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Simplification of shapley value for cooperative games via minimum carrier

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Control Theory and Technology 2021年第2期19卷 157-169页

作者： Haitao Li Shuling Wang Aixin Liu Meixia Xia School of Mathematics and Statistics Shandong Normal UniversityJinan250014ShandongChina

shapley value is one of the most fundamental concepts in cooperative *** paper investigates the calculation of the shapley value for cooperative games and establishes a new formula via ***,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 ***,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 ***,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 ***,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.

关键词： shapley value Cooperative game Carrier Algebraic form Semi-tensor product of matrices

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

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Clean Energy 2023年第6期7卷 1381-1390页

作者： Yujiao Liu Yan Li Yiping Rong Guoliang Li Ruiqi Wang Haini Zhou Zaozhuang Power Supply Company of State Grid Shandong Province Electric Power Company Zaozhuang CityShandong 277101China State Grid Shandong Integrated Energy Services Jinan CityShandong 250021China

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 *** 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 *** 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 *** with the independent mode,the overall benefits of the integrated energy system increase in the cooperative mode and the benefits of all subjects *** 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 *** 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 *** 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 m

关键词： integrated energy system power-to-gas shapley value benefit allocation hydrogen energy

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

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Journal of Beijing Institute of Technology 2009年第1期18卷 106-111页

作者：于晓辉张强 School of Management and Economics Beijing Institute of Technology

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.

关键词： fuzzy cooperative game bi-capacity shapley value Choquet integral supply-chain

The Core and shapley value of M Sum-Compound Game

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中国科学院大学学报 1992年第3期 333-340页

作者： Zhao Jingzhu(Research Center for Eco-Environmental Sciences, Academia Sinica)

The M sum-compound game of two games G=(N) and G=(N) with intersection sets of players is defined to be a game G=(N,v),where N=NUNand v(S)=u(S∩M)+u(S∩M)+max{u(S∩M),u(S∩M)} (M=N∩N,M=N-M, i=1,2). The core and Shapl... 详细信息

关键词： M sum-compound game core shapley value

The shapley value of Cooperative Game with Stochastic Payoffs

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The Shapley Value of Cooperative Game with Stochastic Payoff...

Distributionally Robust shapley value Estimator: An Application to Industrial Predictive Modeling

第26届中国控制与决策会议

作者： Cheng-Guo E Quan-Lin Li Shi-Yong Li School of Economics and Management Yanshan University Liren College Yanshan University

ISBN: (纸本)9781479937097

In this paper, we consider cooperative game with stochastic payoffs and give the definition of the shapley value for it, which is obtained by extending the classical case. Then we provide explicit expression for the shapley value of the cooperative game with stochastic payoffs, and discuss its existence and uniqueness. Finally, the properties of the shapley value of convex cooperative game with stochastic payoffs are investigated.

关键词： cooperative game convexity stochastic payoffs shapley value

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Distributionally Robust Shapley Value Estimator: An Applicat...

Matrix expression of shapley values and its application to distributed resource allocation

第35届中国过程控制会议

作者： Cheng Lu Jiusun Zeng Yi Liu BingBing Shen Jinhui Cai Shihua Luo College of Metrology Measurement and Instrument China Jiliang University School of Mathematics Hangzhou Normal University School of Information Science and Engineering Hangzhou Normal University School of Statistics Jiangxi University of Finance and Economics

Predictive models based on deep learning techniques have become one of the most popular data-driven approaches in the industrial process. Nevertheless, these models often lack interpretability due to their black-box nature. In order to interpret the predictions of deep learning models, this paper proposes a novel explainable artificial intelligence(XAI) method based on the shapley value. By introducing the Wasserstein ambiguity set into the interpretability framework of KernelSHAP(Kernel shapley Additive explanation), a distributionally robust shapley value estimator is developed. Furthermore, we illustrate the conversion of this estimator into a regularized estimator and propose an efficient ADMM(Alternating Direction Method of Multipliers) algorithm to solve the optimization problem. An application study on a real-world industrial process validates the effectiveness of the proposed method.

关键词： Explainable artificial intelligence deep learning shapley value predict modeling

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Science China(Information Sciences) 2019年第2期62卷 46-56页

作者： Yuanhua WANG Daizhan CHENG Xiyu LIU School of Management Science and Engineering Shandong Normal University Academy of Mathematics and Systems Science Chinese Academy of Sciences

The symmetric and weighted shapley values for cooperative n-person games are studied. Using the semi-tensor product of matrices, it is first shown that a characteristic function can be expressed as a pseudo-Boolean function. Then, two simple matrix formulas are obtained for calculating the symmetric and weighted shapley values. Finally, using these new formulas, a design technique for the agents’ payoff functions in distributed resource allocation problems is proposed. It is possible to design payoff functions with the weighted shapley value by the nonsymmetric weights defined on the players, thus ensuring that the optimal allocation is a pure Nash equilibrium. Practical examples are presented to illustrate the theoretical results.

关键词： semi-tensor product of matrices shapley value matrix formula distributed resource allocation

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

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Journal of Modern Power Systems and Clean Energy 2023年第1期11卷 144-155页

作者： Dong Han Lei Wu Xijun Ren Shiwei Xia Electrical Engineering Department University of Shanghai for Science and TechnologyShanghai 200093China State Grid Anhui Electric Power Economic Research Institute Hefei 230022China Electrical Engineering Department North China Electric Power UniversityBeijing 102206China

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 ***,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 *** 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,*** 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 *** then build the NUC calculation model by coupling the NB model and AC optimal power flow *** also employ the shapley value to allocate the NUC to consumers fairly for the NUC model of CB ***,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.

关键词： Electricity market network usage charge distribution locational marginal prices shapley value Nash bargaining transactive energy peer-to-peer transaction community-based transaction

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

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Petroleum Science 2023年第3期20卷 1788-1805页

作者： Yun-Tian Chen Dong-Xiao Zhang Qun Zhao De-Xun Liu Eastern Institute for Advanced Study Zhejiang315200China Department of Mathematics and Theories Peng Cheng LaboratoryGuangdong518055China National Center for Applied Mathematics Shenzhen(NCAMS) Southern University of Science and TechnologyGuangdong518055China Research Institute of Petroleum Exploration and Development CNPCBejing100083China

An algorithm named InterOpt for optimizing operational parameters is proposed based on interpretable machine learning,and is demonstrated via optimization of shale gas *** 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 *** 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.

关键词： Interpretable machine learning Operational parameters optimization shapley value Shale gas development Neural network