IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v438y2015icp161-168.html
   My bibliography  Save this article

Weber–Fechner relation and Lévy-like searching stemmed from ambiguous experiences

Author

Listed:
  • Sakiyama, T.
  • Gunji, Y.P.

Abstract

Here, we show that an optimized Lévy-like walk (μ≈2.00) and the Weber–Fechner law can be achieved in our new multi-agent based model that depends on step lengths. Weber–Fechner equation is strongly related to power-law. This equation is sometimes used in order to obtain power-law tailed distributions in observational levels. However, no study has reported how these two popular equations were achieved in micro or mechanistic levels. We propose a new random walk algorithm based on a re-valued algorithm, in which an agent has limited memory capacity, i.e., an agent has a memory of only four recent random numbers (limitation number). Using these random numbers, the agent alters the directional heuristic if the agent experiences moving directional biases. In this paper, the initial limitation number varies depending on the interaction among agents. Thus, agents change their limitation number and produce time delay in respect to rule change events. We show that slope values are variable compared with isolate foraging even though both indicate power-law tailed walks derived from Weber–Fechner equation.

Suggested Citation

  • Sakiyama, T. & Gunji, Y.P., 2015. "Weber–Fechner relation and Lévy-like searching stemmed from ambiguous experiences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 161-168.
  • Handle: RePEc:eee:phsmap:v:438:y:2015:i:c:p:161-168
    DOI: 10.1016/j.physa.2015.06.038
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437115005981
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    File URL: https://libkey.io/10.1016/j.physa.2015.06.038?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Reynolds, A.M. & Geritz, S.A.H., 2015. "Tsallis distributions, Lévy walks and correlated-type anomalous diffusion result from state-dependent diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 424(C), pages 317-321.
    2. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(3), pages 739-767.
    3. Sakiyama, Tomoko & Gunji, Yukio-Pegio, 2014. "The relationship between randomness and power-law distributed move lengths in random walk algorithms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 402(C), pages 76-83.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Michel DIMOU & Alexandra SCHAFFAR & Zhihong CHEN & Shihe FU, 2008. "LA CROISSANCE URBAINE CHINOISE RECONSIDeReE," Region et Developpement, Region et Developpement, LEAD, Universite du Sud - Toulon Var, vol. 27, pages 109-131.
    2. Bosker, Maarten & Brakman, Steven & Garretsen, Harry & Schramm, Marc, 2008. "A century of shocks: The evolution of the German city size distribution 1925-1999," Regional Science and Urban Economics, Elsevier, vol. 38(4), pages 330-347, July.
    3. Klein, Alexander & Leunig, Tim, 2013. "Gibrat’s Law and the British Industrial Revolution," CAGE Online Working Paper Series 146, Competitive Advantage in the Global Economy (CAGE).
    4. Satyajit Chatterjee & Esteban Rossi‐Hansberg, 2012. "Spinoffs And The Market For Ideas," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(1), pages 53-93, February.
    5. Stephen J. Redding, 2010. "The Empirics Of New Economic Geography," Journal of Regional Science, Wiley Blackwell, vol. 50(1), pages 297-311, February.
    6. Donald R. Davis & David E. Weinstein, 2008. "A Search For Multiple Equilibria In Urban Industrial Structure," Journal of Regional Science, Wiley Blackwell, vol. 48(1), pages 29-65, February.
    7. Chen, Zhimin & Ibragimov, Rustam, 2019. "One country, two systems? The heavy-tailedness of Chinese A- and H- share markets," Emerging Markets Review, Elsevier, vol. 38(C), pages 115-141.
    8. Lena SANDERS, 2012. "Regards Scientifiques Croisés Sur La Hiérarchie Des Systèmes De Peuplement : De L’Empirie Aux Systèmes Complexes," Region et Developpement, Region et Developpement, LEAD, Universite du Sud - Toulon Var, vol. 36, pages 127-146.
    9. Sokołowski Dariusz & Jażdżewska Iwona, 2021. "Zipf's Law for cities: estimation of regression function parameters based on the weight of American urban areas and Polish towns," Bulletin of Geography. Socio-economic Series, Sciendo, vol. 53(53), pages 147-156, September.
    10. Xavier Gabaix & Jean‐Michel Lasry & Pierre‐Louis Lions & Benjamin Moll, 2016. "The Dynamics of Inequality," Econometrica, Econometric Society, vol. 84, pages 2071-2111, November.
    11. di Giovanni, Julian & Levchenko, Andrei A. & Rancière, Romain, 2011. "Power laws in firm size and openness to trade: Measurement and implications," Journal of International Economics, Elsevier, vol. 85(1), pages 42-52, September.
    12. Mr. Kenneth Rogoff & Yuanchen Yang, 2022. "A Tale of Tier 3 Cities," IMF Working Papers 2022/196, International Monetary Fund.
    13. Costas Efthimiou & Adam Wearne, 2016. "Household Income Distribution in the USA," Papers 1602.06234, arXiv.org.
    14. Oshiro, Jun & Sato, Yasuhiro, 2021. "Industrial structure in urban accounting," Regional Science and Urban Economics, Elsevier, vol. 91(C).
    15. Birkmaier, Daniel & Wohlrabe, Klaus, 2014. "The Matthew effect in economics reconsidered," Journal of Informetrics, Elsevier, vol. 8(4), pages 880-889.
    16. Duranton, Gilles & Puga, Diego, 2014. "The Growth of Cities," Handbook of Economic Growth, in: Philippe Aghion & Steven Durlauf (ed.), Handbook of Economic Growth, edition 1, volume 2, chapter 5, pages 781-853, Elsevier.
    17. Daron Acemoglu & James A. Robinson, 2015. "The Rise and Decline of General Laws of Capitalism," Journal of Economic Perspectives, American Economic Association, vol. 29(1), pages 3-28, Winter.
    18. J. Vernon Henderson & Sebastian Kriticos, 2018. "The Development of the African System of Cities," Annual Review of Economics, Annual Reviews, vol. 10(1), pages 287-314, August.
    19. Rafael González-Val, 2012. "A Nonparametric Estimation of the Local Zipf Exponent for all US Cities," Environment and Planning B, , vol. 39(6), pages 1119-1130, December.
    20. Monras, Joan, 2015. "Economic Shocks and Internal Migration," IZA Discussion Papers 8840, Institute of Labor Economics (IZA).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:438:y:2015:i:c:p:161-168. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.