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Are there multiple equilibria in the spatial economy? This paper develops a unified framework that integrates systems of cities and regional models to address this question within a general geographic space. A key feature is the endogenous…

Theoretical Economics · Economics 2025-05-01 Gianandrea Lanzara , Matteo Santacesaria

This paper studies the evolution of economic activities using a continuous time-space aggregation-diffusion model, which encompasses competing effects of agglomeration and congestion. To bring the model to the real data, a novel…

General Economics · Economics 2024-07-31 Davide Fiaschi , Angela Parenti , Cristiano Ricci

Urban land cover doubled between 1985 and 2015, yet the spatial dynamics of urban form remain under-quantified, despite its importance for sustainability, infrastructure planning, and climate risk. Urban expansion is a non-equilibrium…

Physics and Society · Physics 2026-03-10 Marc Barthelemy , Ulysse Marquis

The sustainable management of common resources often leads to a social dilemma known as the tragedy of the commons: individuals benefit from rapid extraction of resources, while communities as a whole benefit from more sustainable…

Populations and Evolution · Quantitative Biology 2025-02-11 Tianyong Yao , Daniel B. Cooney

Many large cities are found at locations with certain first nature advantages. Yet, those exogenous locational features may not be the most potent forces governing the spatial pattern of cities. In particular, population size, spacing and…

General Economics · Economics 2019-08-27 Tomoya Mori

In this paper we explore the dynamic relationship between income inequality and economic mobility through a pairing of a population-scale partial differential equation (PDE) model and an associated individual-based stochastic differential…

Physics and Society · Physics 2025-03-25 Scott A. McKinley , Gary A. Hoover

This paper proposes a spatial model with a realistic geography where a continuous distribution of agents (e.g., farmers) engages in economic interactions with one location from a finite set (e.g., cities). The spatial structure of the…

Theoretical Economics · Economics 2023-06-02 Gianandrea Lanzara , Matteo Santacesaria

How does transport cost affect the spatial organization of economic activities? This study develops a theoretical framework that distinguishes between two types of dispersion forces in spatial models: "local" dispersion forces acting within…

General Economics · Economics 2026-03-02 Takashi Akamatsu , Tomoya Mori , Minoru Osawa , Yuki Takayama

Income redistribution is the transfer of income from some individuals to others directly or indirectly by means of social mechanisms, such as taxation, public services and so on. Employing a spatial public goods game, we study the influence…

Physics and Society · Physics 2017-03-08 Zhenhua Pei , Baokui Wang , Jinming Du

Involution, a phenomenon of excessive competition with diminishing returns, has become a pressing socio-economic concern in contemporary China, prompting both academic inquiry and policy interventions. This paper proposes an evolutionary…

Physics and Society · Physics 2026-03-16 Bo Li , Qiwen Ge , Yong Shi

We propose a simple semi-discrete spatial model where rents, wages and the density of population in a city can be deduced from free-mobility and equilibrium conditions on the labour and residential housing markets. We prove existence and…

Optimization and Control · Mathematics 2022-07-27 Yves Achdou , Guillaume Carlier , Quentin Petit , Daniela Tonon

In the recent literature dealing with spatial extensions of the continuous Ramsey model, the capital accumulation process via time and space is modeled as a linear parabolic partial differential equation. The process of capital movement…

Optimization and Control · Mathematics 2019-09-06 L. Fredrick , G. Müller-Fürstenberger , E. W. Sachs , L. Somorowsky

While the use of spatial agent-based and individual-based models has flourished across many scientific disciplines, the complexities these models generate are often difficult to manage and quantify. This research reduces population-driven,…

Physics and Society · Physics 2021-08-24 John C. Stevenson

Understanding urban growth is one with understanding how society evolves to satisfy the needs of its individuals in sharing a common space and adapting to the territory. We propose here a quantitative analysis of the historical development…

Physics and Society · Physics 2016-04-27 Alessandro Fiasconaro , Emanuele Strano , Vincenzo Nicosia , Sergio Porta , Vito Latora

Growth is a multi-layered phenomenon in human societies, composed of socioeconomic and demographic change at many different scales. Yet, standard macroeconomic indicators average over most of these processes, blurring the spatial and…

Physics and Society · Physics 2025-11-11 Jordan T Kemp , Laura Fürsich , Luís M A Bettencourt

In this paper we analyze urban spatial segregation phenomenon in terms of the income distribution over a population, and inflationary parameter weighting the evolution of housing prices. For this, we develop a discrete, spatially extended…

Adaptation and Self-Organizing Systems · Physics 2007-08-29 Antonio Aguilera , Edgardo Ugalde

This paper studies spatial patterns formed by proximate population migration driven by real wage gradients and other idiosyncratic factors. The model consists of a tractable core-periphery model incorporating a quasi-linear log utility…

Theoretical Economics · Economics 2025-07-23 Kensuke Ohtake

One of the most significant findings in the study of spatial Solow-Swan models is the emergence of economic agglomeration, in which economic activities concentrate in specific regions. Such agglomeration provides a fundamental mechanism…

Analysis of PDEs · Mathematics 2025-10-23 Fanze Kong , Jiayi Sun , Shuangquan Xie

Intricate interactions among firms, institutions, and spatial structures shape urban economic systems. In this study, we propose a framework based on three structural dimensions -- abundance, diversity, and longevity (ADL) of economic units…

Physics and Society · Physics 2026-01-28 Marco A. Rosas Pulido , Roberto Murcio , Omar R. Vázquez , Carlos Gershenson

We propose a stochastic dynamic model of migration and economic aggregation in a system of employed (immobile) and unemployed (mobile) agents which respond to local wage gradients. Dependent on the local economic situation, described by a…

adap-org · Physics 2007-05-23 Frank Schweitzer
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