Transboundary pollution control and environmental absorption efficiency management

Fouad El Ouardighi, Konstantin Kogan, Giorgio Gnecco, Marcello Sanguineti

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


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.

Original languageEnglish
Pages (from-to)653-681
Number of pages29
JournalAnnals of Operations Research
Issue number2
StatePublished - 1 Apr 2020

Bibliographical note

Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.


  • Environmental absorption efficiency
  • Hamilton–Jacobi–Bellman approximation
  • Transboundary pollution


Dive into the research topics of 'Transboundary pollution control and environmental absorption efficiency management'. Together they form a unique fingerprint.

Cite this