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An evolutionary game on compliant and non-compliant firms in groundwater exploitation

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Abstract

This paper studies how to counter the illegal exploitation of common groundwater resource in an evolutionary game approach. The access is not free and firms have to pay a royalty depending on the quantity of water pumped. However, some firms could decide to not pay the royalty and face the risk of being sanctioned by the regulator authority. The overall sanction is composed of a fixed amount and of the royalty not payed. From the analysis of the model it emerges that coexistence at the equilibrium between compliant and non-compliant firms is possible and policy instruments are partially able to counter the unauthorized exploitation. In particular, increasing the sanction level reduces the number of non-compliant firms but raises the incidence of illegal pumping. The opposite occurs if the regulatory authority increases the royalty price. To pursue both goals, applying a balance of policies is necessary.

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Notes

  1. Conference on “Water & Agriculture” Events at Mercure Hotel, Boulevard de Lauzelle 61, Louvain-La-Nueve (Belgium), September 2010.

  2. FollowingXepapadeas (2005), we assume that the public authority does not change its amount over time. In this way, we can use \(\sigma \) to derive policy implications in Sect. 5.

  3. Although a water linear demand is not the most favorable functional form, it nevertheless simplifies the analysis of the model and for this reason it is widely used in literature.

  4. In Sect. 4 we relax this assumption assuming \(\rho \) function of water pumped by both types of firms.

  5. Another possibility to represent probability (4) is to model it as a function of the water table, that is the difference between the effective water level and the one compatible with compliant pumping. Also in this case, the probability of being discovered discovered, \(\phi \), will be a function of the share of non-compliant firms. Therefore, we prefer to represent it as (4), for obvious reasons of tractability, following Petrohilos-Andrianos and Xepapadeas (2017).

  6. Pumping costs and natural resource parameters are given by Gisser and Sanchez (1980), regulatory authority parameters are given by Petrohilos-Andrianos and Xepapadeas (2017), the rest is given by our calibration.

  7. In all simulations, we change \(\sigma \) from 100 to 900, while \(\delta \) from 0.0007 to 0.0013. Both intervals are such that the inner steady state (\(x^\star ,H^\star \)) exists.

  8. All the new functions will be denoted with symbol \('\).

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Acknowledgements

We would like to thank the two anonymous reviewers whose comments and suggestions helped improve and clarify an earlier version of this manuscript.

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Authors and Affiliations

  1. Department of Economics and Finance, University of Bari, Bari, Italy

    Marta Biancardi & Giovanni Villani

  2. Department of Economics and Management, University of Firenze, Via delle Pandette 9, l-50127, Florence, Italy

    Gianluca Iannucci

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  1. Marta Biancardi
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  2. Gianluca Iannucci
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Correspondence to Gianluca Iannucci.

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Biancardi, M., Iannucci, G. & Villani, G. An evolutionary game on compliant and non-compliant firms in groundwater exploitation. Ann Oper Res 318, 831–847 (2022). https://doi.org/10.1007/s10479-021-04297-5

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