摘要翻译：
我们考虑了Harris和Wilson提出的城市空间结构模型（环境与规划a,1978）。该模型由快速动力学和慢动力学组成，前者通过熵最大化原理表示位置之间的空间相互作用，后者表示促进这种空间相互作用的局部因素的空间分布演变。Harris和Wilson模型的一个已知的局限性是它可以有多个局部稳定的平衡点，导致预测依赖于初始状态。为了克服这一点，我们利用随机稳定性的平衡精化。我们建立在这样一个事实上，即模型是一个大种群势博弈，势博弈中的随机稳定状态对应于全局势极大化。与确定性动态下的局部稳定性不同，随机稳定性方法允许对城市空间配置进行唯一和明确的预测。我们发现，在最可能的空间配置中，零售集聚的数量会随着消费者购物成本的降低或集聚效应的增强而减少。
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英文标题：
《Stochastic stability of agglomeration patterns in an urban retail model》
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作者：
Minoru Osawa, Takashi Akamatsu, and Yosuke Kogure
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最新提交年份：
2020
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分类信息：

一级分类：Economics 经济学
二级分类：Theoretical Economics 理论经济学
分类描述：Includes theoretical contributions to Contract Theory, Decision Theory, Game Theory, General Equilibrium, Growth, Learning and Evolution, Macroeconomics, Market and Mechanism Design, and Social Choice.
包括对契约理论、决策理论、博弈论、一般均衡、增长、学习与进化、宏观经济学、市场与机制设计、社会选择的理论贡献。
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一级分类：Economics 经济学
二级分类：General Economics 一般经济学
分类描述：General methodological, applied, and empirical contributions to economics.
对经济学的一般方法、应用和经验贡献。
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一级分类：Mathematics 数学
二级分类：Dynamical Systems 动力系统
分类描述：Dynamics of differential equations and flows, mechanics, classical few-body problems, iterations, complex dynamics, delayed differential equations
微分方程和流动的动力学，力学，经典的少体问题，迭代，复杂动力学，延迟微分方程
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一级分类：Physics 物理学
二级分类：Pattern Formation and Solitons 图形形成与孤子
分类描述：Pattern formation, coherent structures, solitons
图案形成，相干结构，孤子
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一级分类：Quantitative Finance 数量金融学
二级分类：Economics 经济学
分类描述：q-fin.EC is an alias for econ.GN. Economics, including micro and macro economics, international economics, theory of the firm, labor economics, and other economic topics outside finance
q-fin.ec是econ.gn的别名。经济学，包括微观和宏观经济学、国际经济学、企业理论、劳动经济学和其他金融以外的经济专题
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英文摘要：
We consider a model of urban spatial structure proposed by Harris and Wilson (Environment and Planning A, 1978). The model consists of fast dynamics, which represent spatial interactions between locations by the entropy-maximizing principle, and slow dynamics, which represent the evolution of the spatial distribution of local factors that facilitate such spatial interactions. One known limitation of the Harris and Wilson model is that it can have multiple locally stable equilibria, leading to a dependence of predictions on the initial state. To overcome this, we employ equilibrium refinement by stochastic stability. We build on the fact that the model is a large-population potential game and that stochastically stable states in a potential game correspond to global potential maximizers. Unlike local stability under deterministic dynamics, the stochastic stability approach allows a unique and unambiguous prediction for urban spatial configurations. We show that, in the most likely spatial configuration, the number of retail agglomerations decreases either when shopping costs for consumers decrease or when the strength of agglomerative effects increases.
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