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Replicator dynamics: Old and new 复制因子动力学:新旧
IF 0.9 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2020-01-01 DOI: 10.3934/jdg.2020028
S. Sorin
We introduce the unilateral version associated to the replicator dynamics and describe its connection to on-line learning procedures, in particular to the multiplicative weight algorithm. We show the interest of handling simultaneously discrete and continuous time analysis. We then survey recent results on extensions of this dynamics as maximization of the cumulative outcome with alternative regularization functions and variable weights. This includes no regret algorithms, time average version and link to best reply dynamics in two person games, application to equilibria and variational inequalities, convergence properties in potential and dissipative games.
我们介绍了与复制器动力学相关的单边版本,并描述了它与在线学习过程的联系,特别是与乘法加权算法的联系。我们展示了同时处理离散时间和连续时间分析的兴趣。然后,我们调查了最近关于这种动态扩展的结果,作为具有可选正则化函数和可变权重的累积结果的最大化。这包括不后悔算法,时间平均版本和最佳回复动态的链接,平衡和变分不等式的应用,潜在和耗散博弈的收敛特性。
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引用次数: 8
Sequencing grey games 灰色游戏排序
IF 0.9 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2020-01-01 DOI: 10.3934/jdg.2020002
S. Ergün, O. Palanci, S. Z. A. Gök, Şule Nizamoğlu, G. Weber
The job scheduling problem is a notoriously difficult problem in combinatorial optimization and Operational Research. In this study, we handle the job scheduling problem by using a cooperative game theoretical approach. In the sequel, sequencing situations arising grom grey uncertainty are considered. Cooperative grey game theory is applied to analyze these situations. Further, grey sequencing games are constructed and grey equal gain splitting (GEGS) rule is introduced. It is shown that cooperative grey games are convex. An application is given based on Priority Based Scheduling Algorithm. The paper ends with a conclusion.
作业调度问题是组合优化和运筹学中一个众所周知的难题。在本研究中,我们使用合作博弈理论的方法来处理作业调度问题。其次,考虑了灰色不确定性引起的排序情况。运用合作灰色博弈论对这些情况进行分析。在此基础上,构造了灰色排序博弈,并引入了灰色等增益分割规则。证明了合作灰色对策是凸的。给出了基于优先级调度算法的一个应用。论文以结论结束。
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引用次数: 4
On class of non-transferable utility cooperative differential games with continuous updating 一类具有持续更新的不可转让效用的合作微分对策
IF 0.9 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2020-01-01 DOI: 10.3934/jdg.2020020
Zeyang Wang, O. Petrosian
This paper considers and describes the class of cooperative differential games with the non-transferable utility and continuous updating. It is the first detailed paper about the application of continuous updating approach to the non-transferable utility differential games. The process of how to construct Pareto optimal strategy with continuous updating and Pareto trajectory is described. Another important contribution is that the property of subgame consistency is adopted for the class of games with continuous updating. The resource extraction game model is used as an example. The Pareto optimal strategies and corresponding trajectory are constructed, and the set of Pareto optimal strategies satisfying the subgame consistency property is presented. The results of numerical simulation are demonstrated in the Matlab environment, and the conclusion is drawn.
考虑并描述了一类效用不可转移且持续更新的合作微分对策。本文首次详细探讨了持续更新方法在不可转移效用微分对策中的应用。描述了如何构造具有连续更新和Pareto轨迹的Pareto最优策略的过程。另一个重要的贡献是,对于持续更新的博弈类,采用了子博弈一致性的性质。以资源抽取博弈模型为例。构造了Pareto最优策略及其轨迹,给出了满足子对策一致性的Pareto最优策略集。在Matlab环境下对数值模拟结果进行了验证,并得出了结论。
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引用次数: 7
Emerging patterns in inflation expectations with multiple agents 多重动因下通胀预期的新模式
IF 0.9 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2020-01-01 DOI: 10.3934/jdg.2020012
Emiliano Alvarez, Silvia London
Macroeconomic theory and central Banks' policy recommendations have analyzed for decades the link between the expected value of future inflation and its subsequent realization. Agents' inflation expectations have thus become a fundamental input of the economic policy: they allow to know if economic agents are synchronized with the policies and allow the Central Banks to anticipate the market trends. In this paper, we found evidence for the case of Uruguay of a discrepancy between the distribution of agents' inflation expectations and the distribution expected by traditional models. A first consequence is an increase in uncertainty in the estimates; problems related to its asymptotic distribution and the assumptions that arise from this aggregate distribution are analyzed. Another consequence is related to the existence of a structure in the data and the notion of equilibrium in the model. It is concluded that a discussion regarding the nature of the economic phenomenon is essential for the correct specification of the model studied.
几十年来,宏观经济理论和中央银行的政策建议一直在分析未来通胀预期值与其随后实现之间的联系。因此,经济主体的通胀预期已成为经济政策的基本输入:它们可以了解经济主体是否与政策同步,并允许央行预测市场趋势。在本文中,我们在乌拉圭的案例中发现了经济主体通胀预期分布与传统模型预期分布之间存在差异的证据。第一个后果是估算的不确定性增加;分析了其渐近分布的有关问题和由该总体分布产生的假设。另一个结果与数据中结构的存在和模型中平衡的概念有关。结论是,对经济现象的性质进行讨论对于所研究的模型的正确规范是必不可少的。
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引用次数: 0
Long-range dependence in the volatility of returns in Uruguayan sovereign debt indices 乌拉圭主权债务指数回报波动性的长期依赖性
IF 0.9 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2020-01-01 DOI: 10.3934/jdg.2020016
Juan Kalemkerian, Andr'es Sosa
One consequence of the fact that a large number of agents with different behaviors operate in financial systems is the emergence of certain statistical properties in some time series. Some of these properties contradict the hypotheses that are established in the traditional models of efficient market and portfolio optimization. Among them is the long-range dependence that is the objective of this work. The approach is proposed by fractional calculus, as a generalization of the classic approach to financial markets through semi-martingales. This paper study the existence of this property in variables dependent on the term structure curves of Uruguayan sovereign debt after the 2002 economic crisis.
在金融系统中,大量具有不同行为的主体运作的一个结果是,在某些时间序列中出现了某些统计特性。其中一些性质与有效市场和投资组合优化的传统模型中建立的假设相矛盾。其中包括作为本工作目标的长期依赖。该方法是由分数阶微积分提出的,作为通过半鞅分析金融市场的经典方法的推广。本文研究了2002年经济危机后乌拉圭主权债务期限结构曲线相关变量的这一性质的存在性。
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引用次数: 7
Pricing equilibrium of transportation systems with behavioral commuters 具有行为通勤者的交通系统定价均衡
IF 0.9 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2020-01-01 DOI: 10.3934/jdg.2020026
J. Lien, V. Mazalov, Jie Zheng
We study Wardrop equilibrium in a transportation system with profit-maximizing firms and heterogeneous commuters. Standard commuters minimize the sum of monetary costs and equilibrium travel time in their route choice, while "oblivious" commuters choose the route with minimal idle time. Three possible scenarios can arise in equilibrium: A pooling scenario where all commuters make the same transport choice; A separating scenario where different types of commuters make different transport choices; A partial pooling scenario where some standard commuters make the same transport choice as the oblivious commuters. We characterize the equilibrium existence condition, derive equilibrium flows, prices and firms' profits in each scenario, and conduct comparative analyses on parameters representing route conditions and heterogeneity of commuters, respectively. The framework nests the standard model in which all commuters are standard as a special case, and also allows for the case in which all commuters are oblivious as the other extreme. Our study shows how the presence of behavioral commuters under different route conditions affects equilibrium behavior of commuters and firms, as well a the equilibrium outcome of the transportation system.
研究了具有利润最大化企业和异质通勤者的运输系统中的Wardrop均衡。标准通勤者在选择路线时将货币成本和均衡出行时间的总和最小化,而“遗忘”通勤者则选择空闲时间最少的路线。均衡中可能出现三种情况:所有通勤者都选择相同的交通工具的合用情况;不同类型的通勤者选择不同的交通工具的分离场景;一个部分合用的场景,其中一些标准的通勤者与遗忘的通勤者做出相同的交通选择。我们描述了均衡存在条件,推导出了每种情景下的均衡流量、均衡价格和均衡企业利润,并分别对代表路线条件和通勤者异质性的参数进行了比较分析。该框架将所有通勤者都是标准的标准模型作为一种特殊情况,并允许所有通勤者都被遗忘作为另一种极端情况。研究揭示了不同路径条件下行为通勤者的存在如何影响通勤者和企业的均衡行为,以及交通系统的均衡结果。
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引用次数: 2
A regularization interpretation of the proximal point method for weakly convex functions 弱凸函数的近点法的正则化解释
IF 0.9 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2020-01-01 DOI: 10.3934/jdg.2020005
Tim Hoheisel, M. Laborde, Adam M. Oberman
Empirical evidence and theoretical results suggest that the proximal point method can be computed approximately and still converge faster than the corresponding gradient descent method, in both the stochastic and exact gradient case. In this article we provide a perspective on this result by interpreting the method as gradient descent on a regularized function. This perspective applies in the case of weakly convex functions where proofs of the faster rates are not available. Using this analysis we find the optimal value of the regularization parameter in terms of the weak convexity.
经验证据和理论结果表明,无论在随机情况还是精确梯度情况下,近点法都可以近似地计算,并且仍然比相应的梯度下降法收敛得快。在本文中,我们通过将该方法解释为正则化函数的梯度下降来提供对该结果的看法。这种观点适用于弱凸函数的情况,在这种情况下,更快的速率的证明是不可用的。利用这种分析,我们找到了正则化参数在弱凸性方面的最优值。
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引用次数: 10
A stochastic model for computer virus propagation 计算机病毒传播的随机模型
IF 0.9 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2020-01-01 DOI: 10.3934/jdg.2020010
M. Lefebvre
A three-dimensional continuous-time stochastic model based on the classic Kermack-McKendrick model for the spread of epidemics is proposed for the propagation of a computer virus. Moreover, control variables are introduced into the model. We look for the controls that either minimize or maximize the expected time it takes to clean the infected computers, or to protect them from the virus. Using dynamic programming, the equations satisfied by the value functions are derived. Particular problems are solved explicitly.
在经典Kermack-McKendrick模型的基础上,提出了计算机病毒传播的三维连续时间随机模型。并在模型中引入控制变量。我们寻找最小化或最大化清理受感染计算机所需的预期时间,或保护它们免受病毒侵害的控制措施。利用动态规划的方法,导出了数值函数所满足的方程。具体问题得到明确解决。
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引用次数: 3
Foundations of semialgebraic gene-environment networks 半代数基因-环境网络的基础
IF 0.9 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2020-01-01 DOI: 10.3934/jdg.2020018
Erik Kropat, G. Weber, E. B. Tirkolaee
Gene-environment network studies rely on data originating from different disciplines such as chemistry, biology, psychology or social sciences. Sophisticated regulatory models are required for a deeper investigation of the unknown and hidden functional relationships between genetic and environmental factors. At the same time, various kinds of uncertainty can arise and interfere with the system's evolution. The aim of this study is to go beyond traditional stochastic approaches and to propose a novel framework of semialgebraic gene-environment networks. Foundation is laid for future research, methodology and application. This approach is a natural extension of interconnected systems based on stochastic, polyhedral, ellipsoidal or fuzzy (linguistic) uncertainty. It allows for a reconstruction of the underlying network from uncertain (semialgebraic) data sets and for a prediction of the uncertain futures states of the system. In addition, aspects of network pruning for large regulatory systems in genome-wide studies are discussed leading to mixed-integer programming (MIP) and continuous programming.
基因-环境网络研究依赖于来自不同学科的数据,如化学、生物学、心理学或社会科学。为了更深入地研究遗传和环境因素之间未知和隐藏的功能关系,需要复杂的调节模型。与此同时,各种不确定性会出现并干扰系统的演化。本研究的目的是超越传统的随机方法,提出一种半代数基因-环境网络的新框架。为今后的研究、方法和应用奠定了基础。这种方法是基于随机、多面体、椭球体或模糊(语言)不确定性的互联系统的自然扩展。它允许从不确定(半代数)数据集重建底层网络,并对系统的不确定未来状态进行预测。此外,讨论了全基因组研究中大型调控系统的网络修剪方面,导致混合整数规划(MIP)和连续规划。
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引用次数: 16
Real option value and poverty trap 实物期权价值与贫困陷阱
IF 0.9 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2020-01-01 DOI: 10.3934/jdg.2020025
G. Calcagnini, E. Carrera, G. Travaglini
In recent years concerns about poverty traps have risen to the forefront of policy. Accordingly, the decision on investing or waiting in specific sectors or locations of poor countries is in part assigned to the government of that country. We study the optimal timing of a foreign direct investment (FDI) where the returns are stochastic and the cost irreversible. A model of real option value compares the benefits and costs of a risky FDI with those of a riskless official development assistance (ODA). Once FDIs take place, the local government can shift ODAs towards different sectors or locations to hinder poverty. We show that with uncertainty and irreversibility, the policy decision has an opportunity value that must be included as a part of the full value of the FDI. This option value is highly sensitive to uncertainty over the future returns, so that changing actual economic conditions in poor countries can have a large impact on the poverty trap. Simulations show that this option value can be significant to explain the prevalence of hysteresis, that is the tendency of a poor country to persist in poverty.
近年来,对贫困陷阱的担忧已经上升到政策的前沿。因此,在贫穷国家的特定部门或地点投资或等待的决定部分地交给了该国政府。本文研究了收益是随机的、成本是不可逆的外商直接投资的最优时机。实物期权价值模型比较了有风险的外国直接投资与无风险的官方发展援助的收益和成本。一旦有了外国直接投资,地方政府就可以将官方发展援助转移到不同的部门或地区,以消除贫困。我们表明,由于不确定性和不可逆性,政策决策具有机会价值,必须将其作为外国直接投资全部价值的一部分。这一选择值对未来收益的不确定性高度敏感,因此穷国不断变化的实际经济状况可能对贫困陷阱产生重大影响。模拟表明,这个选项值对于解释滞后现象的普遍性具有重要意义,滞后现象是一个贫穷国家持续贫困的趋势。
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引用次数: 2
期刊
Journal of Dynamics and Games
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