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An extension of the Antoci-Dei-Galeotti evolutionary model for environment protection through financial instruments


  • Gian Italo Bischi

    () (Department of Economics, Society & Politics, Università di Urbino "Carlo Bo")

  • Davide Radi

    () (Department of Mathematics, Statistics, Computing and Applications "Lorenzo Mascheroni", Università di Bergamo)


This work moves from a recent paper by Antoci, Dei and Galeotti [1] where a dynamic model is proposed to describe an innovative method to improve environmental quality based on the exchange of financial activities, promoted by a Public Administration, between firms and tourists in a given region. We extend their analysis in two directions: we first perform a global analysis of the basins of attraction to check the stability extents of the coexisting stable attractors of the model, and we show that some undesirable and sub-optimal stable equilibria always exist, whose basins may be quite intermingled with those of the optimal equilibrium; then we introduce a structural change of the model by assuming that the Public Administration, besides its action as an intermediary between visitors and polluting firms, also performs a direct action for the pollution control. We show how the cost of this direct action of the Public Administration can be balanced by proper taxes and we prove that undesired equilibria can be ruled out by a suitable balance of financial instruments and direct actions of Public Administration for environmental remediation.

Suggested Citation

  • Gian Italo Bischi & Davide Radi, 2011. "An extension of the Antoci-Dei-Galeotti evolutionary model for environment protection through financial instruments," Working Papers 1105, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2011.
  • Handle: RePEc:urb:wpaper:11_05

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    Cited by:

    1. Angelo Antoci & Marcello Galeotti & Davide Radi, 2011. "Financial Tools for the Abatement of Traffic Congestion: A Dynamical Analysis," Computational Economics, Springer;Society for Computational Economics, vol. 38(3), pages 389-405, October.
    2. Lamantia, F. & Radi, D., 2015. "Exploitation of renewable resources with differentiated technologies: An evolutionary analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 108(C), pages 155-174.

    More about this item


    Environmental economics; evolutionary dynamics; replicator equations; multistability; basins of attraction.;

    JEL classification:

    • D6 - Microeconomics - - Welfare Economics
    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods
    • N4 - Economic History - - Government, War, Law, International Relations, and Regulation
    • Q2 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation

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