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An adaptive decisional mechanism leading to chaos

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  • Ahmad Naimzada
  • Marina Pireddu

Abstract

In this paper we propose a framework in order to analyze the dynamical process of decision and opinion formation of two economic homogeneous and boundedly rational agents that interact and learn from each other over time. The decisional process described in our model is an adaptive adjustment mechanism in which two agents take into account the difference between their own opinion and the opinion of the other agent. The smaller that difference, the larger the weight given to the comparison of the opinions. We also assume that if the distance between the two opinions is larger than a given threshold, then there is no interaction and the agents do not change their opinion anymore. Introducing an auxiliary variable describing the distance between the opinions, we obtain a one-dimensional map for which we investigate, mainly via analytical tools, the stability of the steady states, their bifurcations, as well as the existence of chaotic dynamics and multistability phenomena, i.e., the presence of coexisting attractors.

Suggested Citation

  • Ahmad Naimzada & Marina Pireddu, 2013. "An adaptive decisional mechanism leading to chaos," Working Papers 252, University of Milano-Bicocca, Department of Economics, revised Jul 2013.
  • Handle: RePEc:mib:wpaper:252
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    File URL: http://dems.unimib.it/repec/pdf/mibwpaper252.pdf
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    More about this item

    Keywords

    Adaptive decisional mechanism; bifurcations; multistability; complex dynamics;

    JEL classification:

    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles
    • D79 - Microeconomics - - Analysis of Collective Decision-Making - - - Other
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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