Profit Allocation Scheme Among Players in Supply-Chain Based on Shapley Value of Fuzzy Bi-cooperative Games

The Shapley value of fuzzy bi-eooperative game is developed based on the conventional Shapley value of bi-cooperative game. From the viewpoint that the players can participate in the coalitions to a certain extent and there are at least two independent cooperative projects for every player to choose, Shapley value which is introduced by Grabisch is extended to the case of fuzzy bi-cooperative game by Choquet integral. Moreover, the explicit fuzzy Shapley value is given. The explicit fuzzy Shapley function can be used to allocate the profits among players in supply-chain under the competitive and uncertain environment.

Profit Allocation Scheme among Partners in Virtual Enterprises Based on Fuzzy Shapley Values

Fuzzy Shapley values are developed based on classical Shapley values and used to allocate profit among partners in virtual enterprises （VE）. Axioms of the classical Shapley value are extended to Shapley values with fuzzy payoffs by using fuzzy sets theory. Fuzzy Shapley function is defined based on these extended axioms. From the viewpoint the allocation for each partner should be a crisp value rather a fuzzy membership function at the end of cooperation, a crisp allocation scheme based on fuzzy Shapley values is proposed.

Shapley Value for Cooperative Games with Fuzzy Coalition

Fuzzy Shapley values are developed based on conventional Shapley value. This kind of fuzzy cooperative games admit the representation of rates of players＇ participation to each coalition. And they can be applicable to both supperadditive and subadditvie cooperative games while other kinds of fuzzy cooperative games can only be superadditive. An explicit form of the Shapley function on fuzzy games with λ-fuzzy measure was also proposed.

Risk Sharing Method of PPP Model for Rural Sewage Treatment - Based on Interval Fuzzy Shapley Value

Rural sewage treatment is in need of more capital investment,in which the financing model of PPP(public-private partnership)is able to encourage the investment of social capital in this sector.Risk sharing is one of the core features in the PPP model.In view that the risk loss of projects cannot be accurately estimated,this article describes the uncertainty of risk loss with fuzzy numbers and allocates the distribution of risk loss among the participants of rural sewage treatment PPP projects with interval fuzzy Shapley value to ensure a more reasonable and effective risk distribution.

Benefit allocation of electricity-gas-heat-hydrogen integrated energy system based on Shapley value

The integrated energy system is an important development direction for achieving energy transformation in the context of the low-carbon development era,and an integrated energy system that uses renewable energy can reduce carbon emissions and improve energy utilization efficiency.The electric power network and the natural gas network are important transmission carriers in the en-ergy field,so the coupling relationship between them has been of wide concern.This paper establishes an integrated energy system considering electricity,gas,heat and hydrogen loads;takes each subject in the integrated energy system as the research object;anal-yses the economic returns of each subject under different operation modes;applies the Shapley value method for benefit allocation;and quantifies the contribution value of the subject to the alliance through different influencing factors to revise the benefit allocation value.Compared with the independent mode,the overall benefits of the integrated energy system increase in the cooperative mode and the benefits of all subjects increase.Due to the different characteristics of different subjects in terms of environmental benefits,collaborative innovation and risk sharing,the benefit allocation is reduced for new-energy subjects and increased for power-to-gas sub-jects and combined heat and power generation units after revising the benefit allocation,to improve the matching degree between the contribution level and the benefit allocation under the premise of increased profit for each subject.The cooperative mode effectively enhances the economic benefits of the system as a whole and individually,and provides a useful reference for the allocation of benefits of integrated energy systems.The analysis shows that the revised benefit distribution under the cooperative model increases by 3.86%,4.08%and 3.13%for power-to-gas subjects,combined heat and power generation units,and new-energy units,respectively,compared with the independent function model.

Simplification of Shapley value for cooperative games via minimum carrier

Shapley value is one of the most fundamental concepts in cooperative games.This paper investigates the calculation of the Shapley value for cooperative games and establishes a new formula via carrier.Firstly,a necessary and sufficient condition is presented for the verification of carrier,based on which an algorithm is worked out to find the unique minimum carrier.Secondly,by virtue of the properties of minimum carrier,it is proved that the profit allocated to dummy players(players which do not belong to the minimum carrier)is zero,and the profit allocated to players in minimum carrier is only determined by the minimum carrier.Then,a new formula of the Shapley value is presented,which greatly reduces the computational complexity of the original formula,and shows that the Shapley value only depends on the minimum carrier.Finally,based on the semi-tensor product(STP)of matrices,the obtained new formula is converted into an equivalent algebraic form,which makes the new formula convenient for calculation via MATLAB.

Shapley value cooperative game theory-based locational marginal price computation for loss and emission reduction

An iterative method based on Shapley Value Cooperative Game Theory is proposed for the calculation of local marginal price (LMP) for each Distributed Generator (DG) bus on a network. The LMP value is determined for each DG on the basis of its contribution to reduce loss and emission reduction, which is assessed using the Shapley Value approach. The proposed approach enables the Distribution Company (DISCO) decision-maker to operate the network optimally in terms of loss and emission. The proposed method is implemented in the Taiwan Power Company distribution network 7 warnings consisting of 84 buses and 11 feeders in the MATLAB environment. The results show that the proposed approach allows DISCO to operate the network on the basis of its priority between the reduction of active power loss and emission in the network.

Market Transition and Income Inequality in Urban China： Evidence from Shapley Value Decomposition

China＇s market-oriented reform is expected to strengthen the role of the market in allocating resources, which raises concerns over the impact of market transformation on income distribution and earnings inequality in the past decades. This paper decomposes the sources of inequality based on the newly developed Shapley value approach and examines the contributions of the market, along with other nonmarket factors, to total inequality. Using the China Health and Nutrition Survey data over the period 1989-2009, we find that the income gap between laborers with a higher level of education and those with a lower level has widened since the transformational reforms of the economy. Our results suggest that the largest contribution of changes in income inequality can be attributed to the increase in returns to education, while the relative contributions of the household registration （hukou） system, type of sector ownership, geographic location, and gender to inequality experienced a downward trend between 1989 and 2009. The authors argue that rising income inequality is the consequence of efficiency improvements and an imperfect economic system, and that the market is a decisive force in economic development as it releases competitive signals and creates incentive mechanisms for innovation. Creating a more efficient labor market and increasing investment in human capital, particularly equalizing educational opportunities and improving the quality of education in lagging rural and inland regions to disadvantaged groups, are significant for an equitable distribution of income and sustainable development in the long run.

The Triple Helix of innovation as a double game involving domestic and foreign actors

Purpose:The collaboration relationships between innovation actors at a geographic level may be considered as grouping two separate layers,the domestic and the foreign.At the level of each layer,the relationships and the actors involved constitute a Triple Helix game.The paper distinguished three levels of analysis:the global grouping together all actors,the domestic grouping together domestic actors,and the foreign related to only actors from partner countries.Design/methodology/approach:Bibliographic records data from the Web of Science for South Korea and West Africa breakdown per innovation actors and distinguishing domestic and international collaboration are analyzed with game theory.The core,the Shapley value,and the nucleolus are computed at the three levels to measure the synergy between actors.Findings:The synergy operates more in South Korea than in West Africa;the government is more present in West Africa than in South Korea;domestic actors create more synergy in South Korea,but foreign more in West Africa;South Korea can consume all the foreign synergy,which is not the case of West Africa.Research limitations:Research data are limited to publication records;techniques and methods used may be extended to other research outputs.Practical implications:West African governments should increase their investment in science,technology,and innovation to benefit more from the synergy their innovation actors contributed at the foreign level.However,the results of the current study may not be sufficient to prove that greater investment will yield benefits from foreign synergies.Originality/value:This paper uses game theory to assess innovation systems by computing the contribution of foreign actors to knowledge production at an area level.It proposes an indicator to this end.

对抗环境中基于种群多样性的鲁棒策略生成方法

在对抗博弈环境中,目标智能体希望生成具有高鲁棒性的博弈策略,使得目标智能体在面对不同对手策略时,始终具有较高的收益。现有的基于自我博弈的策略生成方法通常会过拟合到针对对手某个特定策略进行学习,所学习到的策略鲁棒性低且容易受到其他对手策略的攻击。此外,现有的结合深度强化学习和博弈论方法迭代生成对手策略的方法在复杂且具有庞大决策空间的对抗场景下收敛效率低。鉴于此,提出一种基于种群多样性的鲁棒策略生成方法,其中对抗双方各自维护一个种群策略池,并且需要保证种群中的策略是具有多样性的,以此生成鲁棒的目标策略。为了保证种群多样性,将从策略的行为和质量2个视角度量策略的多样性,其中行为多样性是指不同策略状态-动作轨迹的差异性,质量多样性是指不同策略面对相同对手时最终获得的收益的差异性。最后,在典型的具有连续状态、连续动作的对抗环境中验证了所提出的基于种群多样性所生成的策略的鲁棒性。

Personalized assessment and training of neurosurgical skills in virtual reality:An interpretable machine learning approach

Background Virtual reality technology has been widely used in surgical simulators,providing new opportunities for assessing and training surgical skills.Machine learning algorithms are commonly used to analyze and evaluate the performance of participants.However,their interpretability limits the personalization of the training for individual participants.Methods Seventy-nine participants were recruited and divided into three groups based on their skill level in intracranial tumor resection.Data on the use of surgical tools were collected using a surgical simulator.Feature selection was performed using the Minimum Redundancy Maximum Relevance and SVM-RFE algorithms to obtain the final metrics for training the machine learning model.Five machine learning algorithms were trained to predict the skill level,and the support vector machine performed the best,with an accuracy of 92.41%and Area Under Curve value of 0.98253.The machine learning model was interpreted using Shapley values to identify the important factors contributing to the skill level of each participant.Results This study demonstrates the effectiveness of machine learning in differentiating the evaluation and training of virtual reality neurosurgical performances.The use of Shapley values enables targeted training by identifying deficiencies in individual skills.Conclusions This study provides insights into the use of machine learning for personalized training in virtual reality neurosurgery.The interpretability of the machine learning models enables the development of individualized training programs.In addition,this study highlighted the potential of explanatory models in training external skills.

面向服务等级的网络流多任务分类方法

在网络流分类实践中,网络运营商通常只需要知道网络流所需的服务类别(class of service,CoS),就可对网络流优先级和资源分配做出决定。为了满足用户对体验质量的需求,提出了面向服务等级的网络流多任务分类方法。该方法是直接进行面向CoS的流分类,而不需要推断应用类型。同时提出多任务框架,利用领域知识定义宏特征组及应用合作博弈中的Shapley Value模型来合理分析特征,并用决策树分箱来解决CoS阈值划分问题。采用真实网络数据集进行实验,通过在少量标记数据的情况下,优化网络参数和调整各网络模型时间损耗和分类准确性的稳定相关系数。结果表明,该方法分类准确度(提高了12.66%)和时间消耗(减少了39.23%)性能优于现有文献方法,同时分析了多分类实验结果并给出有关建议。

Interpretable machine learning optimization(InterOpt)for operational parameters:A case study of highly-efficient shale gas development

An algorithm named InterOpt for optimizing operational parameters is proposed based on interpretable machine learning,and is demonstrated via optimization of shale gas development.InterOpt consists of three parts:a neural network is used to construct an emulator of the actual drilling and hydraulic fracturing process in the vector space(i.e.,virtual environment);:the Sharpley value method in inter-pretable machine learning is applied to analyzing the impact of geological and operational parameters in each well(i.e.,single well feature impact analysis):and ensemble randomized maximum likelihood(EnRML)is conducted to optimize the operational parameters to comprehensively improve the efficiency of shale gas development and reduce the average cost.In the experiment,InterOpt provides different drilling and fracturing plans for each well according to its specific geological conditions,and finally achieves an average cost reduction of 9.7%for a case study with 104 wells.

含有风险的供应链联盟伙伴利益分配法

利益分配是供应链联盟形成及运作的核心问题,关系到联盟的稳定与成败。本文在研究供应链联盟利益分配原则的基础上,提出了供应链联盟两步利益分配法,使分配结果体现多劳多得和互惠互利的原则;并根据供应链联盟伙伴在联盟中承担风险的不同,给与相应的风险补偿。

Invasive Species Control Based on a Cooperative Game

We develop a long-term dynamic model for controlling invasive species using the theory of cooperative games. The model is applied to control of invasive buffelgrass in the Arizona desert, which directly competes with indigenous species and can increase wildfire risk. Interest groups care about damages to three threatened resources: saguaro, cactus, riparian vegetation, and buildings. The model optimally allocates labor and a budget to protect these resources by controlling the buffelgrass population over a multi-period planning horizon. The solution is based on computing the Shapley values for the interest groups. A homeowner strategy of creating defensible space around structures to protect against wildfire affords less protection to the other resources. A similar result holds for protection of saguaros, which are also spatially concentrated. Under the optimal solution, groups caring about spatially-dispersed, riparian vegetation would compensate homeowners and groups caring about saguaros for a reallocation of resources toward greater protection of dispersed vegetation. Results highlight the importance of the spatial configuration of players and the resources they wish to protect in invasive species control problems.

A Dynamic Network Game of the Fintech Industry

Economies of scale,economies of scope,and technology spillover are decisive eco-nomic elements that are crucial to the development in the Fintech industry.Thesepositive externalities are often realized through network links.In this paper,we presenta dynamic network offinancialfirms which exhibits these decisive elements.Thenetwork game equilibria are characterized.A Pareto efficient solution involving col-laboration of allfirms is provided.To obtain a fair-share distribution of cooperativegains,the Shapley value is adopted as the sharing mechanism.Payoff distributionmechanisms which guarantee the fulfilment of the Shapley value distribution in eachstage of the cooperation duration are derived.

On the Semivalues and the Least Square Values Average Per Capita Formulas and Relationships

In this paper, it is shown that both the Semivalues and the Least Square Values of cooperative transferable utilities games can be expressed in terms of n^2 averages of values of the characteristic function of the game, by means of what we call the Average per capita formulas. Moreover, like the case of the Shapley value earlier considered, the terms of the formulas can be computed in parallel, and an algorithm is derived. From these results, it follows that each of the two values mentioned above are Shapley values of games easily obtained from the given game, and this fact gives another computational opportunity, as soon as the computation of the Shapley value is efficiently done.

Generalizations of Sobolev’s Consistency and Values for TU-Games

In the framework of cooperative game theory,Sobolev(Advances in game theory,Izdat.,“Minitis”,Vilnius,pp 151–153,1973)axiomatized the well-known Shapley value by means of consistency property with reference to a specifically chosen reduced game.The goal of this paper is to generalize Sobolev’s consistency approach to the class of efficient,symmetric and linear values.

Calculation Model and Allocation Strategy of Network Usage Charge for Peer-to-peer and Community-based Energy Transaction Market

The emergence of prosumers in distribution systems has enabled competitive electricity markets to transition from traditional hierarchical structures to more decentralized models such as peer-to-peer(P2P)and community-based(CB)energy transaction markets.However,the network usage charge(NUC)that prosumers pay to the electric power utility for network services is not adjusted to suit these energy transactions,which causes a reduction in revenue streams of the utility.In this study,we propose an NUC calculation method for P2P and CB transactions to address holistically economic and technical issues in transactive energy markets and distribution system operations,respectively.Based on the Nash bargaining(NB)theory,we formulate an NB problem for P2P and CB transactions to solve the conflicts of interest among prosumers,where the problem is further decomposed into two convex subproblems of social welfare maximization and payment bargaining.We then build the NUC calculation model by coupling the NB model and AC optimal power flow model.We also employ the Shapley value to allocate the NUC to consumers fairly for the NUC model of CB transactions.Finally,numerical studies on IEEE 15-bus and 123-bus distribution systems demonstrate the effectiveness of the proposed NUC calculation method for P2P and CB transactions.

Cooperative Game Theory Based Coordinated Scheduling of Two-Machine Flow-Shop and Transportation

A cooperative game theoretical approach is taken to production and transportation coordinated scheduling problems of two-machine flow-shop(TFS-PTCS problems)with an interstage transporter.The authors assume that there is an initial scheduling order for processing jobs on the machines.The cooperative sequencing game models associated with TFS-PTCS problems are established with jobs as players and the maximal cost savings of a coalition as its value.The properties of cooperative games under two different types of admissible rearrangements are analysed.For TFS-PTCS problems with identical processing time,it is proved that,the corresponding games areσ_(0)-component additive and convex under one admissible rearrangement.The Shapley value gives a core allocation,and is provided in a computable form.Under the other admissible rearrangement,the games neither need to beσ_(0)-component additive nor convex,and an allocation rule of modified Shapley value is designed.The properties of the cooperative games are analysed by a counterexample for general problems.