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Self-organization of hexagonal agglomeration patterns in new economic geography models

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  • Ikeda, Kiyohiro
  • Murota, Kazuo
  • Akamatsu, Takashi
  • Kono, Tatsuhito
  • Takayama, Yuki

Abstract

Self-organization of agglomeration patterns for economic models in a two-dimensional economic space is studied from a multi-disciplinary viewpoint of new economic geography, central place theory, and bifurcation theory. Emergence of hexagonal distributions of various sizes in a homogeneous space is predicted theoretically for core–periphery models. The existence of hexagonal distributions as stable equilibria is demonstrated by a comparative static analysis with respect to transport costs for specific core–periphery models. These distributions are the ones envisaged by central place theory and also inferred to emerge by Krugman (1996) for a core–periphery model in two dimensions.

Suggested Citation

  • Ikeda, Kiyohiro & Murota, Kazuo & Akamatsu, Takashi & Kono, Tatsuhito & Takayama, Yuki, 2014. "Self-organization of hexagonal agglomeration patterns in new economic geography models," Journal of Economic Behavior & Organization, Elsevier, vol. 99(C), pages 32-52.
    • Handle: RePEc:eee:jeborg:v:99:y:2014:i:c:p:32-52
    DOI: 10.1016/j.jebo.2013.12.008
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    as
    1. B. Curtis Eaton & Richard G. Lipsey, 1975. "The Principle of Minimum Differentiation Reconsidered: Some New Developments in the Theory of Spatial Competition," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(1), pages 27-49.
    2. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    3. Behrens, Kristian & Thisse, Jacques-Francois, 2007. "Regional economics: A new economic geography perspective," Regional Science and Urban Economics, Elsevier, vol. 37(4), pages 457-465, July.
    4. Yannis M. Ioannides & Henry G. Overman, 2004. "Spatial evolution of the US urban system," Journal of Economic Geography, Oxford University Press, vol. 4(2), pages 131-156, April.
    5. Rikard Forslid & Gianmarco I.P. Ottaviano, 2003. "An analytically solvable core-periphery model," Journal of Economic Geography, Oxford University Press, vol. 3(3), pages 229-240, July.
    6. Pierre Picard & Takatoshi Tabuchi, 2010. "Self-organized agglomerations and transport costs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(3), pages 565-589, March.
    7. Ikeda, Kiyohiro & Akamatsu, Takashi & Kono, Tatsuhito, 2012. "Spatial period-doubling agglomeration of a core–periphery model with a system of cities," Journal of Economic Dynamics and Control, Elsevier, vol. 36(5), pages 754-778.
    8. Flam, Harry & Helpman, Elhanan, 1987. "Industrial policy under monopolistic competition," Journal of International Economics, Elsevier, vol. 22(1-2), pages 79-102, February.
    9. Tabuchi, Takatoshi & Thisse, Jacques-François, 2011. "A new economic geography model of central places," Journal of Urban Economics, Elsevier, vol. 69(2), pages 240-252, March.
    10. Dixit, Avinash K & Stiglitz, Joseph E, 1977. "Monopolistic Competition and Optimum Product Diversity," American Economic Review, American Economic Association, vol. 67(3), pages 297-308, June.
    11. J.Peter Neary, 2001. "Of Hype and Hyperbolas: Introducing the New Economic Geography," Journal of Economic Literature, American Economic Association, vol. 39(2), pages 536-561, June.
    12. Krugman, Paul, 1991. "Increasing Returns and Economic Geography," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 483-499, June.
    13. Murata, Yasusada, 2003. "Product diversity, taste heterogeneity, and geographic distribution of economic activities:: market vs. non-market interactions," Journal of Urban Economics, Elsevier, vol. 53(1), pages 126-144, January.
    14. Masahisa Fujita & Tomoya Mori, 2005. "Frontiers of the New Economic Geography," Papers in Regional Science, Wiley Blackwell, vol. 84(3), pages 377-405, August.
    15. Krugman, Paul, 1993. "On the number and location of cities," European Economic Review, Elsevier, vol. 37(2-3), pages 293-298, April.
    16. Akamatsu, Takashi & Takayama, Yuki & Ikeda, Kiyohiro, 2012. "Spatial discounting, Fourier, and racetrack economy: A recipe for the analysis of spatial agglomeration models," Journal of Economic Dynamics and Control, Elsevier, vol. 36(11), pages 1729-1759.
    17. Fujita, Masahisa & Krugman, Paul & Mori, Tomoya, 1999. "On the evolution of hierarchical urban systems1," European Economic Review, Elsevier, vol. 43(2), pages 209-251, February.
    18. Eaton, B Curtis & Lipsey, Richard G, 1982. "An Economic Theory of Central Places," Economic Journal, Royal Economic Society, vol. 92(365), pages 56-72, March.
    19. Martin, Philippe & Rogers, Carol Ann, 1994. "Trade Effects of Regional Aid," CEPR Discussion Papers 910, C.E.P.R. Discussion Papers.
    20. Tabuchi, Takatoshi & Thisse, Jacques-Francois, 2002. "Taste heterogeneity, labor mobility and economic geography," Journal of Development Economics, Elsevier, vol. 69(1), pages 155-177, October.
    21. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, December.
    22. Baldwin,Richard & Haapararanta,Pertti & Kiander,Jaakko (ed.), 1995. "Expanding Membership of the European Union," Cambridge Books, Cambridge University Press, number 9780521481342, January.
    23. Hofbauer, Josef & Sandholm, William H., 2007. "Evolution in games with randomly disturbed payoffs," Journal of Economic Theory, Elsevier, vol. 132(1), pages 47-69, January.
    24. M Sanglier & P M Allen, 1989. "Evolutionary Models of Urban Systems: An Application to the Belgian Provinces," Environment and Planning A, , vol. 21(4), pages 477-498, April.
    25. Munz, M & Weidlich, W, 1990. "Settlement Formation: Part II: Numerical Simulation," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 24(3), pages 177-196.
    26. Arthur, W. Brian, 1990. "'Silicon Valley' locational clusters: when do increasing returns imply monopoly?," Mathematical Social Sciences, Elsevier, vol. 19(3), pages 235-251, June.
    27. Dirk Stelder, 2005. "Where Do Cities Form? A Geographical Agglomeration Model for Europe," Journal of Regional Science, Wiley Blackwell, vol. 45(4), pages 657-679, November.
    28. Maarten Bosker & Steven Brakman & Harry Garretsen & Marc Schramm, 2010. "Adding geography to the new economic geography: bridging the gap between theory and empirics," Journal of Economic Geography, Oxford University Press, vol. 10(6), pages 793-823, November.
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    Cited by:

    1. Minoru Osawa & Takashi Akamatsu & Yuki Takayama, 2017. "Harris And Wilson (1978) Model Revisited: The Spatial Period‐Doubling Cascade In An Urban Retail Model," Journal of Regional Science, Wiley Blackwell, vol. 57(3), pages 442-466, June.
    2. Carolina Guevara, 2015. "The effect of trade on agglomeration within regions," Working Papers halshs-01233389, HAL.
    3. Ikeda, Kiyohrio & Onda, Mikihisa & Takayama, Yuki, 2017. "Bifurcation theory of a square lattice economy: Racetrack economy analogy in an economic geography model," MPRA Paper 78120, University Library of Munich, Germany.
    4. Qindong Fan & Fengtian Du & Hu Li, 2020. "A Study of the Spatial Form of Maling Village, Henan, China," Sustainability, MDPI, vol. 12(18), pages 1-24, September.
    5. MORI Tomoya, 2018. "Spatial Pattern and City Size Distribution," Discussion papers 18053, Research Institute of Economy, Trade and Industry (RIETI).
    6. Kiyohiro Ikeda & Mikihisa Onda & Yuki Takayama, 2019. "Bifurcation Theory of a Racetrack Economy in a Spatial Economy Model," Networks and Spatial Economics, Springer, vol. 19(1), pages 57-82, March.
    7. Takashi Akamatsu & Tomoya Mori & Minoru Osawa & Yuki Takayama, 2019. "Spatial scale of agglomeration and dispersion: Number, spacing, and the spatial extent of cities," Papers 1912.05113, arXiv.org, revised Aug 2024.
    8. Ikeda, Kiyohiro & Onda, Mikihisa & Takayama, Yuki, 2018. "Spatial period doubling, invariant pattern, and break point in economic agglomeration in two dimensions," Journal of Economic Dynamics and Control, Elsevier, vol. 92(C), pages 129-152.
    9. Takeda, Yoshihiro & Kono, Tatsuhito & Zhang, Yang, 2019. "Welfare effects of floor area ratio regulation on landowners and residents with different levels of income," Journal of Housing Economics, Elsevier, vol. 46(C).
    10. Marcus Berliant & Tomoya Mori, 2017. "Beyond urban form: How Masahisa Fujita shapes us," International Journal of Economic Theory, The International Society for Economic Theory, vol. 13(1), pages 5-28, March.
    11. Minoru Osawa & Takashi Akamatsu & Yosuke Kogure, 2020. "Stochastic stability of agglomeration patterns in an urban retail model," Papers 2011.06778, arXiv.org.
    12. Kogure, Yosuke & Ikeda, Kiyohiro, 2022. "Group-theoretic Study of Economic Agglomerations on a Square Lattice," MPRA Paper 112842, University Library of Munich, Germany.
    13. Kiyohiro Ikeda & Kazuo Murota & Takashi Akamatsu & Yuki Takayama, 2017. "Agglomeration patterns in a long narrow economy of a new economic geography model: Analogy to a racetrack economy," International Journal of Economic Theory, The International Society for Economic Theory, vol. 13(1), pages 113-145, March.
    14. Kiyohiro Ikeda & Minoru Osawa & Yuki Takayama, 2022. "Time Evolution of City Distributions in Germany," Networks and Spatial Economics, Springer, vol. 22(1), pages 125-151, March.
    15. Takashi Akamatsu & Tomoya Mori & Yuki Takayama, 2015. "Agglomerations in a multi-region economy: Poly-centric versus mono-centric patterns," KIER Working Papers 929, Kyoto University, Institute of Economic Research.
    16. Ching-mu Chen, 2019. "The effect of capital flow on the agglomeration evolution of footloose entrepreneurs," Asia-Pacific Journal of Regional Science, Springer, vol. 3(3), pages 761-791, October.
    17. Akamatsu, Takashi & Mori, Tomoya & Osawa, Minoru & Takayama, Yuki, 2017. "Spatial scale of agglomeration and dispersion: Theoretical foundations and empirical implications," MPRA Paper 80689, University Library of Munich, Germany.
    18. José M. Gaspar & Sofia B. S. D. Castro & João Correia-da-Silva, 2018. "Agglomeration patterns in a multi-regional economy without income effects," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(4), pages 863-899, December.
    19. José M. Gaspar, 2018. "A prospective review on New Economic Geography," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 61(2), pages 237-272, September.
    20. Ohtake, Kensuke, 2023. "Agglomeration and welfare of the Krugman model in a continuous space," Mathematical Social Sciences, Elsevier, vol. 123(C), pages 137-142.
    21. Aizawa, Hiroki & Kono, Tatsuhito, 2022. "Two-dimensional Geographical Position as a Factor in Determining the Growth and Decline of Retail Agglomeration," MPRA Paper 112274, University Library of Munich, Germany.
    22. Kalantari, Somayeh & Nazemi, Eslam & Masoumi, Behrooz, 2021. "Entropy-based goal-oriented emergence management in self-organizing systems through feedback control loop: A case study in NASA ANTS mission," Reliability Engineering and System Safety, Elsevier, vol. 210(C).

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    More about this item

    Keywords

    Bifurcation; Central place theory; Core–periphery models; Group-theoretic bifurcation theory; Hexagons; New economic geography; Self-organization;
    All these keywords.

    JEL classification:

    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)
    • R13 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - General Equilibrium and Welfare Economic Analysis of Regional Economies
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • F12 - International Economics - - Trade - - - Models of Trade with Imperfect Competition and Scale Economies; Fragmentation

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