A Three-Stage Stochastic Dynamic Pricing Game Model Affected by New Products into the Market

In real-life marketing, a common phenomenon is that the prices of current product will have been cut down even the new product has not gone into market yet. Thus, it is very important for merchant to set the strategy which can make the excepted revenue maximum. So, this paper constructs a three-stage stochastic dynamic pricing game model for analyzing the influence of the uncertainty of entry timing of the new products on pricing of products being sold. By analyzing of the pricing strategy, there are big differences in the predictions of new product going into market between merchant and customers;the merchant will adopt cutting price for promotion strategy to reduce negative influence of the new products on the demand of the products sold now. Otherwise, the merchant will adopt the strategy of maximizing current period’s profit.

Relationship between Maximum Principle and Dynamic Programming in Stochastic Differential Games and Applications

This paper is concerned with the relationship between maximum principle and dynamic programming in zero-sum stochastic differential games. Under the assumption that the value function is enough smooth, relations among the adjoint processes, the generalized Hamiltonian function and the value function are given. A portfolio optimization problem under model uncertainty in the financial market is discussed to show the applications of our result.

Network Defense Decision-Making Based on Deep Reinforcement Learning and Dynamic Game Theory

Existing researches on cyber attackdefense analysis have typically adopted stochastic game theory to model the problem for solutions,but the assumption of complete rationality is used in modeling,ignoring the information opacity in practical attack and defense scenarios,and the model and method lack accuracy.To such problem,we investigate network defense policy methods under finite rationality constraints and propose network defense policy selection algorithm based on deep reinforcement learning.Based on graph theoretical methods,we transform the decision-making problem into a path optimization problem,and use a compression method based on service node to map the network state.On this basis,we improve the A3C algorithm and design the DefenseA3C defense policy selection algorithm with online learning capability.The experimental results show that the model and method proposed in this paper can stably converge to a better network state after training,which is faster and more stable than the original A3C algorithm.Compared with the existing typical approaches,Defense-A3C is verified its advancement.

Research on Maneuver Decision-Making of Multi-Agent Adversarial Game in a Random Interference Environment

The strategy evolution process of game players is highly uncertain due to random emergent situations and other external disturbances.This paper investigates the issue of strategy interaction and behavioral decision-making among game players in simulated confrontation scenarios within a random interference environment.It considers the possible risks that random disturbances may pose to the autonomous decision-making of game players,as well as the impact of participants’manipulative behaviors on the state changes of the players.A nonlinear mathematical model is established to describe the strategy decision-making process of the participants in this scenario.Subsequently,the strategy selection interaction relationship,strategy evolution stability,and dynamic decision-making process of the game players are investigated and verified by simulation experiments.The results show that maneuver-related parameters and random environmental interference factors have different effects on the selection and evolutionary speed of the agent’s strategies.Especially in a highly uncertain environment,even small information asymmetry or miscalculation may have a significant impact on decision-making.This also confirms the feasibility and effectiveness of the method proposed in the paper,which can better explain the behavioral decision-making process of the agent in the interaction process.This study provides feasibility analysis ideas and theoretical references for improving multi-agent interactive decision-making and the interpretability of the game system model.

A Game-Based Approach for PCTL＊ Stochastic Model Checking with Evidence

Stochastic model checking is a recent extension and generalization of the classical model checking, which focuses on quantitatively checking the temporal property of a system model. PCTL＊ is one of the important quantitative property specification languages, which is strictly more expressive than either PCTL （probabilistic computation tree logic） or LTL （linear temporal logic） with probability bounds. At present, PCTL＊ stochastic model checking algorithm is very complicated, and cannot provide any relevant explanation of why a formula does or does not hold in a given model. For dealing with this problem, an intuitive and succinct approach for PCTL＊ stochastic model checking with evidence is put forward in this paper, which includes： presenting the game semantics for PCTL＊ in release-PNF （release-positive normal form）, defining the PCTL＊ stochastic model checking game, using strategy solving in game to achieve the PCTL＊ stochastic model checking, and refining winning strategy as the evidence to certify stochastic model checking result. The soundness and the completeness of game-based PCTL＊ stochastic model checking are proved, and its complexity matches the known lower and upper bounds. The game-based PCTL＊ stochastic model checking algorithm is implemented in a visual prototype tool, and its feasibility is demonstrated by an illustrative example.

Bi-Level Programming for the Optimal Nonlinear Distance-Based Transit Fare Structure Incorporating Principal-Agent Game

The urban transit fare structure and level can largely affect passengers’travel behavior and route choices.The commonly used transit fare policies in the present transit network would lead to the unbalanced transit assignment and improper transit resources distribution.In order to distribute transit passenger flow evenly and efficiently,this paper introduces a new distance-based fare pattern with Euclidean distance.A bi-level programming model is developed for determining the optimal distance-based fare pattern,with the path-based stochastic transit assignment(STA)problem with elastic demand being proposed at the lower level.The upper-level intends to address a principal-agent game between transport authorities and transit enterprises pursing maximization of social welfare and financial interest,respectively.A genetic algorithm(GA)is implemented to solve the bi-level model,which is verified by a numerical example to illustrate that the proposed nonlinear distance-based fare pattern presents a better financial performance and distribution effect than other fare structures.

可再生能源投资的政企随机演化博弈研究——基于动态碳价视角

针对传统确定性演化博弈模型的不足,引入几何布朗运动模型模拟动态的碳价参数,构建了具有随机支付矩阵的演化博弈模型,以全国碳市场背景下的发电企业为例,研究了政企双方的演化过程和策略选择,探究了不同因素对演化均衡和政企决策的影响.结果显示:碳价是影响政企决策的重要因素,碳价较低时,政企的最优决策分别是选择作为策略即采取奖惩措施和不投资可再生能源,碳价较高时最优决策转变为不作为和投资.火力发电的成本、收益和碳排放系数以及可再生能源发电的成本、收益和建设成本是影响政府和发电企业策略选择的关键因素.发电企业投资意愿与政府的奖惩力度正相关,政府作为意愿与奖惩力度负相关,短期内提高政府的奖惩力度可激励发电企业的投资行为,但会缩短政府作为时长.

澜湄次区域减灾合作发展的随机演化博弈模型

长期以来,澜沧江—湄公河次区域一直深受灾害风险的威胁,给次区域的社会经济发展造成了很大阻碍,开展减灾合作是提升减灾能力的有效方式。该文为探析次区域内各国减灾合作机制和影响减灾合作关系的关键因素,建立随机演化博弈模型,并引入灾害抗逆力与国际关系来探讨各国博弈策略动态演化过程及影响因素。研究结果表明:一国灾害抗逆力的提升无论是在随机因素影响强或弱的条件下,均不确定其能否促进合作发展局面的形成,国际关系的亲近则对于合作发展局面有着正向的促进作用,在当前时代背景下,各国对减灾合作的积极性在不断提高,同时,我国当前的决策行为能够对合作局面产生促进作用。基于澜湄次区域内国家间合作演化规律的探讨,可进一步为各国提升防灾减灾救灾能力与优化减灾合作机制提供借鉴,助力经济社会发展。

环境不确定情景下绿色技术创新动态扩散模型分析

为探究不确定性因素对绿色技术创新动态扩散过程的影响,推动绿色技术创新以解决气候变化、资源稀缺和环境破坏等问题,通过构建以企业和消费者为主体的随机演化博弈模型,并对其进行了稳定性分析,得到3种扩散稳定情形,并完成了仿真测试。结果表明:在实施绿色技术创新策略的企业比重以及选择绿色消费的消费者比重均较小时,在不同的随机干扰下,最终都不能实现有效稳定;随着两者比例的增大,在经历混沌状态后,绿色技术创新策略和绿色消费能分别在企业和消费者中成功扩散,且在不同的干扰程度下实现有效稳定。

考虑随机用户均衡的区县级电动汽车快充站规划

电动汽车渗透率的提高和城市化进程的发展使得区县级充电设施的建设具有重要意义。综合考虑用户充电需求时空分布和用户充电决策中的有限理性,提出一种面向区县的电动汽车快充站优化规划模型。首先,针对区县用户的出行特征,构建包含外部连接的交通网络拓扑扩展形式,采用出行链仿真捕捉用户快充需求;其次,结合影响用户充电选择的多种因素,建立用户充电决策模型并给出随机用户均衡条件;然后,建立以投资运行成本、用户绕行距离最小为目标的多场景快充站选址定容优化模型,通过多种线性化手段处理指数等式均衡约束,将优化问题转换为混合整数线性规划以高效求解;最后,以33节点交通系统为例对快充站规划结果进行分析,验证所提模型和线性近似方法的合理性。

基于随机博弈网的窃密木马诱导式博弈模型

为实现长期窃取信息的目的,窃密木马通常采用触发执行策略来实施其恶意行为,使得其恶意行为的执行具有高隐蔽性和不确定性。主流的窃密木马防御模型采用被动监测窃密木马行为并加以检测的被动防御策略,容易出现漏报和检测不及时的情况。为了提升窃密木马防御模型的防御效果,文章引入诱导操作以构建窃密木马诱导式防御策略,并使用随机博弈网对窃密木马和防御方的攻防对抗过程进行建模分析,构建了IGMDT-SGN。IGMDT-SGN直观揭示了防御方运用诱导式防御策略来对抗窃密木马的策略性逻辑和时序关系。通过模型量化计算对IGMDT-SGN中诱导式防御策略的防御效果进行定量分析,结果表明,窃密木马诱导式防御策略在防御成功率、防御平均时间上优于窃密木马被动防御策略,可为窃密木马的防御提供有益参考。

碳交易制度下企业低碳技术创新的激励研究

碳交易是实现“双碳”目标和驱动经济高质量发展的重要政策工具。文章研究了碳交易制度下,处于不完全竞争市场企业的低碳技术创新决策问题。通过构建市场势力差异下企业的低碳技术创新策略和末端治理策略选择随机演化博弈模型,分析随机干扰、创新成本和遵规成本对主导企业和边缘企业策略选择的影响。理论分析和仿真结果表明,市场势力影响环境规制的低碳技术创新效应;引入碳交易制度后,不同市场势力企业的低碳技术创新策略选择存在差异,主导企业更倾向低碳技术创新策略,创新成本对其策略选择的影响最明显;边缘企业在一定条件下偏向低碳技术创新策略,但容易因强随机干扰、高创新成本和高遵规成本而偏离;研发外溢为0.7的适度水平有利于激励边缘企业采用低碳技术创新策略。文章的研究结论为政府完善碳交易制度、制定企业低碳技术创新激励政策提供启示。

基于随机演化博弈的新能源汽车发展策略研究

新能源汽车的投入使用是减少空气污染的有效手段,长期以来一直是政府关注的焦点,但目前新能源汽车的产销量依旧较低,提高新能源汽车市场份额以解决环境污染和能源短缺问题迫在眉睫。首先建立汽车市场中政府和消费者的两方确定性演化博弈模型,其次通过引入高斯白噪声表示系统受不确定性因素的影响,建立随机演化博弈模型,通过模型分析得到随机扰动下该系统达到稳定状态的条件,最后通过Matlab软件进行数值仿真并根据仿真结果对促进新能源汽车发展提出相应的建议。研究表明:油价、零部件成本、电池价格等不确定性因素会对汽车市场中消费者和政府的两方博弈造成随机干扰,导致该系统演化出现不同程度的波动,同时会改变达到演化稳定状态所需要的时间;政府选择补贴的行为比消费者购买新能源汽车的行为对随机干扰强度σ更敏感;加强随机干扰强度,政府选择补贴和消费者选择购买新能源汽车的两种策略概率都能更快达到稳定状态。

Perturbation analysis of stochastic hybrid systems and applications to resource contention games

We provide an overview of the recently developed general infinitesimal perturbation analysis(IPA)framework for stochastic hybrid systems(SHSs),and establish some conditions under which this framework can be used to obtain unbiased performance gradient estimates in a particularly simple and efficient manner.We also propose a general scheme for systematically deriving an abstraction of a discrete event system(DES)in the form of an SHS.Then,as an application of the general IPA framework,we study a class of stochastic non-cooperative games termed“resource contention games”modeled through stochastic flow models(SFMs),where two or more players(users)compete for the use of a sharable resource.Simulation results are provided for a simple version of such games to illustrate and contrast system-centric and user-centric optimization.

基于随机博弈模型的网络攻防量化分析方法

针对日益普遍和多样的网络攻击和破坏行为,如何利用模拟真实网络的虚拟环境,实现对网络各种攻防过程的实验推演,并分析评价网络系统安全性,已逐渐成为热点研究方向.对此文中提出了采用随机博弈模型的网络攻防实验整体架构,提出了由网络连接关系、脆弱性信息等输入数据到网络攻防博弈模型的快速建模方法,基于最终生成的攻防模型可以对目标网络的攻击成功率、平均攻击时间、脆弱节点以及潜在攻击路径等方面进行安全分析与评价.最后,应用研究所得的网络攻防模型与分析方法对一个典型的企业网络攻防过程进行分析和推演.结果表明了模型和分析方法的有效性.

面向恶意程序传播的传感网可靠度评估

为评估恶意程序传播环境中的传感网可靠度,引入"死亡"状态扩展了传统的SEIR传染病模型,采用马尔可夫链确切地描述了传感节点的状态动态变化过程.利用随机博弈,提出了传感网恶意程序传播检测模型来预测恶意程序的传播行为概率,再将得到的结果整合到马尔可夫链的状态转换矩阵,实现了恶意程序传播故意性和马尔可夫链随机性的关联.建立了利用马尔可夫链计算恶意程序传播环境中传感节点可靠度的公式,分别给出了具有星形和簇状拓扑结构的传感网可靠度评估方法.实验给出了恶意程序传播对传感节点可靠度的影响,结果表明所提出的方法能有效评估整个传感网的可靠度.

基于攻防随机博弈模型的防御策略选取研究

由于网络安全攻防双方的目标对立性和策略依存性,使得最优防御策略选取问题十分复杂.形式化定义了网络安全防御策略选取问题.提出了一种刻画网络安全攻防矛盾,解决防御策略选取问题的攻防随机博弈模型.该模型是矩阵型攻防博弈模型和Markov决策过程的扩展,是多人、多状态的动态攻防推演模型.将攻击者在网络实体上的特权状态作为攻防随机博弈模型的元素,建模网络攻防状态的动态变化,并预测攻击行为和决策最优防御策略.给出了基于上述模型的防御策略选取算法.用一个网络实例分析了该模型和算法在攻击策略预测和防御策略决策方面的有效性.

网络群体行为的演化博弈模型与分析方法

随着社会关系网络和在线社会网络应用的不断发展,如何理解和分析群体合作行为的稳定维持和演化是社会关系网络研究中面临的最大的挑战之一.文中综述了网络群体行为和随机演化博弈模型与分析方法等方面的研究工作,介绍了可用于网络群体行为分析评价的指标和模型,总结了网络群体行为和随机演化博弈模型的若干研究和分析方法,探讨了应用随机演化博弈模型进行网络群体行为研究的可行性.基于这些讨论,展望了社会关系网络中的网络群体行为研究所面临的主要挑战.

考虑配电网安全性的虚拟电厂优化调度博弈模型

以往的虚拟电厂(VPP)优化调度模型仅考虑VPP的经济性,所得最优调度方案往往无法满足配电网的安全需求,会造成线路过负荷、节点电压越限等问题,影响电力系统的安全稳定运行。为了权衡VPP的经济性与配电网的安全性,建立了基于非合作博弈理论的VPP优化调度博弈模型,并且采用随机规划法处理风/光可再生能源以及电价的不确定性。以某市城北变八引线配电网为算例,对VPP优化调度模型、配电网安全性模型以及非合作博弈模型三者的优化结果进行了比较,结果表明:当VPP与配电网以非合作方式进行博弈时,会采取相对保守的调度策略,削减各聚合单元的发电量,使VPP在获得较大利润的同时,配电网也能够保持较高的安全性,验证了所提非合作博弈模型的有效性和合理性。

随机需求与政府补贴条件下的低碳供应链协调

研究了政府低碳减排价格补贴对于由供应商主导的两级供应链决策的影响。在改进的报童模型基础上,分别针对单独补贴和同时补贴的情形,建立了分散决策时的Stackelberg博弈模型和集中决策模型,求解最优订货量、批发价格和减排努力量。发现同时补贴两个节点企业时供应链趋于协调,优于只补贴其中一个企业的情形。证明了政府制定的减排价格补贴函数,可以是一个关于减排努力量的线性函数或者非线性的凹函数。