IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v58y2010i5p1450-1468.html
   My bibliography  Save this article

Aggregate Diffusion Dynamics in Agent-Based Models with a Spatial Structure

Author

Listed:
  • Gadi Fibich

    (Department of Applied Mathematics, Tel Aviv University, Tel Aviv 69978, Israel)

  • Ro'i Gibori

    (Department of Applied Mathematics, Tel Aviv University, Tel Aviv 69978, Israel)

Abstract

We explicitly calculate the aggregate diffusion dynamics in one-dimensional agent-based models of adoption of new products, without using the mean-field approximation. We then introduce a clusters-dynamics approach, and use it to derive an analytic approximation of the aggregate diffusion dynamics in multidimensional agent-based models. The clusters-dynamics approximation shows that the aggregate diffusion dynamics does not depend on the average distance between individuals, but rather on the expansion rate of clusters of adopters. Therefore, the grid dimension has a large effect on the aggregate adoption dynamics, but a small-world structure and heterogeneity among individuals have only a minor effect. Our results suggest that the one-dimensional model and the Bass model provide a lower bound and an upper bound, respectively, for the aggregate diffusion dynamics in agent-based models with “any” spatial structure.

Suggested Citation

  • Gadi Fibich & Ro'i Gibori, 2010. "Aggregate Diffusion Dynamics in Agent-Based Models with a Spatial Structure," Operations Research, INFORMS, vol. 58(5), pages 1450-1468, October.
    • Handle: RePEc:inm:oropre:v:58:y:2010:i:5:p:1450-1468
    DOI: 10.1287/opre.1100.0818
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.1100.0818
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.1100.0818?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
    ---><---

    References listed on IDEAS

    as
    1. Tal Garber & Jacob Goldenberg & Barak Libai & Eitan Muller, 2004. "From Density to Destiny: Using Spatial Dimension of Sales Data for Early Prediction of New Product Success," Marketing Science, INFORMS, vol. 23(3), pages 419-428, August.
    2. Christopher J. Easingwood & Vijay Mahajan & Eitan Muller, 1983. "A Nonuniform Influence Innovation Diffusion Model of New Product Acceptance," Marketing Science, INFORMS, vol. 2(3), pages 273-295.
    3. Shun-Chen Niu, 2002. "A Stochastic Formulation of the Bass Model of New-Product Diffusion," Review of Marketing Science Working Papers 1-4-1000, Berkeley Electronic Press.
    4. Jackson Matthew O. & Rogers Brian W., 2007. "Relating Network Structure to Diffusion Properties through Stochastic Dominance," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 7(1), pages 1-16, February.
    5. Bart J. Bronnenberg & Carl F. Mela, 2004. "Market Roll-Out and Retailer Adoption for New Brands," Marketing Science, INFORMS, vol. 23(4), pages 500-518, September.
    6. Frank M. Bass, 1969. "A New Product Growth for Model Consumer Durables," Management Science, INFORMS, vol. 15(5), pages 215-227, January.
    7. López-Pintado, Dunia, 2008. "Diffusion in complex social networks," Games and Economic Behavior, Elsevier, vol. 62(2), pages 573-590, March.
    8. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2006. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521871525.
    9. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2006. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521692083.
    10. David Bell & Sangyoung Song, 2007. "Neighborhood effects and trial on the internet: Evidence from online grocery retailing," Quantitative Marketing and Economics (QME), Springer, vol. 5(4), pages 361-400, December.
    11. Vijay Mahajan & Eitan Muller & Frank M. Bass, 1995. "Diffusion of New Products: Empirical Generalizations and Managerial Uses," Marketing Science, INFORMS, vol. 14(3_supplem), pages 79-88.
    12. Delre, S.A. & Jager, W. & Bijmolt, T.H.A. & Janssen, M.A., 2007. "Targeting and timing promotional activities: An agent-based model for the takeoff of new products," Journal of Business Research, Elsevier, vol. 60(8), pages 826-835, August.
    13. 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.
    14. Floortje Alkemade & Carolina Castaldi, 2005. "Strategies for the Diffusion of Innovations on Social Networks," Computational Economics, Springer;Society for Computational Economics, vol. 25(1), pages 3-23, February.
    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. Chunlin Wu & Han Yao & Xin Ning & Lei Wang, 2021. "Emergence of Informal Safety Leadership: A Social–Cognitive Process for Accident Prevention," Production and Operations Management, Production and Operations Management Society, vol. 30(11), pages 4288-4305, November.
    2. Guseo, Renato & Guidolin, Mariangela, 2015. "Heterogeneity in diffusion of innovations modelling: A few fundamental types," Technological Forecasting and Social Change, Elsevier, vol. 90(PB), pages 514-524.
    3. Emanuele Borgonovo & Marco Pangallo & Jan Rivkin & Leonardo Rizzo & Nicolaj Siggelkow, 2022. "Sensitivity analysis of agent-based models: a new protocol," Computational and Mathematical Organization Theory, Springer, vol. 28(1), pages 52-94, March.
    4. Jakob Grazzini & Matteo G. Richiardi & Lisa Sella, 2013. "Analysis of Agent-based Models," LABORatorio R. Revelli Working Papers Series 135, LABORatorio R. Revelli, Centre for Employment Studies.
    5. Li, Feng & Du, Timon C. & Wei, Ying, 2023. "This is what’s in store for you: How online social learning affects product positioning," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 179(C).
    6. Laciana, Carlos E. & Rovere, Santiago L. & Podestá, Guillermo P., 2013. "Exploring associations between micro-level models of innovation diffusion and emerging macro-level adoption patterns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(8), pages 1873-1884.
    7. Xiao, Yu & Han, Jingti, 2016. "Forecasting new product diffusion with agent-based models," Technological Forecasting and Social Change, Elsevier, vol. 105(C), pages 167-178.
    8. Fibich, Gadi & Levin, Tomer, 2020. "Percolation of new products," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    9. Guseo, Renato & Schuster, Reinhard, 2021. "Modelling dynamic market potential: Identifying hidden automata networks in the diffusion of pharmaceutical drugs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    10. Vahideh Manshadi & Sidhant Misra & Scott Rodilitz, 2020. "Diffusion in Random Networks: Impact of Degree Distribution," Operations Research, INFORMS, vol. 68(6), pages 1722-1741, November.
    11. Abedi, Vahideh Sadat, 2019. "Compartmental diffusion modeling: Describing customer heterogeneity & communication network to support decisions for new product introductions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    12. Grazzini,Jakob & Richiardi, Matteo & Sella, Lisa, 2013. "Is there a Double-Negative Effect? Gender and Ethnic Wage Differentials," Department of Economics and Statistics Cognetti de Martiis. Working Papers 201352, University of Turin.
    13. Delli Gatti,Domenico & Fagiolo,Giorgio & Gallegati,Mauro & Richiardi,Matteo & Russo,Alberto (ed.), 2018. "Agent-Based Models in Economics," Cambridge Books, Cambridge University Press, number 9781108400046.

    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. Elmar Kiesling & Markus Günther & Christian Stummer & Lea Wakolbinger, 2012. "Agent-based simulation of innovation diffusion: a review," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(2), pages 183-230, June.
    2. Frank M. Bass, 2004. "Comments on "A New Product Growth for Model Consumer Durables The Bass Model"," Management Science, INFORMS, vol. 50(12_supple), pages 1833-1840, December.
    3. Jacob Goldenberg & Oded Lowengart & Daniel Shapira, 2009. "Zooming In: Self-Emergence of Movements in New Product Growth," Marketing Science, INFORMS, vol. 28(2), pages 274-292, 03-04.
    4. John Hauser & Gerard J. Tellis & Abbie Griffin, 2006. "Research on Innovation: A Review and Agenda for," Marketing Science, INFORMS, vol. 25(6), pages 687-717, 11-12.
    5. Rand, William & Rust, Roland T., 2011. "Agent-based modeling in marketing: Guidelines for rigor," International Journal of Research in Marketing, Elsevier, vol. 28(3), pages 181-193.
    6. Toka, Agorasti & Iakovou, Eleftherios & Vlachos, Dimitrios & Tsolakis, Naoum & Grigoriadou, Anastasia-Loukia, 2014. "Managing the diffusion of biomass in the residential energy sector: An illustrative real-world case study," Applied Energy, Elsevier, vol. 129(C), pages 56-69.
    7. Kováč, Eugen & Schmidt, Robert C., 2014. "Market share dynamics in a duopoly model with word-of-mouth communication," Games and Economic Behavior, Elsevier, vol. 83(C), pages 178-206.
    8. Rixen, Martin & Weigand, Jürgen, 2014. "Agent-based simulation of policy induced diffusion of smart meters," Technological Forecasting and Social Change, Elsevier, vol. 85(C), pages 153-167.
    9. López-Pintado, Dunia, 2008. "Diffusion in complex social networks," Games and Economic Behavior, Elsevier, vol. 62(2), pages 573-590, March.
    10. Giovanni Pegoretti & Francesco Rentocchini & Giuseppe Vittucci Marzetti, 2012. "An agent-based model of innovation diffusion: network structure and coexistence under different information regimes," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 7(2), pages 145-165, October.
    11. Delre, S.A. & Jager, W. & Bijmolt, T.H.A. & Janssen, M.A., 2007. "Targeting and timing promotional activities: An agent-based model for the takeoff of new products," Journal of Business Research, Elsevier, vol. 60(8), pages 826-835, August.
    12. Barnes, Belinda & Southwell, Darren & Bruce, Sarah & Woodhams, Felicity, 2014. "Additionality, common practice and incentive schemes for the uptake of innovations," Technological Forecasting and Social Change, Elsevier, vol. 89(C), pages 43-61.
    13. Bryan Bollinger & Kenneth Gillingham, 2012. "Peer Effects in the Diffusion of Solar Photovoltaic Panels," Marketing Science, INFORMS, vol. 31(6), pages 900-912, November.
    14. Michel Grabisch & Agnieszka Rusinowska & Xavier Venel, 2019. "Diffusion in countably infinite networks," Documents de travail du Centre d'Economie de la Sorbonne 19017, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    15. Olivier Toubia & Jacob Goldenberg & Rosanna Garcia, 2014. "Improving Penetration Forecasts Using Social Interactions Data," Management Science, INFORMS, vol. 60(12), pages 3049-3066, December.
    16. Nejad, Mohammad G. & Amini, Mehdi & Babakus, Emin, 2015. "Success Factors in Product Seeding: The Role of Homophily," Journal of Retailing, Elsevier, vol. 91(1), pages 68-88.
    17. William Rand & Roland T. Rust & Min Kim, 2018. "Complex systems: marketing’s new frontier," AMS Review, Springer;Academy of Marketing Science, vol. 8(3), pages 111-127, December.
    18. Rajkumar Venkatesan & Trichy V. Krishnan & V. Kumar, 2004. "Evolutionary Estimation of Macro-Level Diffusion Models Using Genetic Algorithms: An Alternative to Nonlinear Least Squares," Marketing Science, INFORMS, vol. 23(3), pages 451-464, August.
    19. Shin, Euncheol, 2017. "Monopoly pricing and diffusion of social network goods," Games and Economic Behavior, Elsevier, vol. 102(C), pages 162-178.
    20. Christophe Van den Bulte & Yogesh V. Joshi, 2007. "New Product Diffusion with Influentials and Imitators," Marketing Science, INFORMS, vol. 26(3), pages 400-421, 05-06.

    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:inm:oropre:v:58:y:2010:i:5:p:1450-1468. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.