Internal structure of coalitions in competitive and altruistic graphical coalitional games

This paper introduces a certain graphical coalitional game where the internal topology of the coalition depends on a prescribed communication graph structure among the agents. The game Value Function is required to satisfy four Axioms of Value. These axioms make it possible to provide a refined study of coalition structures on graphs by defining a formal graphical game and by assigning a Positional Advantage, based on the Shapley value, to each agent in a coalition based on its connectivity properties within the graph. Using the Axioms of Value the graphical coalitional game can be shown to satisfy properties such as convexity, fairness, cohesiveness, and full cooperativeness. Three measures of the contributions of agents to a coalition are introduced: marginal contribution, competitive contribution, and altruistic contribution. The mathematical framework given here is used to establish results regarding the dependence of these three types of contributions on the graph topology, and changes in these contributions due to changes in graph topology. Based on these different contributions, three online sequential decision games are defined on top of the graphical coalitional game, and the stable graphs under each of these sequential decision games are studied. It is shown that the stable graphs under the objective of maximizing the marginal contribution are any connected graph. The stable graphs under the objective of maximizing the competitive contribution are the complete graph. The stable graphs under the objective of maximizing the altruistic contribution are any tree.     

Cooperation and profit allocation in two-echelon logistics joint distribution network optimization

Collaborative two-echelon logistics joint distribution network can be organized through a negotiation process via logistics service providers or participants existing in the logistics system, which can effectively reduce the crisscross transportation phenomenon and improve the efficiency of the urban freight transportation system. This study establishes a linear optimization model to minimize the total cost of two-echelon logistics joint distribution network. An improved ant colony optimization algorithm integrated with genetic algorithm is presented to serve customer clustering units and resolve the model formulation by assigning logistics facilities. A two-dimensional colony encoding method is adopted to generate the initial ant colonies. Improved ant colony optimization combines the merits of ant colony optimization algorithm and genetic algorithm with both global and local search capabilities. Finally, an improved Shapley value model based on cooperative game theory and a cooperative mechanism strategy are presented to obtain the optimal profit allocation scheme and sequential coalitions respectively in two-echelon logistics joint distribution network. An empirical study in Guiyang City, China, reveals that the improved ant colony optimization algorithm is superior to the other three methods in terms of the total cost. The improved Shapley value model and monotonic path selection strategy are applied to calculate the best sequential coalition selection strategy. The proposed cooperation and profit allocation approaches provide an effective paradigm for logistics companies to share benefit, achieve win–win situations through the horizontal cooperation, and improve the negotiation power for logistics network optimization.     

Parallel characterizations of a generalized Shapley value and a generalized Banzhaf value for cooperative games with level structure of cooperation

We present parallel characterizations of two different values in the framework of restricted cooperation games. The restrictions are introduced as a finite sequence of partitions defined on the player set, each of them being coarser than the previous one, hence forming a structure of different levels of a priori unions. On the one hand, we consider a value first introduced in Ref. [18], which extends the Shapley value to games with different levels of a priori unions. On the other hand, we introduce another solution for the same type of games, which extends the Banzhaf value in the same manner. We characterize these two values using logically comparable properties.     

A Rough Set Approach to Estimating the Game Value and the Shapley Value from Data

A value of a game v is a function which to each coalition S assigns the value v(S) of this coalition, meaning the expected pay–off for players in that coalition. A classical approach of von Neumann and Morgenstern [6] had set some formal requirements on v which contemporary theories of value adhere to. A Shapley value of the game with a value v [14] is a functional Φ giving for each player p the value Φ_p(v) estimating the expected pay-off of the player p in the game. Game as well as conflict theory have been given recently much attention on the part of rough and fuzzy set communities [11,8,1,4,7,2]. In particular, problems of plausible strategies [1] in conflicts as well as problems related to Shapley's value [3,2] have been addressed.We confront here the problem of estimating a value as well as Shapley's value of a game from a partial data about the game. We apply to this end the rough set ideas of approximations, defining the lower and the upper value of the game and, respectively, the lower and upper Shapley value. We also define a notion of an exact coalition, on which both values coincide giving the true value of the game; we investigate the structure of the family of exact sets showing its closeness on complements, disjoint sums, and intersections of coalitions covering the set of players. This work sets open a new area of rough set applications in mining constructs from data. The construct mined in this case are values as well as Shapley values of games.     

基于合作博弈的虚拟化资源效用分配策略

效用分配是网格虚拟化资源提供者结成联盟完成用户任务时的关键问题。针对资源提供者建立联盟来提高网格整体效用的情况,研究了利用合作博弈论分配网格资源。给出了资源建立联盟的依据,并以基于费用最小化的MIN_COST算法得到了资源的最优化映射方案。在效用分配中,分别从联盟效用的平均分配和Shapley值分配两方面进行了分析,提出了基于Shapley值的资源联盟效用分配策略。算例结果表明,网格资源联盟可以提高任务的执行效率和资源整体收益,而Shapley值法在均衡联盟个体的效用分配方面也是有效可行的。     

多主体目标优化的动态合作博弈方法

通过多目标优化和动态合作博弈理论,定义了联盟中多主体目标优化问题,提出了能够适应动态环境的基于合作博弈的多主体目标优化模型。该模型的组成一方面能够利用主体的协作能力,另一方面又能够充分考虑动态联盟的特征,适合大规模网络中多主体协作,避免模型中主体理性和团体理性的冲突。基于所提出的多主体目标优化模型,设计了一种联盟效用分配算法。仿真实验表明,联盟效用分配算法能够使多主体根据最优共识原则,分配各方的合作效用,从而达到多赢的帕累托最优局面。     

基于萤火虫优化算法的微网源-荷博弈模型及分析

以实现微网负荷间利益最大化和微源容量配置经济高效为策略,提出基于萤火虫优化算法的微网源—荷博弈方法。首先,在充分考虑微源成本、微源容量、负荷成本、负荷用电量之间相互关系的基础上,建立了具有博弈关系的微源和负荷博弈模型,以及非合作和合作博弈下的目标函数。然后,设计了萤火虫优化算法在博弈迭代中的应用流程,利用吸引度和亮度参数对各博弈者的策略进行更新,实现了目标函数的最优。最后,提出利用收益微调系数和稳定指标进行搜索的改进Shapley值法,对合作后的收益进行重新分配,保证了合作全联盟的稳定性。通过对微源博弈者和负荷博弈者的收益分析,验证了所提博弈模型在负荷优化中的可行性,及萤火虫优化算法在求解博弈均衡解时的有效性。     

计及LCA碳排放的源荷双侧合作博弈调度研究

为实现新型电力系统的低碳经济目标,提出一种计及生命周期评价(lifecycleassessment, LCA)的源荷双侧合作博弈优化调度模型。首先,考虑灵活可调度的柔性负荷,构建含热电联产机组、燃气锅炉、电转气等设备的源荷双侧合作运行框架。然后,运用LCA方法分析源荷双侧中不同能源链的温室气体排放,并结合碳交易机制,建立碳交易成本计算模型。最后,基于合作博弈策略,建立以源荷合作联盟总成本最小为目标的源荷双侧协同运行优化模型,并利用改进的Shapley值法对成员合作收益进行分配。算例分析表明,所提模型有利于降低系统运行的总成本、减少系统碳排放量、提升可再生能源消纳量,有效促进系统低碳经济的发展。     

Benefit-based cost allocation for residentially distributed photovoltaic systems in China: A cooperative game theory approach

Distributed photovoltaic (PV) systems have constantly been the key to achieve a low-carbon economy in China. However, the development of Chinese distributed PV systems has failed to meet expectations because of their irrational profit and cost allocations. In this study, the methodology for calculating the levelized cost of energy (LCOE) for PV is thoroughly discussed to address this issue. A mixed-integer linear programming model is built to determine the optimal system operation strategy with a benefit analysis. An externality-corrected mathematical model based on Shapley value is established to allocate the cost of distributed PV systems in 15 Chinese cities between the government, utility grid and residents. Results show that (i) an inverse relationship exists between the LCOEs and solar radiation levels; (ii) the government and residents gain extra benefits from the utility grid through net metering policies, and the utility grid should be the highly subsidized participant; (iii) the percentage of cost assigned to the utility grid and government should increase with the expansion of battery bank to weaken the impact of demand response on increasing theoretical subsidies; and (iv) apart from the LCOE, the local residential electricity prices remarkably impact the subsidy calculation results.     

光伏阵列故障诊断的可解释性智能集成方法

针对现有光伏阵列故障检测和诊断智能方法存在的泛化性不强、可解释性差的问题,提出了一种可解释性智能集成方法。对采集的光伏阵列输出时序电压、电流波形进行特征挖掘,并将多个已成熟应用于光伏故障诊断的智能算法作为不同基学习器与元学习器,构建结合不同智能算法优势且更具泛化性的Stacking集成学习模型;以沙普利可加性特征解释方法为总框架,并结合局部近似可解释性方法,对模型训练过程与结果进行解释分析,通过获取各特征的贡献、分析该集成模型的决策机制,并了解其如何进行诊断,提高其可靠度和可信度。算例实验结果表明,所提可解释性智能集成方法在不同规模数据集的测试中均实现了高精度的故障诊断,模型的可解释性结果表明由该智能集成模型建立的故障特征和诊断结果的映射遵循物理见解,增强了智能方法的可信度和透明性。