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An adaptive decisional mechanism leading to chaos


  • Ahmad Naimzada
  • Marina Pireddu


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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    References listed on IDEAS

    1. Alessandro Santoro, 2008. "Taxpayers’Choices Under Studi Di Settore:What Do We Know And How We Can Interpret It?," Giornale degli Economisti, GDE (Giornale degli Economisti e Annali di Economia), Bocconi University, vol. 67(2), pages 161-184, July.
    2. Gerlinde Fellner & Rupert Sausgruber & Christian Traxler, 2009. "Testing Enforcement Strategies in the Field: Legal Threat, Moral Appeal and Social Information," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2009_31, Max Planck Institute for Research on Collective Goods.
    3. Lipatov, Vilen, 2012. "Corporate tax evasion: The case for specialists," Journal of Economic Behavior & Organization, Elsevier, vol. 81(1), pages 185-206.
    4. Crocker, Keith J. & Slemrod, Joel, 2005. "Corporate tax evasion with agency costs," Journal of Public Economics, Elsevier, vol. 89(9-10), pages 1593-1610, September.
    5. Dina Pomeranz, 2015. "No Taxation without Information: Deterrence and Self-Enforcement in the Value Added Tax," American Economic Review, American Economic Association, vol. 105(8), pages 2539-2569, August.
    6. Joel Slemrod & Caroline Weber, 2012. "Evidence of the invisible: toward a credibility revolution in the empirical analysis of tax evasion and the informal economy," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 19(1), pages 25-53, February.
    7. Iacus, Stefano M. & King, Gary & Porro, Giuseppe, 2011. "Multivariate Matching Methods That Are Monotonic Imbalance Bounding," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 345-361.
    8. Slemrod, Joel & Blumenthal, Marsha & Christian, Charles, 2001. "Taxpayer response to an increased probability of audit: evidence from a controlled experiment in Minnesota," Journal of Public Economics, Elsevier, vol. 79(3), pages 455-483, March.
    9. Henrik Jacobsen Kleven & Martin B. Knudsen & Claus Thustrup Kreiner & Søren Pedersen & Emmanuel Saez, 2011. "Unwilling or Unable to Cheat? Evidence From a Tax Audit Experiment in Denmark," Econometrica, Econometric Society, vol. 79(3), pages 651-692, May.
    10. Bayer, Ralph & Cowell, Frank, 2009. "Tax compliance and firms' strategic interdependence," Journal of Public Economics, Elsevier, vol. 93(11-12), pages 1131-1143, December.
    11. Alessandro Santoro & Carlo V. Fiorio, 2011. "Taxpayer Behavior When Audit Rules Are Known: Evidence from Italy," Public Finance Review, , vol. 39(1), pages 103-123, January.
    12. Blumenthal, Marsha & Christian, Charles W. & Slemrod, Joel, 2001. "Do Normative Appeals Affect Tax Compliance? Evidence From a Controlled Experiment in Minnesota," National Tax Journal, National Tax Association, vol. 54(1), pages 125-138, March.
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    More about this item


    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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