IDEAS home Printed from https://ideas.repec.org/a/jas/jasssj/2006-52-2.html
   My bibliography  Save this article

Taking into Account the Variations of Neighbourhood Sizes in the Mean-Field Approximation of the Threshold Model on a Random Network

Author

Abstract

We compare the individual-based 'threshold model' of innovation diffusion in the version which has been studied by Young (1998), with an aggregate model we derived from it. This model allows us to formalise and test hypotheses on the influence of individual characteristics upon global evolution. The classical threshold model supposes that an individual adopts a behaviour according to a trade-off between a social pressure and a personal interest. Our study considers only the case where all have the same threshold. We present an aggregated model, which takes into account variations of the neighbourhood sizes, whereas previous work assumed this size fixed (Edwards et al. 2003a). The comparison between the aggregated models (the first one assuming a neighbourhood size and the second one, a variable one) points out an improvement of the approximation in most of the value of parameter space. This proves that the average degree of connectivity (first aggregated model) is not sufficient for characterising the evolution, and that the node degree variability has an impact on the diffusion dynamics. Remaining differences between both models give us some clues about the specific ability of individual-based model to maintain a minority behaviour which becomes a majority by an addition of stochastic effects.

Suggested Citation

  • Sylvie Huet & Margaret Edwards & Guillaume Deffuant, 2007. "Taking into Account the Variations of Neighbourhood Sizes in the Mean-Field Approximation of the Threshold Model on a Random Network," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 10(1), pages 1-10.
    • Handle: RePEc:jas:jasssj:2006-52-2
    as

    Download full text from publisher

    File URL: https://www.jasss.org/10/1/10/10.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Blume Lawrence E., 1995. "The Statistical Mechanics of Best-Response Strategy Revision," Games and Economic Behavior, Elsevier, vol. 11(2), pages 111-145, November.
    2. Margaret Edwards & Sylvie Huet & François Goreaud & Guillaume Deffuant, 2003. "Comparing an Individual-Based Model of Behaviour Diffusion with Its Mean Field Aggregate Approximation," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 6(4), pages 1-9.
    3. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    4. Robert Axelrod, 1995. "The Convergence and Stability of Cultures: Local Convergence and Global Polarization," Working Papers 95-03-028, Santa Fe Institute.
    5. Ben-Naim, E & Krapivsky, P.L & Vazquez, F & Redner, S, 2003. "Unity and discord in opinion dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 330(1), pages 99-106.
    6. Joshua M. Epstein & Robert L. Axtell, 1996. "Growing Artificial Societies: Social Science from the Bottom Up," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262550253, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Matthew Oremland & Reinhard Laubenbacher, 2014. "Using difference equations to find optimal tax structures on the SugarScape," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 9(2), pages 233-253, October.
    2. Sylvie Huet & Floriana Gargiulo & Felicia Pratto, 2020. "Can gender inequality be created without inter-group discrimination?," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-25, August.
    3. José Manuel Galán & Luis R. Izquierdo & Segismundo S. Izquierdo & José Ignacio Santos & Ricardo del Olmo & Adolfo López-Paredes & Bruce Edmonds, 2009. "Errors and Artefacts in Agent-Based Modelling," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 12(1), pages 1-1.
    4. Segismundo S. Izquierdo & Luis R. Izquierdo & Nicholas M. Gotts, 2008. "Reinforcement Learning Dynamics in Social Dilemmas," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 11(2), pages 1-1.

    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. Robert Axtell, 2007. "What economic agents do: How cognition and interaction lead to emergence and complexity," The Review of Austrian Economics, Springer;Society for the Development of Austrian Economics, vol. 20(2), pages 105-122, September.
    2. Cassar, Alessandra, 2007. "Coordination and cooperation in local, random and small world networks: Experimental evidence," Games and Economic Behavior, Elsevier, vol. 58(2), pages 209-230, February.
    3. Szabó, György & Borsos, István & Szombati, Edit, 2019. "Games, graphs and Kirchhoff laws," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 416-423.
    4. Michael Kosfeld, 2002. "Stochastic strategy adjustment in coordination games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(2), pages 321-339.
    5. Zhang, Boyu & Hofbauer, Josef, 2016. "Quantal response methods for equilibrium selection in 2×2 coordination games," Games and Economic Behavior, Elsevier, vol. 97(C), pages 19-31.
    6. Sheri M. Markose, 2005. "Computability and Evolutionary Complexity: Markets as Complex Adaptive Systems (CAS)," Economic Journal, Royal Economic Society, vol. 115(504), pages 159-192, 06.
    7. Kreindler, Gabriel E. & Young, H. Peyton, 2013. "Fast convergence in evolutionary equilibrium selection," Games and Economic Behavior, Elsevier, vol. 80(C), pages 39-67.
    8. Kosfeld, Michael, 2002. "Why shops close again: An evolutionary perspective on the deregulation of shopping hours," European Economic Review, Elsevier, vol. 46(1), pages 51-72, January.
    9. Sornette, Didier & Zhou, Wei-Xing, 2006. "Importance of positive feedbacks and overconfidence in a self-fulfilling Ising model of financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 704-726.
    10. Avner Shaked & Larry Samuelson & George J. Mailath, 1997. "Correlated equilibria and local interactions (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(3), pages 551-556.
    11. T. Kaizoji & D. Sornette, 2008. "Market bubbles and crashes," Papers 0812.2449, arXiv.org.
    12. Blume,L.E. & Durlauf,S.N., 2005. "Identifying social interactions : a review," Working papers 12, Wisconsin Madison - Social Systems.
    13. Alós-Ferrer, Carlos & Weidenholzer, Simon, 2008. "Contagion and efficiency," Journal of Economic Theory, Elsevier, vol. 143(1), pages 251-274, November.
    14. Hsiao-Chi Chen & Yunshyong Chow & Li-Chau Wu, 2013. "Imitation, local interaction, and coordination," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(4), pages 1041-1057, November.
    15. David O'Sullivan & Mordechai Haklay, 2000. "Agent-Based Models and Individualism: Is the World Agent-Based?," Environment and Planning A, , vol. 32(8), pages 1409-1425, August.
    16. Fagiolo, Giorgio, 2005. "Endogenous neighborhood formation in a local coordination model with negative network externalities," Journal of Economic Dynamics and Control, Elsevier, vol. 29(1-2), pages 297-319, January.
    17. Ge Jiang & Simon Weidenholzer, 2017. "Local interactions under switching costs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(3), pages 571-588, October.
    18. Suren Basov, 2002. "Evolution of Social Behavior in the Global Economy: The Replicator Dynamics with Migration," Department of Economics - Working Papers Series 847, The University of Melbourne.
    19. Matthew Oremland & Reinhard Laubenbacher, 2014. "Using difference equations to find optimal tax structures on the SugarScape," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 9(2), pages 233-253, October.
    20. Horst, Ulrich, 2010. "Dynamic systems of social interactions," Journal of Economic Behavior & Organization, Elsevier, vol. 73(2), pages 158-170, February.

    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:jas:jasssj:2006-52-2. 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: Francesco Renzini (email available below). General contact details of provider: .

    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.