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.

Transboundary pollution control and environmental absorption efficiency management

G. Gnecco;
2020-01-01

Abstract

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.
2020
Transboundary pollution; Environmental absorption efficiency; Hamilton–Jacobi–Bellman approximation
File in questo prodotto:
File Dimensione Formato  
ElOuardighi2018_Article_TransboundaryPollutionControlA.pdf

non disponibili

Tipologia: Versione Editoriale (PDF)
Licenza: Nessuna licenza
Dimensione 1.61 MB
Formato Adobe PDF
1.61 MB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11771/11073
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 22
social impact