Discrete-space agglomeration model with social interactions: Multiplicity, stability, and continuous limit of equilibria

Akamatsu, Takashi; Fujishima, Shota; Takayama, Yuki

doi:10.1016/j.jmateco.2016.12.007

Cited by 7 publications

(6 citation statements)

References 31 publications

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“…Bragard and Mossay (2016) studied a relocation dynamics in the continuous-space framework of Mossay and Picard (2011). Akamatsu et al (2017) formulated a discrete-space version of Beckmann (1976)'s model as a potential game and elucidated its properties. Unification of this line of researches can lead to a fruitful field of applications of the potential game method.…”

Section: Related Literaturementioning

confidence: 99%

Equilibrium refinement for a model of non-monocentric internal structures of cities: A potential game approach

Osawa

Akamatsu

2020

Journal of Economic Theory

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Using the theory of potential games, this paper addresses the emergence of polycentric structures in cities, resulting from trade-offs between agglomeration economies and congestion effects. We consider a model that explains the formation of multiple business centers in cities as an equilibrium outcome under the presence of households' commuting costs and positive technological externalities between firms. We first show that the model is a large-population (non-atomic) potential game. To elucidate properties of stable spatial equilibria in the model, we consider local and global maximizations of the potential function of the model, which are known to correspond to various equilibrium refinement criteria. We find that (i) the formation of business centers (agglomeration of firms) is possible only when households' commuting costs are sufficiently low and that (ii) the size (number) of business centers increases (decreases) monotonically as communication between firms becomes easier.

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Section: Related Literaturementioning

confidence: 99%

Equilibrium refinement for a model of non-monocentric internal structures of cities: A potential game approach

Osawa

Akamatsu

2020

Journal of Economic Theory

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“…See, for instance, previous studies by (Akamatsu et al, 2012;Ikeda et al, 2012;Osawa et al, 2017;Ikeda et al, 2018).…”

Section: Evolution Of Spatial Structurementioning

confidence: 85%

“…Remark 5.1. The empirical evidence on regional agglomeration presented by Duranton and This is the "spatial period-doubling cascade" behavior discussed by (Akamatsu et al, 2012;Osawa et al, 2017;Ikeda et al, 2018). Next, Figure 11 shows the results for a Class II model, namely, the Allen and Arkolakis (2014).…”

Section: Evolution Of Spatial Structurementioning

confidence: 89%

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Multimodal agglomeration in economic geography

Akamatsu¹,

Mori²,

Osawa³

et al. 2019

Preprint

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We theoretically study a general family of economic geography models that features endogenous agglomeration. In many-region settings, the spatial scale-global or local-of the dispersion force(s) in a model plays a key role in determining the resulting endogenous spatial patterns and comparative statics. A global dispersion force accrues from competition between different locations and leads to the formation of multiple economic clusters, or cities. A local dispersion force is caused by crowding effects within each location and induces the flattening of each city. By distinguishing local and global dispersion forces, we can reduce a wide variety of extant models into only three prototypical classes that are qualitatively different in implications.Our framework adds consistent interpretations to the empirical literature and also provides general predictions on treatment effects in structural economic geography models.

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“…Stability characterization in such continuous-space models is difficult, although some authors have tackled this problem (for example, Bragard and Mossay, 2016). Instead, by considering discrete-space versions of Beckmanntype models, Akamatsu et al (2017) provided a potential function that can be used to characterize the stability of equilibria through more elementary means of finite-strategy evolutionary dynamics (as surveyed by Sandholm, 2010). Similarly, Osawa and Akamatsu (2020) showed that Fujita and Ogawa (1982)'s seminal urban economics model on the formation of multiple business districts in a city is an instance of potential games when formulated in discrete space; global maximization of the potential function is also an effective method of analysis in this model.…”

Section: Introductionmentioning

confidence: 99%

Stochastic stability of agglomeration patterns in an urban retail model

Osawa,

Akamatsu,

Kogure

2020

Preprint

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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 largepopulation 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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Discrete-space agglomeration model with social interactions: Multiplicity, stability, and continuous limit of equilibria

Cited by 7 publications

References 31 publications

Equilibrium refinement for a model of non-monocentric internal structures of cities: A potential game approach

Equilibrium refinement for a model of non-monocentric internal structures of cities: A potential game approach

Multimodal agglomeration in economic geography

Stochastic stability of agglomeration patterns in an urban retail model

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