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Evolution of imitation networks in Minority Game model

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  • H. Lavička
  • F. Slanina

Abstract

The Minority Game is adapted to study the “imitation dilemma”, i.e. the tradeoff between local benefit and global harm coming from imitation. The agents are placed on a substrate network and are allowed to imitate more successful neighbours. Imitation domains, which are oriented trees, are formed. We investigate size distribution of the domains and in-degree distribution within the trees. We use four types of substrate: one-dimensional chain; Erdös-Rényi graph; Barabási-Albert scale-free graph; Barabási-Albert 'model A' graph. The behaviour of some features of the imitation network strongly depend on the information cost epsilon, which is the percentage of gain the imitators must pay to the imitated. Generally, the system tends to form a few domains of equal size. However, positive epsilon makes the system stay in a long-lasting metastable state with complex structure. The in-degree distribution is found to follow a power law in two cases of those studied: for Erdös-Rényi substrate for any epsilon and for Barabási-Albert scale-free substrate for large enough epsilon. A brief comparison with empirical data is provided. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Suggested Citation

  • H. Lavička & F. Slanina, 2007. "Evolution of imitation networks in Minority Game model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 56(1), pages 53-63, March.
    • Handle: RePEc:spr:eurphb:v:56:y:2007:i:1:p:53-63
    DOI: 10.1140/epjb/e2007-00091-9
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    Citations

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    Cited by:

    1. Shu-Heng Chen & Umberto Gostoli, 2017. "Coordination in the El Farol Bar problem: The role of social preferences and social networks," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 12(1), pages 59-93, April.
    2. Lustosa, Bernardo C. & Cajueiro, Daniel O., 2010. "Constrained information minority game: How was the night at El Farol?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(6), pages 1230-1238.
    3. Xin-Jie Zhang & Yong Tang & Jason Xiong & Wei-Jia Wang & Yi-Cheng Zhang, 2018. "Dynamics of Cooperation in Minority Games in Alliance Networks," Sustainability, MDPI, vol. 10(12), pages 1-17, December.
    4. Stefan, F.M. & Atman, A.P.F., 2015. "Is there any connection between the network morphology and the fluctuations of the stock market index?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 630-641.
    5. Bryce Morsky & Fuwei Zhuang & Zuojun Zhou, 2023. "Social and individual learning in the Minority Game," Papers 2307.11846, arXiv.org, revised Mar 2024.

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