-level determines the robust decisions of internal scheduling within MGs and peer-to-peer (P2P) energy trading between MGs using a distributionally robust optimization model under an ambiguity set formed by principal component analysis (PCA). The ambiguity set accurately captures distributional information from renewable power generation data, reducing the unnecessary conservatism of robust solutions. The lower-level develops an asymmetric Nash bargaining game model with a new index, named fuzzy bargaining power (FBP), to fairly allocate trading benefits to MGs. This fuzzy index incentivizes MGs to proactively trade energy throughout the entire day, not just when energy selling or buying is in their interest. The upper and lower level problems are solved in a privacy-preserving manner by proposing a decentralized optimization algorithm based on the asynchronous alternating direction method of multipliers (ADMM). Numerical tests demonstrate the effectiveness of the proposed models in terms of solution robustness, profit distribution fairness, and computational performance.

Assessing the policy synergy among power, carbon emissions trading and tradable green certificate market mechanisms on strategic GENCOs in China

The establishment of carbon emissions trading (CET) and tradable green certificate (TGC) markets in China will cause great alterations in the bidding behavior for generation companies (GENCOs) and affect the low-carbon transformation of power industry. In this paper, a Nash bargaining game model is constructed to assess the synergy of power, CET and TGC markets on decision behavior of non-renewable energy GENCOs, renewable energy GENCOs and power purchasers. The simulation results show that there is transition incentive effect, price interaction effect and profit blocking effect between three markets. With the introduction of emissions trading scheme and renewable portfolio standard (RPS), the scheduled power of renewable energy GENCOs will increase by 21.43%, and transaction prices will reduce to 449.58 CNY/MWh; while the scheduled power of non-renewable energy GENCOs will reduce by 4.66%, and transaction prices will increase to 443.71 CNY/MWh, which make all power generation types compete at equivalent price level. Under the current installed capacity distribution and load demand, it is the critical point when RPS is 18.7% and the benchmark value of free carbon quota for units above and below 300 MW are 0.857 tCO2/MWh and 0.959 tCO2/MWh. Once exceeded, it will affect social benefits and emission reduction efficiency.

Privacy-preserving energy trading management in networked microgrids via data-driven robust optimization assisted by machine learning

Trading mechanism design, uncertainty treatment and privacy protection are the main issues in the energy management of networked microgrids (MGs). To address these issues in a comprehensive manner, this paper proposes a data-driven two-level transactive energy management framework, where the upper-level determines the optimal strategies of internal scheduling within MGs and external trading between MGs while the lower-level formulates a Nash bargaining game model for the fair allocation of trading benefits. The uncertainties of renewable energy sources are fully captured by an adjustable data-driven robust optimization approach with an uncertainty set constructed using the robust kernel density estimation (RKDE) as a machine learning technique. The resulting uncertainty set can provide robust scheduling and trading schemes even when the power generation data of wind turbines and photovoltaic systems are contaminated with anomalous samples, whereas conventional sets are not reliable in the case of contaminated data. To preserve the operational independence and information privacy of MGs, the proposed model is solved in a distributed manner by the alternating direction method of multipliers (ADMM) and the augmented Lagrange-based alternating direction inexact Newton (ALADIN) algorithms. ADMM is commonly used in previous studies, but it has low computational efficiency for handling the consensus process among a large number of MGs. This paper applies ADMM and ALADIN to enhance the applicability of the proposed model when the size and complexity of the networks increase. Numerical tests show the effectiveness of the proposed framework and solution methodology in terms of system cost, solution robustness, and convergence speed.

Central robust decision-making structure for reverse supply chain: a real pharmaceutical case

Tons of hazardous pharmaceutical waste is introduced to the environment each year, showing the significance of medicines reverse channels. Meanwhile, establishing a pharmaceutical reverse channel is complex and costly, and therefore misestimation of uncertainty in waste collection operations can lead to severe financial losses. As conventional methods for uncertainty often fail to mitigate the risk and protect the system, we propose a central robust approach, inspired by scenario-based robust optimization and supply chain coordination concepts, which can significantly reduce waste management costs in the face of uncertainty. We study the profitability in a two-layer reverse channel, where the initial number of unwanted medications is subject to discrete uncertainty. Then, we extend our problem, assuming that the customer willingness to return the items is subject to random uncertainty. A non-linear programming model, a flexible transfer price agreement, and the Nash-bargaining game model are developed to optimize and coordinate the system performance. The analytical results provide reliable insights for industry owners to manage uncertainty in the collection process. We illustrate that implementing the proposed model boosts the return quantity, leads to a remarkable improvement in the profitability of the entire chain, and improves the system adaptability with respect to changing significant market parameters or revenue fluctuations.

Two-stage water resources allocation negotiation model for transboundary rivers under scarcity

In this article, the bankruptcy theory and bargaining games are used to construct a two-stage water resources allocation negotiation model (TSANM). A Nash-bargaining game model is used for the initial allocation, followed by an adjustment stage which considers factors such as water circumstances, water satisfaction, water risk, and water efficiency. The TSANM systematically considers the multi-dimensional attributes of water resources in the allocation process and may likely increase the participation of riparian countries. The proposed method is applied to allocate the contested water capital of the Tigris-Euphrates River. This gives initial allocation to Turkey, Syria, and Iraq of 30.00%, 22.00%, and 48.00%, respectively, and adjusted allocation of 24.98%, 21.30%, and 53.72%. Through collective bargaining and group negotiation, the stability and acceptability of allocation are effectively improved, absolute egalitarianism and utilitarianism are both avoided, and instead objectivity and fairness are emphasized in the water resources allocation process.

Second order cone programming formulation of the fixed cost allocation in DEA based on Nash bargaining game

<p style='text-indent:20px;'>A vital issue in many organizations is the fair allocation of fixed cost among its subsets. In this paper, using data envelopment analysis, first we study fixed cost allocation based on both additive and multiplicative efficiency decompositions in the cooperative context for a two-stage structure in the presence of exogenous inputs and outputs. A conic relaxation formulation of multiplicative decomposition is given. Then, fixed cost allocation based on the leader-follower paradigm are presented. In the sequel, for allocating a fair fixed cost between the stages, using the results of the leader-follower model, we present the nonlinear Nash bargaining game model that independent of the efficiency score of each unit, allocates fixed cost to the stages. The nonlinear model is reformulated as a second order cone program which is an imporvement over the parametric linear models in the literature. Finally, two examples are used to illustrate the proposed models and compare their results with the existing models.</p>

Centralized Resource Allocation Based on the Bargaining Approach

In a centralized decision-making environment, the central unit supervises all the operating units’ production activities and focuses on achieving the overall goals of the entire organization from a global viewpoint by allocating available resources to them. However, all the current models about resource allocation under the centralized decision-making commonly exhibit the non-unique optimal solutions and neglect the competition and trade-off among all the DMUs to maximize the individual aggregated output of each DMU. This phenomenon makes the allocation result imbalanced and unacceptable to all the DMUs. To overcome this problem, this paper introduces Nash bargaining game theory to develop a new centralized resource allocation model which not only takes into account the overall goals of the organization from an overall perspective, but also considers competition and trade-off among all the DMUs. Finally, an empirical example is used to demonstrate the applicability of our proposed approach. The results show that our Nash bargaining game model not only guarantees the uniqueness of the optimal resource allocation results, but also improves the balance of the resource allocation result, which makes it acceptable to all the DMUs.

A novel cooperative game-based method to coordinate a sustainable supply chain under psychological uncertainty in fairness concerns

This paper investigates how retailers’ fairness concerns affect cooperative relationships in a three-party sustainable supply chain (TSSC) and how to coordinate such a supply chain when the degree of fairness concern is treated as an interval. Utilizing the Nash equilibrium strategy, this study seeks equilibrium solutions and profits under five non-cooperative and cooperative models and reveals that fairness concerns indeed affect members’ decisions and their cooperation for sustainable supply chain management. Furthermore, we develop a novel coordination method by incorporating the interval-valued least square pre-nucleolus (IVLSPN) approach and the three-party Nash bargaining game model to perfectly coordinate this TSSC.

Drug recall management and channel coordination under stochastic product defect severity: a game-Theoretic analytical study

This paper analytically explores drug recall programmes in the pharmaceutical industry by considering the product defect severity as a source of uncertainty. Under the Stackelberg game model, a pharma-manufacturer outsources the drug recall management and pays collecting fees to a third party logistics provider (3PL) for collecting the defective medications. On the other side, the 3PL provides incentives to customers to facilitate product recall. In this research, we first analytically show the negative effect of lack of coordination between the pharma-manufacturer and 3PL. Then, a new coordination model, namely collecting fee agreement is proposed under which the pharma-manufacturer aims to motivate the 3PL to collect more defective medications. This research also analytically explores the effect of orchestrating the collecting fees and incentives under stochastic product defect severity. Finally, a Nash-bargaining game model is proposed to share the profits between the pharma-manufacturer and 3PL under the collecting fee agreement. Both analytical and numerical results reveal that the collecting fee agreement not only increases the collection rate of defective items and protects the patients from unsafe products, but also simultaneously improves the performances of whole pharmaceutical supply chain and its members while reducing the governmental penalties imposed on the pharma-manufacturer.

An Efficient Dynamic Load Balancing Scheme Based on Nash Bargaining in SDN

Static multi-controller deployment architecture cannot adapt to the drastic changes of network traffic, which will lead to a load imbalance between controllers, resulting in a high packet loss rate, high latency, and other network performance degradation problems. In this paper, an efficient dynamic load balancing scheme based on Nash bargaining is proposed for a distributed software-defined network. Firstly, considering the connectivity of network nodes, the switch migration problem is transformed into a network mapping relationship reconstruction problem. Then, we establish the Nash bargaining game model to fairly optimize the two contradictory goals of migration cost and load balance. Finally, the model is solved by an improved firefly algorithm, and the optimal network mapping state is obtained. The experimental results show that this scheme can optimize the migration cost and load balance at the same time. Compared with the existing research schemes, the migration process of the switch is optimized, and, while effectively balancing the load of the control plane, the migration cost is reduced by 14.5%.

A bargaining game model for performance assessment in network DEA considering sub-networks: a real case study in banking

Several network-data envelopment analysis (DEA) performance assessment models have been proposed in the literature; however, the conflicts between stages and insufficient number of decision-making units (DMUs) challenge the researchers. In this paper, a novel game-DEA model is proposed for efficiency assessment of network structure DMUs. We propose a two-stage modeling, where in the first stage network is divided into several sub-networks; we at the same time categorize input variables to measure efficiency of sub-networks within each input category. In the second stage, we calculate efficiency of the network by aggregating efficiency scores of sub-networks within each category. In this way, the issue of insufficient number of DMUs when there are many input/output variables can be handled as well. One of the main contributions of this paper is assuming each category and stage as a player in Nash bargaining game. Using the concept borrowed from Nash bargaining game model, the proposed game-DEA model tries to maximize distances of efficiency scores of each player form their corresponding breakdown points. The usefulness of the model is presented using a real case study to measure the efficiency of bank branches.

Target intermediate products setting in a two-stage system with fairness concern

In a two-stage system with two divisions connected in series, fairly setting the target outputs for the first stage or equivalently the target inputs for the second stage is critical, in order to ensure that the two stages have incentives to collaborate with each other to achieve the best performance of the whole system. Data envelopment analysis (DEA) as a non-parametric approach for efficiency evaluation of multi-input, multi-output systems has drawn a lot of attention. Recently, many two-stage DEA models were developed for studying the internal structures of two-stage systems. However, there was no work studying fair setting of the target intermediate products (or intermediate measures) although unreasonable setting will result in unfairness to the two stages because setting higher (fewer) intermediate measures means that the first (second) stage must make more efforts to achieve the overall production plan. In this paper, a new DEA model taking account of fairness in the setting of the intermediate products is proposed, where the fairness is interpreted based on Nash bargaining game model, in which the two stages negotiate their target efficiencies in the two-stage system based on their individual efficiencies. This approach is illustrated by an empirical application to insurance companies.

Supplier evaluation based on Nash bargaining game model

Traditional DEA method is improper for supplier evaluation and selection, as it adopts varying weights in evaluation, and fails to consider competition among the suppliers. In order to solve these two problems, Nash bargaining game DEA model is applied to supplier evaluation in present paper. However, there is a non-uniqueness problem with Nash bargaining game efficiency of supplier in existing Nash bargaining game DEA model. The existing Nash bargaining game DEA model is improved in present paper on this issue, then the improved model is applied to the third party logistics service provider evaluation. The result of supplier evaluation based on the improved model is more persuasive compared with the existing research achievement, owing to adopting common weights in evaluation, and the game between suppliers being taken account.

A bargaining game model for efficiency decomposition in the centralized model of two-stage systems

Data envelopment analysis (DEA) is a non-parametric approach for measuring the relative efficiencies of peer decision making units (DMUs). The centralized model has been widely used to examine the efficiencies of two-stage systems, where all the outputs from the first stage are the only inputs to the second stage. Since there may exist some flexibility in decomposing the overall efficiency between the two stages when multiple optimal weights exist, we develop a Nash bargaining game model to obtain a fair efficiency decomposition for the two stages while keeping the overall efficiency unchanged under this circumstance. The minimal achievable efficiencies for the two stages are used as the breakdown point and the unique bargaining decomposition of the overall efficiency is obtained subsequently. The Nash bargaining game model is applied to evaluate the performance of 10 branches of China Construction Bank.

Nash bargaining game model for two parallel stages process evaluation with shared inputs

Data envelopment analysis is a non-parametric technique for evaluating peer decision making units (DMUs) with using multiple inputs to produce multiple outputs. In the real world, DMUs usually have complex structures. One of these structures is a two-stage process with intermediate measures. In this structure, there are two stages and each stage uses inputs to produce outputs, separately where the outputs of the first stage are the inputs for the second stage. Cooperative model such as centralized model and non-cooperative model are game theoretic approaches to evaluate two-stage processes. Non-cooperative model supposes that one of the stages is the leader and another stage is the follower, whereas in the centralized model, both stages are evaluated simultaneously. In this paper, we propose a game theoretic model based on the Nash bargaining game to calculate weights when parallel stages with shared inputs compete to reach a high efficiency in the competitive strategy. Two data sets including the bank branches and thermal power plants in Iran are used to show the abilities of proposed model. This model can be applied in other processes such as supply chain, manufacturing and public service units.

A bargaining game model for measuring performance of two-stage network structures

Data envelopment analysis (DEA) is a method for measuring the efficiency of peer decision making units (DMUs), where the internal structures of DMUs are treated as a black-box. Recently DEA has been extended to examine the efficiency of DMUs that have two-stage network structures or processes, where all the outputs from the first stage are intermediate measures that make up the inputs to the second stage. The resulting two-stage DEA model not only provides an overall efficiency score for the entire process, but also yields an efficiency score for each of the individual stages. The current paper develops a Nash bargaining game model to measure the performance of DMUs that have a two-stage structure. Under Nash bargaining theory, the two stages are viewed as players and the DEA efficiency model is a cooperative game model. It is shown that when only one intermediate measure exists between the two stages, our newly developed Nash bargaining game approach yields the same results as applying the standard DEA approach to each stage separately. Two real world data sets are used to demonstrate our bargaining game model.

Bargaining game model in the evaluation of decision making units

Data envelopment analysis (DEA) has been proven an effective tool for performance evaluation and benchmarking, which can provide a relative efficiency measure for peer decision making units (DMUs) with multiple inputs and outputs. Nevertheless, its flexibility in weighted inputs and weighted outputs as well as its nature of self-evaluation has been criticized. The cross-evaluation method is developed as a DEA extensive tool being utilized to identify the best practice DMUs and to rank all DMUs using cross-efficiency scores that are associated with all DMUs, however, it still seems imperfect since the non-uniqueness of cross-efficiency measure possibly derogates the practicability of this method, and especially, the average cross-efficiency measure is not a Pareto one, so not all DMUs have the motivation to accept it. In this paper, we adopt a Nash bargaining game to improve the usual cross efficiency evaluation method. In the game, each DMU will be an independent player, and the bargaining solution between CCR efficiency and cross-efficiency can be obtained by using the classical Nash bargaining game model. The advantage of the bargaining efficiency lies on that it is a Pareto one and all the DMUs will have motivation to accept it, as well as that the adoption of common weights in evaluation will result in the equitableness of ranking all DMUs. Finally, the comparisons of those efficiency scores mentioned above and the corresponding weights are demonstrated by an example of R&D project selection.