Equilibrium Strategy of the Pursuit-Evasion Game in Three-Dimensional Space

The pursuit-evasion game models the strategic interaction among players, attracting attention in many realistic scenarios, such as missile guidance, unmanned aerial vehicles, and target defense. Existing studies mainly concentrate on the cooperative pursuit of multiple players in two-dimensional pursuit-evasion games. However, these approaches can hardly be applied to practical situations where players usually move in three-dimensional space with a three-degree-of-freedom control. In this paper,we make the first attempt to investigate the equilibrium strategy of the realistic pursuit-evasion game, in which the pursuer follows a three-degree-of-freedom control, and the evader moves freely. First, we describe the pursuer's three-degree-of-freedom control and the evader's relative coordinate. We then rigorously derive the equilibrium strategy by solving the retrogressive path equation according to the Hamilton-Jacobi-Bellman-Isaacs(HJBI) method, which divides the pursuit-evasion process into the navigation and acceleration phases. Besides, we analyze the maximum allowable speed for the pursuer to capture the evader successfully and provide the strategy with which the evader can escape when the pursuer's speed exceeds the threshold. We further conduct comparison tests with various unilateral deviations to verify that the proposed strategy forms a Nash equilibrium.

Equilibrium dividend strategies in the dual model with a random time horizon

This paper investigates the dividend problem with non-exponential discounting in a dual model.We assume that the dividends can only be paid at a bounded rate and that the surplus process is killed by an exponential random variable.Since the non-exponential discount function leads to a time inconsistent control problem,we study the equilibrium HJB-equation and give the associated verification theorem.For the case of a mixture of exponential discount functions and exponential gains,we obtain the explicit equilibrium dividend strategy and the corresponding equilibrium value function.Besides,numerical examples are shown to illustrate our results.

Research on Robust Cooperative Dual Equilibrium with Ellipsoidal Asymmetric Strategy Uncertainty

In this paper,we investigate robust cooperative dual equilibria with two players in which each player minimizes the opponent’s cost and can not evaluate his own strategy while may estimate an asymmetric bounded set of the mixed strategy.Using dual theory and robust optimization technique,we obtain a result that the counterpart of the primitive uncertainty with ellipsoidal norm for each player can be formulated as a second-order cone programming(SOCP)and solving the corresponding equilibrium can be converted to solving a second-order cone complementarity problem(SOCCP).Then we present a numerical experiment to illustrate the behavior of robust cooperative dual equilibrium.

An off-and-towards-equilibrium strategy for vibrational control of structures

Traditional control strategies have difficulty handling nonlinear behavior of structures, time variable features and parameter uncertainties of structural control systems under seismic excitation. An off-and-towardsequilibrium （OTE） strategy combined with fuzzy control is presented in this paper to overcome these difficulties. According to the OTE strategy, the control force is designed from the viewpoint of a mechanical relationship between the motions of the structure, the exciting force and the control force. The advantage of the OTE strategy is that it can be used for a variety of control systems. In order to evaluate the performance of the proposed strategy, the seismic performance of a three-story shear building with an Active Tendon System （ATS） using a Fuzzy Logic Controller （FLC） is studied. The main advantage of the fuzzy controller is its inherent robustness and ability to handle any nonlinear behavior of structures. However, there are no design guidelines to set up the corresponding control rule table for a FLC. Based on the proposed strategy for the FLC, a control rule table associated with the building under study is developed, which then allows formation of a detailed algorithm. The results obtained in this study show that the proposed strategy performs slightly better than the linear quadratic regulator （LQR） strategy, while possessing several advantages over the LQR controller. Consequently, the feasibility and validity of the proposed strategy are verified.

An Improved Particle Swarm Optimization Algorithm with Harmony Strategy for the Location of Critical Slip Surface of Slopes

The determination of optimal values for three parameters required in the original particle swarm optimization algorithm is very difficult. It is proposed that two new parameters simulating the harmony search strategy can be adopted instead of the three parameters which are required in the original particle swarm optimization algorithm to update the positions of all the particles. The improved particle swarm optimization is used in the location of the critical slip surface of soil slope, and it is found that the improved particle swarm optimization algorithm is insensitive to the two parameters while the original particle swarm optimization algorithm can be sensitive to its three parameters.

Commission Strategy of the Auction House

In a SIPV model, when the commission proportion is not certain, but related with bargain price, generally, it is a linear function of the bargain price, this paper gives bidders＇ equilibrium bidding strategies in the first-and secondprice auctions. We find that the equilibrium strategies in second-price auction are dominant strategies. For seller or auction house, whether the fixed proportion or the unfixed proportion is good is not only related with constant item and the linear coefficient of the linear function, the size of the fixed commission proportion, but also related with the value of the item auctioned. So, in the practical auctions, the seller and the auction house negotiated with each other to decide the commission rules for their own advantage.

Bi-matrix Games with Fuzzy Strategies and Fuzzy Payoffs and Their Mathematical Programming Equivalents

A fuzzy bi-matrix game（FBG）,namely a two-person non-zero-sum game with fuzzy strategies and fuzzy payoffs is proposed.We have defined and analyzed the optimal strategies of this FBG,and shown that it can be transformed into a corresponding fuzzy mathematical programming issue,for which a ranking function approach can be applied.In addition,optimal strategies of FBG for both Player I and Player II can be gotten.

Economic Effects of China’s Import Expansion Strategy

Since 2018,China has enacted a string of policy initiatives to increase imports.To quantify this import expansion strategy’s economic effects,we created a large numerical general equilibrium model and quantitatively simulated the economic effects of the reductions of tariff and non-tariff barriers on China and other economies.Our simulation results show that overall,China’s import expansion strategy benefited both itself and others and contributed to employment,welfare,and trade growth in China and the rest of the world.In relative terms,however,China’s import expansion strategy benefited other countries more than it did itself and contributed more to the growth of the world economy.Additionally,the import expansion strategy may effectively promote China’s trade balance,and the trade equilibrium effect driven by the reduction of non-tariff barriers is more significant than that of tariff barriers.Furthermore,regarding the self-benefiting effects of import expansion,the effects of nontariff measures are significantly greater than those of tariff measures,and this result has policy implications for China’s import expansion strategy going forward.

大庆油田SEC储量储采形势及增储策略

大庆油田目前已进入双特高后期开发阶段,储采比逐渐降低,SEC储量替换率仅为0.4左右,增储与稳产需求的矛盾日益加剧。通过对大庆油田目前SEC储采现状、增储特点、影响因素进行分析,认为资源品质下降、长期低油价、成本上升以及评估精细程度不足这4个方面是造成储采失衡的主要原因。为改善储采状况,大庆油田形成了较为有效的增储做法,结合大庆油田实际提出了加强技术创新与应用、提升新区勘探与开发效率、优化天然气资源利用、强化精细管理与成本控制、融入绿色发展与新能源等实现储采平衡的工作方向及增储策略。研究成果为东部同类老油田的长远高质量发展提供决策参考。

EXISTENCE OF STOCHASTIC EQUILIBRIUM WITH INCOMPLETE FINANCIAL MARKETS

This paper analyzes the aritrage free security markets and the general equilibrium existence problem for a stochastic economy with incomplete financial markets. Information structure is given by an event tree. This paper restricts attention to purely financial securities. It is assume that trading takes place in the sequence of spot markets and futures markets for securities payable in units of account. Unlimited short selling in securities is allowed. Financial markets may be incomplete: some consumption streams may be impossible to obtain by any trading strategy. Securities may be individually precluded from trade at arbitrary states and dates. The security price process is arbitrage free the dividend process if and only if there exists a stochstic state price (present value) process: the present value of the security prices at every vertex is the present value of their dividend and capital values over the set of immediate successors; the current value of each security at every vertex is the present value of its future dividend stream over all succeeding vertices. The existence of such an equilibrium is proved under the following condition: continuous, weakly convex, strictly monotone and complete preferences, strictly positive endowments and dividends processes.

不对等权力结构下竞争性闭环供应链的回收模式选择均衡

针对两条具有不对等权力的竞争性闭环供应链,其中双链制造商均可选择己方回收(M模式)、委托零售商回收(R模式)或第三方回收(T模式)的3种模式之一,首先建立和求解博弈模型得到9种可能回收组合下的均衡解、成员利润和链利润,然后基于不同组合的比较推导双链回收模式选择的均衡策略,最后分析均衡组合的Pareto效率。结论表明:①主从链博弈存在“后动优势”现象,特别当从链回收者的回收效率不劣于主链时,从链的各项运营指标完全优于主链;②当从链回收模式任意给定时,无论双链竞争强度如何,主链制造商选择R模式对己方、零售商和整条链最有利;当主链回收模式给定时,随着竞争加剧,M模式、R模式和T模式将依次成为从链制造商和整条从链的最优选择;③RR、RM和RT三种组合均可能是双链的回收模式选择均衡,但在某些条件下RR和RM会陷入低效的囚徒困境。

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。

多品种电力市场交易下负荷聚合商投标策略及市场均衡分析

中国新型电力系统建设正面临灵活资源短缺等问题,亟须发挥负荷侧调节能力。随着电网与负荷双向交互越发频繁,更多负荷聚合商通过整合辖区灵活资源参与市场交易,导致以往由发电侧占主导的市场均衡被打破。为研究多主体负荷聚合商博弈策略,构建了能量-备用电力市场下负荷聚合商双层投标模型,并引入多场景描述非决策者投标不确定性对市场均衡的影响。通过强平稳算法(SSM)将多个双层模型转化为带均衡约束的均衡问题(EPEC)模型,并采用大M法、二进制展开法等线性化方法进行线性化。算例结果验证了模型及求解算法的合理性和有效性,表明基于EPEC模型的负荷聚合商最优投标策略更加契合实际市场规则,有助于系统优化负荷曲线,缓解灵活资源供需紧张。

论无限次重复囚徒困境博弈中的针锋相对策略

在有限次重复囚徒困境博弈中,理性的参与人在每个阶段博弈中选择不合作是唯一的子博弈精炼纳什均衡,因此不会出现合作行为。然而,在无限次重复囚徒困境博弈中,参与人采取某些特定的策略可能会导致合作结果的出现。冷酷触发策略是几乎所有博弈论著作都会讨论的一种促进合作的策略,但学者对于针锋相对策略却甚少涉及。研究严格论证了针锋相对策略构成纳什均衡及子博弈精炼纳什均衡的条件。结果表明,当参与人对未来足够重视时,只有当阶段博弈的支付满足一定条件,针锋相对策略才能构成纳什均衡,其对贴现率的要求要比冷酷触发策略更高。研究还表明针锋相对策略并非不能构成子博弈精炼纳什均衡,只是要求的条件非常严格,除了支付满足特定条件外,贴现率也只能取某一特定值。

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。

基于主从博弈的微电网分布式能量管理策略

针对电力市场运营模式下,新能源微电网的整体优化运行与多方投资者的最大利益化之间的冲突问题,提出了基于双层主从博弈的微电网分布式能量管理策略。为充分考虑能源供需两侧的平衡,引入了电力交易代理商的概念,在用户侧提出基于消费者满意度和可调节负荷的综合需求响应策略;考虑源-荷双方的主动性和决策能力,建立了以电力交易代理商为领导者,分布式电源代理商和负荷代理商为追随者的交易决策博弈模型,证明了stackelberg均衡解存在唯一性,采用结合二次规划的差分进化算法对所提模型进行求解。通过对包含分布式电源和社区用户的案例进行分析,验证了所提模型和策略具有良好的收敛性和经济性。

基于博弈论与强化学习的多智能体路径规划算法

针对平面上多个智能体构成的路径规划求解算法普遍存在的速度慢效率低等问题进行研究,将多智能体路径规划问题归结为非零和随机博弈,使用多智能体强化学习算法赢或快速学习-策略爬山(win or learn fast-policy hill-climbing,WoLF-PHC)得到纳什均衡策略,为各智能体做出无冲突的最优路径决策,提出能够快速自适应的WoLF-PHC(fast adaptive WoLF-PHC,FA-WoLF-PHC)算法,通过构建目标函数,使用梯度下降对学习率进行自适应更新.在猜硬币和自定义收益矩阵2个博弈场景中使用FA-WoLF-PHC,并与策略爬山(policy hill-climbing,PHC)算法和Wolf-PHC算法进行比较.结果表明,FA-WoLF-PHC算法的学习速度较WoLF-PHC算法有所提升,并有效减小了WoLF-PHC算法和PHC算法在学习过程中出现的振荡现象.在多智能体路径规划问题中,FA-WoLF-PHC算法的学习速度比WoLF-PHC算法提高了16.01%.将路径规划问题的环境栅格地图扩大为6×6,智能体数量增加为3个时,FA-WoLF-PHC、WoLF-PSP和多头绒泡菌-人工势场Sarsa(physarum polycephalum-artificial potential state-action-reward-state-action,PP-AP Sarsa)算法在10次实验中学习到最终策略需要的平均时间分别为16.30、20.59和17.72 s.在多智能体路径规划问题中,FA-WoLF-PHC算法能够得到各智能体的纳什均衡策略,学习速度较WoLF-PSP和PP-AP Sarsa算法有显著提高.FA-WoLF-PHC算法在常见的博弈场景中能够快速获得纳什策略,在多智能体路径规划问题中可为多个智能体生成无冲突的最优路径,并且在学习速度等方面较其他算法有显著提高.

中国历史文化名镇名村地域均衡性及其评选策略研究——基于七批名镇名村分布差异分析

将目前七批中国历史文化名镇名村的地理信息空间落图,发现地域空间分布存在明显的非均衡现象。再结合各批次增长结果分析,某些区域数量增长幅度高度集中,而某些区域长期未有增加,呈现一种“强者愈强,弱者愈弱”现象,遵循“马太效应”。通过辽宁省与江苏省进一步论证并非是弱省没有优秀村镇,而是现行评价策略存在不足;结合各省份2021年GDP与名镇名村数量对比,发现经济因素对名镇名村申报评选起到关键作用。马太效应在市场竞争语境下是正常的经济现象,而名镇名村评选也是一种竞争,如果顺其发展,两极分化不可避免。基于人类文化遗产共同体的角度,各个类型的历史村镇应均衡保护发展。该文提出可参考高考制度或世界遗产评选规则来调整现行名镇名村评选策略,使之更为公平合理。

基于Stackelberg博弈的电动汽车充电管理策略

电动汽车的充电效率和充电成本是电动汽车电源管理的重要问题,也是影响电动汽车推广的关键因素。对此,提出一种基于Stackelberg博弈模型的收费控制策略。在博弈中,电网、零售商和用户都参与决策,充电策略可以灵活地满足电网、零售商和用户的不同需求,采用逆归纳法得到博弈模型的均衡解。通过仿真、无序充电过程和基于静态分时电价的充电控制方法对其效益进行比较,分析博弈模型中参数对收费过程的影响,验证了该方法的有效性。

部分信息下带时滞的鲁棒资产负债博弈问题研究

研究了部分可观测信息下带时滞的鲁棒资产负债博弈问题,运用滤波理论,将不完全信息转化为完全信息,以终端相对财富的效用最大化为目标,构建了不完全信息带时滞的鲁棒资产负债博弈问题,借助动态规划原理,得到了均衡投资策略和值函数的显示表达式。最后,通过数值模拟验证了参数对均衡投资策略和值函数的影响,主要得出了不完全信息下投资者的效用低于完全信息。所以,投资者应尽可能的搜集与投资相关的更多信息,以便于做出更加明智的决策。