Interactive Fuzzy Approaches for Solving Multiobjective Two-Person Zero-Sum Games

In this paper, we consider multiobjective two-person zero-sum games with vector payoffs and vector fuzzy payoffs. We translate such games into the corresponding multiobjective programming problems and introduce the pessimistic Pareto optimal solution concept by assuming that a player supposes the opponent adopts the most disadvantage strategy for the self. It is shown that any pessimistic Pareto optimal solution can be obtained on the basis of linear programming techniques even if the membership functions for the objective functions are nonlinear. Moreover, we propose interactive algorithms based on the bisection method to obtain a pessimistic compromise solution from among the set of all pessimistic Pareto optimal solutions. In order to show the efficiency of the proposed method, we illustrate interactive processes of an application to a vegetable shipment problem.

It Is Not A Zero-Sum Game

Nowadays,China is the largest developing country in the world,and the US is the largest developed country in the world.Sino-US economic and trade relations are of great significance to the two nations and may have aprominent impact on the stability and development of the global economy.

Polynomial Time Method for Solving Nash Equilibria of Zero-Sum Games

There are a few studies that focus on solution methods for finding a Nash equilibrium of zero-sum games. We discuss the use of Karmarkar’s interior point method to solve the Nash equilibrium problems of a zero-sum game, and prove that it is theoretically a polynomial time algorithm. We implement the Karmarkar method, and a preliminary computational result shows that it performs well for zero-sum games. We also mention an affine scaling method that would help us compute Nash equilibria of general zero-sum games effectively.

面向6G的生成对抗网络研究进展综述

人工智能(AI,artificial intelligence)与通信技术的深度融合是6G网络的典型特征。一方面,AI为6G网络发展注入了新动力,能够有效利用网络运行产生的历史数据,使网络具备自维护、自优化的功能,加速了网络智能化进程。另一方面,6G网络丰富的场景和大规模的物联设备入网应用为AI提供了广阔的应用渠道和海量的训练数据,使AI能够更好地训练和部署,充分发挥AI的内在优势,为用户提供更加优质的智能服务。尽管如此,在一些实际应用中,受复杂环境的影响,存在数据样本收集困难、收集成本高和样本普适性不足等问题,难以充分发挥AI的性能优势。为此,学术界和工业界将生成对抗网络(GAN,generative adversarial network)引入无线网络的设计中,利用GAN强大的特征学习和特征表达能力产生大量模拟实际的生成样本,实现无线数据库的扩充,从而有效提升面向无线网络的AI模型的泛化能力。由于其优秀的性能表现,以GAN为代表的生成式模型在无线网络领域受到越来越多的关注,并迅速发展成为6G网络新的研究热点。首先,综述了GAN的原理及其改进衍生模型,对各种衍生模型的框架及优缺点进行了分析归纳;然后,综述了这些模型在无线网络领域的研究及应用现状;最后,面向6G网络的需求展望了GAN在6G网络中的研究趋势,为未来的研究提供了一些有价值的探索。

两方零和马尔科夫博弈策略梯度算法及收敛性分析

为了解决基于策略的强化学习方法在两方零和马尔科夫博弈中学习效率低下的问题,提出同时更新双方玩家策略的近似纳什均衡策略优化算法.将两方零和马尔科夫博弈问题描述为最大最小优化问题,针对参数化策略,给出马尔科夫博弈的策略梯度定理,并通过近似随机策略梯度的推导,为算法实施提供可行性基础.通过比较分析不同的最大最小问题梯度更新方法,发现额外梯度相较于其他方法具有更好的收敛性能.基于这一发现,提出基于额外梯度的近似纳什均衡策略优化算法,并给出算法的收敛性证明.在Oshi-Zumo游戏上,使用表格式softmax参数化策略以及神经网络作为参数化策略,验证不同游戏规模场景下算法的有效性.通过对比实验,验证算法相对于其他方法的收敛性和优越性.

主观社会阶层与道德判断的关系:独立型自我构念与零和博弈信念的链式中介作用

本研究选取523名被试,进行道德判断、主观社会阶层、自我构念与零和博弈信念的测量,以探讨主观社会阶层与道德判断之间的中介机制。结果表明:(1)主观社会阶层显著正向预测功利型道德判断;(2)独立型自我构念和零和博弈信念在主观社会阶层预测功利型道德判断中起到链式中介作用;(3)零和博弈信念在主观社会阶层和道德判断中起遮掩作用。本研究有助于研究者深入了解社会性因素影响道德判断的机制。

Adaptive dynamic programming for online solution of a zero-sum differential game

This paper will present an approximate/adaptive dynamic programming(ADP) algorithm,that uses the idea of integral reinforcement learning(IRL),to determine online the Nash equilibrium solution for the two-player zerosum differential game with linear dynamics and infinite horizon quadratic cost.The algorithm is built around an iterative method that has been developed in the control engineering community for solving the continuous-time game algebraic Riccati equation(CT-GARE),which underlies the game problem.We here show how the ADP techniques will enhance the capabilities of the offline method allowing an online solution without the requirement of complete knowledge of the system dynamics.The feasibility of the ADP scheme is demonstrated in simulation for a power system control application.The adaptation goal is the best control policy that will face in an optimal manner the highest load disturbance.

基于双人零和博弈的孤岛微电网有界L2增益负荷频率控制

针对含不确定建模误差和新能源接入的孤岛微电网,提出了一种结合有界L2增益基线控制和扰动补偿的综合负荷频率控制(LFC)方法。首先,推导了微电网的全驱模型,将建模误差和新能源的影响总结成一个综合扰动。为提高系统的鲁棒性,该综合扰动被定义成控制信号的对手玩家。进一步,关于扰动抑制的有界L2增益问题被等价成求解综合扰动和控制信号的零和博弈Nash均衡,由此推导出有界L2增益基线控制器。为改善频率的二次控制,设计了基于五阶广义积分观测器的扰动补偿控制,并在此基础上引入了一种针对发电速率约束(GRC)的新型抗发电速率约束(anti-GRC)措施。最后,搭建了16 MW的新能源-柴油混合微电网仿真模型,并在多种工况下对所提出的综合LFC方法进行测试,验证了其有效性。

集体行动逻辑视角下乡村“零和空间”治理——基于福建晋江市的田野调查

乡村公共空间治理是人居环境整治的关键任务,也是实现乡村振兴的重要抓手。公共空间治理难,主要在于“零和空间”引发的集体行动困境。研究发现福建晋江市乡村通过宗族力量引导村民认知目标、网格化管理降低集体行动规模、研究村民偏好进行选择性激励三种方式,促进乡村达成集体行动目标,使“零和空间”演变为“正和空间”。晋江市农村“零和空间”整治的经验,不仅为其他乡村进行类似公共空间治理提供借鉴,也为今后乡村基层治理通过制度设计,形成长效机制促进集体行动目标达成提供有益启示。

Zero-Sum Stochastic Games with Average Payoffs:New Optimality Conditions

In this paper we study zero-sum stochastic games. The optimality criterion is the long-run expected average criterion, and the payoff function may have neither upper nor lower bounds. We give a new set of conditions for the existence of a value and a pair of optimal stationary strategies. Our conditions are slightly weaker than those in the previous literature, and some new sufficient conditions for the existence of a pair of optimal stationary strategies are imposed on the primitive data of the model. Our results are illustrated with a queueing system, for which our conditions are satisfied but some of the conditions in some previous literatures fail to hold.

Distributed projection subgradient algorithm for two-network zero-sum game with random sleep scheme

In this paper,a zero-sum game Nash equilibrium computation problem with a common constraint set is investigated under two time-varying multi-agent subnetworks,where the two subnetworks have opposite payoff function.A novel distributed projection subgradient algorithm with random sleep scheme is developed to reduce the calculation amount of agents in the process of computing Nash equilibrium.In our algorithm,each agent is determined by an independent identically distributed Bernoulli decision to compute the subgradient and perform the projection operation or to keep the previous consensus estimate,it effectively reduces the amount of computation and calculation time.Moreover,the traditional assumption of stepsize adopted in the existing methods is removed,and the stepsizes in our algorithm are randomized diminishing.Besides,we prove that all agents converge to Nash equilibrium with probability 1 by our algorithm.Finally,a simulation example verifies the validity of our algorithm.

国际大变局背景下美国贸易政策转向及影响研究

2016年美国大选后,其贸易政策格局发生了深刻变化。特朗普推行“美国优先”的保护主义政策,尤其是通过“301调查”对中国产品征税引发了美中贸易战。作为继任者,拜登政府没有推动“自由”贸易和多边贸易改革,而是继续推行前任的民族主义政策,并且联合盟友对中国“脱钩断链”。文章通过对特朗普和拜登政府贸易政策的梳理,分析其政策转向的经济与地缘影响,研判美国贸易政策的未来走向,最后为我国外贸发展提出对策建议。面对如今百年未有之大变局,世界经济的相互联系比以往任何时候都更加紧密,保护主义只能使世界变得更缺乏弹性、更加不平等、更容易发生冲突。中国需要在推动“一带一路”共建、新兴市场及发展中国家合作、世贸组织改革等方面进一步发挥大国作用,为世界发展提供新机遇和新动能。

Z时代青年“外佛内卷”现象的成因和对策

“外佛内卷”是Z时代青年学业消极情绪中的一种重要体现。作为“佛系”与“内卷”的概念矛盾体,“外佛内卷”从多个维度呈现出不同的类型。“外佛内卷”现象是过度“内卷”的再生产,非此即彼的零和博弈思维是过度“内卷”的内因。“外佛内卷”现象是假性“佛性”的新形态,应然和实然的落差是假性“佛性”的外因。实现青年群体间的良性互动,需要培养青年人的共同体思维,同时明确自我定位,做好个人规划。

Nash equilibrium computation of two-network zero-sum games with event-triggered communication

In this paper,a zero-sum game Nash equilibrium computation problem with event-triggered communication is investigated under an undirected weight-balanced multi-agent network.A novel distributed event-triggered projection subgradient algorithm is developed to reduce the communication burden within the subnetworks.In the proposed algorithm,when the difference between the current state of the agent and the state of the last trigger time exceeds a given threshold,the agent will be triggered to communicate with its neighbours.Moreover,we prove that all agents converge to Nash equilibrium by the proposed algorithm.Finally,two simulation examples verify that our algorithm not only reduces the communication burden but also ensures that the convergence speed and accuracy are close to that of the time-triggered method under the appropriate threshold.

Policy Iteration Algorithms for Zero-Sum Stochastic Differential Games with Long-Run Average Payoff Criteria

This paper studies the policy iteration algorithm(PIA)for zero-sum stochastic differential games with the basic long-run average criterion,as well as with its more selective version,the so-called bias criterion.The system is assumed to be a nondegenerate diffusion.We use Lyapunov-like stability conditions that ensure the existence and boundedness of the solution to certain Poisson equation.We also ensure the convergence of a sequence of such solutions,of the corresponding sequence of policies,and,ultimately,of the PIA.

多无人机系统在线强化学习最优安全跟踪控制

在无人机(UAV)编队跟踪任务中,虚假数据注入(FDI)攻击者可向控制指令注入误导性数据,导致无人机无法形成指定的编队构型,故需设计安全编队跟踪控制器。为此,本文利用零和图博弈对攻防过程进行建模,其中FDI攻击者和安全控制器是博弈的参与者,攻击者的目标是最大化设定的成本函数,而安全控制器的目标与之相反,求解博弈并获得最优安全控制策略依赖于求取Hamilton-Jacobi-Isaacs(HJI)方程的解。而HJI方程是耦合偏微分方程,难以直接求解,因此结合经验回放机制引入了有限时间收敛的在线强化学习算法,设计了单评价神经网络近似值函数并获得了最优安全控制策略。最终利用仿真验证了算法的有效性。

Solution of a zero-sum linear quadratic differential game with singular control cost of minimiser

We consider a finite horizon,zero-sum linear quadratic differential game.The feature of this game is that a weight matrix of the minimiser’s control cost in the cost functional is singular.Due to this singularity,the game can be solved neither by applying the Isaacs MinMax principle nor using the Bellman–Isaacs equation approach,i.e.this game is singular.Aprevious paper of one of the authors analysed such a game in the case where the cost functional does not contain the minimiser’s control cost at all,i.e.the weight matrix of this cost equals zero.In this case,all coordinates of the minimiser’s control are singular.In the present paper,we study the general case where the weight matrix of the minimiser’s control cost,being singular,is not,in general,zero.This means that only a part of the coordinates of the minimiser’s control is singular,while others are regular.The considered game is treated by a regularisation,i.e.by its approximate conversion to an auxiliary regular game.The latter has the same equation of dynamics and a similar cost functional augmented by an integral of the squares of the singular control coordinates with a small positive weight.Thus,the auxiliary game is a partial cheap control differential game.Based on a singular perturbation’s asymptotic analysis of this auxiliary game,the existence of the value of the original(singular)game is established,and its expression is obtained.The maximiser’s optimal state feedback strategy and the minimising control sequence in the original game are designed.It is shown that the coordinates of the minimising control sequence,corresponding to the regular coordinates of the minimiser’s control,are point-wise convergent in the class of regular functions.The optimal trajectory sequence and the optimal trajectory in the considered singular game also are obtained.An illustrative example is presented.

Improved zero-sum distinguisher for full round Keccak-f permutation

Keccak is one of the five hash functions selected for the final round of the SHA-3 competition,and its inner primitive is a permutation called Keccak-f.In this paper,we observe that for the inverse of the only nonlinear transformation in Keccak-f,the algebraic degree of any output coordinate and the one of the product of any two output coordinates are both 3,which is 2 less than its size of 5.Combining this observation with a proposition on the upper bound of the degree of iterated permutations,we improve the zero-sum distinguisher for the Keccak-f permutation with full 24 rounds by lowering the size of the zero-sum partition from 21590 to 21575.

两方零和马尔科夫博弈下的策略梯度算法

在两方零和马尔科夫博弈中,由于玩家策略会受到另一个玩家策略的影响,传统的策略梯度定理只适用于交替训练两个玩家的策略.为了实现同时训练两个玩家的策略,文中给出两方零和马尔科夫博弈下的策略梯度定理.然后,基于该策略梯度定理,提出基于额外梯度的REINFORCE算法,可使玩家的联合策略收敛到近似纳什均衡.文中从多个维度分析算法的优越性.首先,在同时移动博弈游戏上的对比实验表明,文中算法的收敛性和收敛速度较优.其次,分析文中算法得到的联合策略的特点,并验证这些联合策略达到近似纳什均衡.最后,在不同难度等级的同时移动博弈游戏上的对比实验表明,文中算法在更大的难度等级下仍能保持不错的收敛速度.