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Transboundary pollution control and environmental absorption efficiency management


  • Fouad El Ouardighi

    () (ESSEC Business School)

  • Konstantin Kogan

    (Bar-Ilan University)

  • Giorgio Gnecco

    (IMT - School for Advanced Studies)

  • Marcello Sanguineti

    (University of Genova)


In this paper, we suggest a two-player differential game model of transboundary pollution that accounts for time-dependent environmental absorption efficiency, which allows the biosphere to switch from a carbon sink to a source. We investigate the impact of negative externalities resulting from a transboundary pollution non-cooperative game wherein countries are dynamically involved. Based on a linear-quadratic specification for the instantaneous revenue function, we assess differences related to both transient path and steady state between cooperative solution, open-loop and Markov perfect Nash equilibria (MPNE). Regarding the methodological contribution of the paper, we suggest a particular structure of the conjectured value function to solve MPNE problems with multiplicative interaction between state variables in one state equation, so that third-order terms that arise in the Hamilton–Jacobi–Bellman equation are made negligible. Using a collocation procedure, we confirm the validity of the particular structure of the conjectured value function. The results suggest unexpected contrasts in terms of pollution control and environmental absorption efficiency management: (i) in the long run, an open-loop Nash equilibrium (OLNE) allows equivalent emissions to the social optimum but requires greater restoration efforts; (ii) although an MPNE is likely to end up with lower emissions and greater restoration efforts than an OLNE, it has a much greater chance of falling in the emergency area; (iii) the absence of cooperation and or precommitment becomes more costly as the initial absorption efficiency decreases; (iv) more heavily discounted MPNE strategies are less robust than OLNE to prevent irreversible switching of the biosphere from a carbon sink to a source.

Suggested Citation

  • Fouad El Ouardighi & Konstantin Kogan & Giorgio Gnecco & Marcello Sanguineti, 2020. "Transboundary pollution control and environmental absorption efficiency management," Annals of Operations Research, Springer, vol. 287(2), pages 653-681, April.
  • Handle: RePEc:spr:annopr:v:287:y:2020:i:2:d:10.1007_s10479-018-2927-7
    DOI: 10.1007/s10479-018-2927-7

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    References listed on IDEAS

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