Institutional Incentives, Game Equilibrium and Social Justice： Toward a Unified Theory of Pure Jurisprudence

本文探讨现代社会科学的统一分析框架对法学理论的建设性推进。我们展示了个体理性决策与博弈论，社会选择与机制设计理论的主要思想，并初步讨论了它们在法律问题中的运用。其核心观念为：法律与其它社会规范一起为组成社会的所有行为主体提供了制度激励，立法者任何合乎社会正义理念的目标，只有作为他们在社会博弈中的均衡行为的结果，才能得到合理实施。

On the finite horizon Nash equilibrium solution in the differential game approach to formation control

The solvability of the coupled Riccati differential equations appearing in the differential game approach to the formation control problem is vital to the finite horizon Nash equilibrium solution.These equations(if solvable)can be solved numerically by using the terminal value and the backward iteration.To investigate the solvability and solution of these equations the formation control problem as the differential game is replaced by a discrete-time dynamic game.The main contributions of this paper are as follows.First,the existence of Nash equilibrium controls for the discretetime formation control problem is shown.Second,a backward iteration approximate solution to the coupled Riccati differential equations in the continuous-time differential game is developed.An illustrative example is given to justify the models and solution.

Game Theory Model and Equilibrium Analysis of Peasant's Production Decision

Unbalanced agricultural production decision becomes the great block that influences the effective distribution of social resources, national grain security, social stability and economic development. This paper took the game theory as an analyzed tool to describe the interactional processes among the peasants, and set up the game theory model of independent decision and joint decision by peasants. It was shown that the government＇s positive guide and the market environment macroscopically controlled by the government could effectively increased the peasants＇ income

Fuzzy Nash equilibrium of fuzzy n-person non-cooperative game

The fuzzy non-cooperative game with fuzzy payoff function is studied. Based on fuzzy set theory with game theory, the fuzzy Nash equilibrium of fuzzy non-cooperative games is proposed. Most of researchers rank fuzzy number by its center of gravity or by the real number with its maximal membership. By reducing fuzzy number into a real number, we lose much fuzzy information that should be kept during the operations between fuzzy numbers. The fuzzy quantities or alternatives are ordered directly by Yuan＇s binary fuzzy ordering relation. In doing so, the existence of fuzzy Nash equilibrium for fuzzy non-cooperative games is shown based on the utility function and the crisp Nash theorem. Finally, an illustrative example in traffic flow patterns of equilibrium is given in order to show the detailed calculation process of fuzzy Nash equilibrium.

Generalized Quantum Games with Nash Equilibrium

We define generalized quantum games by introducing the coherent payoff operators and propose a simple scheme to illustrate it.The scheme is implemented with a single spin qubit system and a two-entangled-qubit system.The Nash Equilibrium Theorem is proved for the models.

QUASI-EQUILIBRIUM PROBLEMS AND CONSTRAINED MULTIOBJECTIVE GAMES IN GENERALIZED CONVEX SPACE

A class of quasi-equilibrium problems and a class of constrained multiobjective games were introduced and studied in generalized convex spaces without linear structure. First, two existence theorems of solutions for quasi-equilibrium problems are proved in noncompact generalized convex spaces. Then, ar applications of the quasi-equilibrium existence theorem, several existence theorems of weighted Nash-equilibria and Pareto equilibria for the constrained multiobjective games are established in noncompact generalized convex spaces. These theorems improve, unify, and generalize the corresponding results of the multiobjective games in recent literatures.

Geometric Study of the Weak Equilibrium in a Weighted Case for a Two-Dimensional Competition Game

In this work, an improvement of the results presented by [1] Abellanas et al. (Weak Equilibrium in a Spatial Model. International Journal of Game Theory, 40(3), 449-459) is discussed. Concretely, this paper investigates an abstract game of competition between two players that want to earn the maximum number of points from a finite set of points in the plane. It is assumed that the distribution of these points is not uniform, so an appropriate weight to each position is assigned. A definition of equilibrium which is weaker than the classical one is included in order to avoid the uniqueness of the equilibrium position typical of the Nash equilibrium in these kinds of games. The existence of this approximated equilibrium in the game is analyzed by means of computational geometry techniques.

A Scalar Compromise Equilibrium for N-Person Prescriptive Games

A scalar equilibrium (SE) is defined for n-person prescriptive games in normal form. When a decision criterion (notion of rationality) is either agreed upon by the players or prescribed by an external arbiter, the resulting decision process is modeled by a suitable scalar transformation (utility function). Each n-tuple of von Neumann-Morgenstern utilities is transformed into a nonnegative scalar value between 0 and 1. Any n-tuple yielding a largest scalar value determines an SE, which is always a pure strategy profile. SEs can be computed much faster than Nash equilibria, for example;and the decision criterion need not be based on the players’ selfishness. To illustrate the SE, we define a compromise equilibrium, establish its Pareto optimality, and present examples comparing it to other solution concepts.

Statistical Learning in Game Theory

In economics, buyers and sellers are usually the main sides in a market. Game theory can perfectly model decisions behind each “player” and calculate an outcome that benefits both sides. However, the use of game theory is not lim-ited to economics. In this paper, I will introduce the mathematical model of general sum game, solutions and theorems surrounding game theory, and its real life applications in many different scenarios.

数字时代农业社会化服务市场决策的机理与实证研究

通过建立静态离散博弈模型,并在可观测决策结果为参与者博弈均衡的假设下,根据中国家庭追踪调查数据库的样本数据,对数字时代农业社会化服务市场决策进行机理与实证分析。结果表明:农业社会化服务市场决策不仅是各类农业经营主体利润最大化的经济选择,更是市场参与者的博弈均衡;农业社会化服务的规模效应和收入效应驱动了专业农户的市场进入决策,但市场进入壁垒呈现明显的正向规模性偏好;在数字时代,潜在进入者间的“数字鸿沟”制约了服务市场发展中数字技术和农业技术的协同效应。因此,在农业社会化服务市场发展过程中,应以数字化农业社会化服务平台为重点,发展服务市场“金融”功能,提升服务主体数字化素养,营造服务市场公平竞争环境,形成服务供需均衡、政策有效的农业社会化服务体系。

再制造供应链中纵向持股策略研究——以废旧纺织服装为例

针对一个由第三方科技企业、制造商和零售商组成的三级供应链,为使第三方科技企业有从回收的废旧纺织服装中研发生产新科技材料的积极性和资金保障,探讨分析了制造商对第三方科技企业的投资持股策略。以供应链成员各自利润最大化为目标,建立了Stackelberg博弈决策模型,给出了各成员利润和价格的均衡解。研究结果表明当制造商对第三方科技企业投资和投资持股时,第三方科技企业提供的原材料具有的附加值的高低对第三方科技企业和制造商的利润分配有积极影响,且持股比例亦可较好地调节和控制利润在供应链成员间的分配,以保证供应链整体的可持续运作。相关成果对解决当前废旧纺织服装回收再制造投入资金不足,废旧纺织服装供应链整体可持续运营管理具有重要的指导意义。

基于博弈论的弹目攻防决策方法研究

针对空战环境中弹目攻防双方的对抗特性,提出了一种基于博弈论的弹目攻防决策方法。基于导弹目标运动数学关系得到状态方程,根据弹目攻防对抗机理建立“一对一导弹-目标”动态博弈模型,确定弹目双方策略集与收益矩阵,提出混合策略纳什均衡求解方法,并结合模型滚动预测方法获得该策略空间的纳什均衡点。算例仿真结果表明,基于混合策略下导弹制导律为该策略空间的纳什均衡点,且该方法可以减小导弹对目标的脱靶量,提高导弹的命中精度,为导弹攻防作战提供了依据。

On Topics in Quantum Games

This work concentrates on simultaneous move non-cooperating quantum games. Part of it is evidently not new, but it is included for the sake self consistence, as it is devoted to introduction of the mathematical and physical grounds of the pertinent topics, and the way in which a simple classical game is modified to become a quantum game (a procedure referred to as a quantization of a classical game). The connection between game theory and information science is briefly stressed, and the role of quantum entanglement (that plays a central role in the theory of quantum games), is exposed. Armed with these tools, we investigate some basic concepts like the existence (or absence) of a pure strategy and mixed strategy Nash equilibrium and its relation with the degree of entanglement. The main results of this work are as follows: 1) Construction of a numerical algorithm based on the method of best response functions, designed to search for pure strategy Nash equilibrium in quantum games. The formalism is based on the discretization of a continuous variable into a mesh of points, and can be applied to quantum games that are built upon two-players two-strategies classical games, based on the method of best response functions. 2) Application of this algorithm to study the question of how the existence of pure strategy Nash equilibrium is related to the degree of entanglement (specified by a continuous parameter γ ). It is shown that when the classical game GC has a pure strategy Nash equilibrium that is not Pareto efficient, then the quantum game GQ with maximal entanglement (γ = π/2) has no pure strategy Nash equilibrium. By studying a non-symmetric prisoner dilemma game, it is found that there is a critical value 0γc such that for γγc there is a pure strategy Nash equilibrium and for γ≥γc there is no pure strategy Nash equilibrium. The behavior of the two payoffs as function of γ starts at that of the classical ones at (D, D) and approaches the cooperative classical ones at (C, C) (C = confess, D = don’t confess). 3) We then study Bayesian quantum games and show that under certain conditions, there is a pure strategy Nash equilibrium in such games even when entanglement is maximal. 4) We define the basic ingredients of a quantum game based on a two-player three strategies classical game. This requires the introduction of trits (instead of bits) and quantum trits (instead of quantum bits). It is proved that in this quantum game, there is no classical commensurability in the sense that the classical strategies are not obtained as a special case of the quantum strategies.

航天器姿态控制群体博弈分布式分配方法

针对由多个细胞星构成的组合卫星的姿态控制问题,提出了一种包含控制力矩计算层与冗余力矩分配层的双层姿态控制方法。将细胞星间的冗余力矩分配问题转化为群体博弈的策略选择问题,综合考虑能量消耗、飞轮输出力矩裕度和飞轮角动量裕度设计收益函数,以力矩分配系数作为群体质量,以细胞星作为策略建立群体博弈模型。考虑群体演化中模仿和比较形成的不同演化策略,分别采用Smith动力学以及复制器动力学修订协议求解博弈的Nash均衡解,并利用有限制策略的群体博弈理论形成分布式冗余力矩分配方式,得到各个细胞星的控制策略。最后通过仿真实验验证了此分配方式的有效性。

基于子博弈完美均衡的启发式聚类算法

聚类是一种典型且重要的数据挖掘方法,但现有聚类算法大多需要人为指定聚类的数量,并且聚类结果对参数敏感.针对上述不足,本文提出一种基于子博弈完美均衡的启发式聚类算法(Heuristic Clustering algorithm based on Sub-game Perfect Equilibrium,HCSPE).该算法充分挖掘数据点自身的分布特征信息,通过启发式方法得到自适应的参数值,从而使数据点局部密度属性值的得出具有客观性和普适性,降低了聚类结果对参数的敏感性.基于博弈的思想,综合局部密度和相对距离两个属性形成数据点的竞争力,依靠竞争机制完成聚类数量的自动计算以及聚类中心的确定.在多个规模和类型均不相同的数据集上的实验结果表明,本文所提出算法的性能指标整体优于其他算法,并且聚类结果更符合客观所需.

考虑碳市场交易的寡头电力市场均衡分析

在碳市场上线的背景下,发电商需同时参与碳市场与电力市场,并对电力市场均衡产生影响。为研究碳市场及电力市场中发电商的交易决策及两个市场之间的交互影响关系,建立了考虑碳市场交易的寡头电力市场双层均衡模型,该模型可同时考虑发电商在电力市场和碳市场中的博弈行为。针对所建立模型,采用协同进化算法进行纳什均衡的求解。最后通过算例验证了相关模型和算法的有效性,并重点研究了碳市场对电力市场均衡及发电商市场博弈行为的影响。结果表明:在当前采用基准线法进行初始碳配额分配情况下,发电商的策略性行为同时抬高了电价与碳价,其中电价的上涨幅度远小于碳价的上涨幅度。

不完全信息Epsilon纳什均衡的航天器末端追逃博弈策略

针对不完全信息下的航天器末端追逃问题,提出了一种满足Epsilon纳什均衡的微分博弈控制策略。首先,建立了完全信息下的有限时间追逃纳什均衡策略对,并将其作为目标航天器实际采取的控制策略,使目标航天器掌握博弈进程的完全信息,进而获得更好的逃逸性能。在此基础上,考虑拦截航天器不能获取目标控制矩阵信息的态势,设计了基于广义卡尔曼滤波的行为学习信息估计算法,使拦截器能够对目标的不完全信息进行估计,并提出了不完全信息下的末端追逃博弈控制策略。经过理论分析,证明了所设计的不完全信息下微分博弈策略对满足Epsilon纳什均衡。最后,仿真结果表明该算法可以有效估计目标的不完全信息,确保拦截器能够在有限时间内快速拦截目标。

基于不完全信息博弈的云制造群智能优化方法

为解决云制造过程中云平台经营方与需求方之间的不完全信息以及相互竞争制约的关系导致制造服务难以抉择的问题,提出了一种基于不完全信息博弈模型的云制造群智能优化方法。以各自理性追求自身收益函数最大化为目标,针对需求方与云平台之间的利益竞争关系建立了基于不完全信息的静态博弈模型,并提出了需求方与云平台之间的竞争规则,通过海萨尼转换引入自然,将其转换为完全信息下的动态博弈得到贝叶斯扩展式,并证明了贝叶斯纳什均衡的存在性和唯一性。提出了一种基于高斯函数与扰动策略更新的粒子群算法对上述模型进行求解。仿真结果表明:改进算法相对其他算法有较快的收敛速度与较高的云制造系统总收益,不完全信息博弈模型能够兼顾不同类型的需求方提高云制造系统的总收益。

基于势博弈的自动化码头路网流量均衡研究

为提高自动化集装箱码头(自动化码头)路网利用率和均衡性,本文基于自动化码头各子路径的拥挤程度、自动导向车(AGV)的运输速度以及各子路径的选择概率等因素,将分布式的AGV流量调度问题转化为AGV之间的博弈模型,提出一种基于势博弈理论的AGV流量调度模型;设计分布式路径选择算法帮助AGV更新策略;系统信息更新算法用于更新道路信息并选择更新策略的AGV;通过这两种算法求解AGV的均衡调度策略。结合3艘实际船舶任务,进行数值仿真实验。仿真结果表明:分布式路径选择方法相较于传统路径选择方式具有更优性,船舶任务量、AGV数量及速度是影响AGV作业效益的关键因素,当AGV的速度为6 m·s-1时,船舶的总收益最大。本文可以为码头管理者确定AGV调度策略提供决策支持。

无人机-无人车跨域编队跟踪的分布式博弈策略

针对无人机-无人车跨域系统的编队跟踪与扰动抑制问题,开展了领-从架构下考虑存在扰动的跨域编队跟踪的分布式博弈策略研究。首先,建立了含扰动的无人机-无人车编队跟踪模型,每架无人机只使用局部信息来最小化自己的性能指标,而整个跨域系统试图寻求基于通信拓扑的最优决策。其次,提出了一种最差扰动下的博弈策略,并严格证明了系统中存在纳什均衡。然后,引入了一个分布式终端状态观测器,得到了所提出博弈策略的局部实现。最后,搭建了一套无人机-无人车跨域系统验证平台,并通过一个跨域编队跟踪应用案例验证了所提出分布式博弈策略不仅可以有效地抑制扰动,还能形成期望编队队形,并且性能指标在数值仿真和实物试验下的差异不超过0.6%,证明所提出分布式博弈策略有良好的实用性。