Spatial vs. non-spatial transboundary pollution control in a class of cooperative and non-cooperative dynamic games

Abstract

We analyze a transboundary pollution differential game where, in addition to the standard temporal dimension, a spatial dimension is introduced to capture the geographical relationships among regions. Each region behaves strategically and maximizes its welfare net of environmental damage caused by the pollutant stock. The emission-output ratio is reduced by investment in region specific clean technology which evolves over time. The spatio-temporal dynamics of the pollutant stock is described by a parabolic partial differential equation. Using aggregate variables we study the feedback Nash equilibrium of a discrete-space model which could be seen as a space discretization of the continuous-space model. The discrete-space model presents the three main features of the original formulation: the model is truly dynamic; the agents behave strategically; and the model incorporates spatial aspects. For special functional forms previously used in the literature we analytically characterize the feedback Nash equilibrium and evaluate the impact of the introduction of the spatial dimension in the economic-environmental model. We show that our spatial model is a generalization of the model that disregards the spatial aspects. We analytically show that as the parameter describing how pollution diffuses among regions tends to infinity the equilibrium policies converge to those in the non-spatial setting. In the non-cooperative framework the spatially non-myopic behavior prescribes lower equilibrium emission rates, and consequently a lower global pollution stock. This is compatible with greater long-run welfares. In the cooperative framework, although the strategic interaction among the players does not exist, the only decision-maker still makes spatially strategic decisions.

Green Veblen effect: Sustainability in pollution management

“…For simplicity, the remainder of the paper omits arguments from the functions whenever there is no confusion, in particular the time argument. Current pollution increases with quantity, q, (Martín-Herrán and Rubio, 2018a,b), and decreases with abatement effort, u (Chang et al, 2018;De Frutos and Martín-Herrán, 2019;Li, 2013Li, , 2016Li and Pan, 2014, El Ouardighi et al 2016bb,2019. If δ > 0, then stock of pollution is naturally degraded in the environment.…”

Optimal Environmental Policy in a Dynamic Transboundary Pollution Game: Emission Standards, Taxes, and Permit Trading

“…De Frutos et al [41] used a differential game model to compare the equilibrium trajectories of the stocks of pollution and cleaner technology as well the regions' welfare. De Frutos and Martín-Herrán [42] analyzed a transboundary pollution differential game and introduced a spatial dimension to capture the geographical relationships among regions. Yanase [43] examined the effects of environmental policy on the total global environment as an international public good with a stock externality, and found that the emission tax game brings about larger strategic distortions than the emission permit game in the absence of global cooperation.…”

Differential decision analysis of transboundary pollution considering the participation of the central government

“…For example, Long and Dockner (1993) pointed out that the spontaneous treatment of transboundary pollution may lead to a loss of profits and found that the optimal environmental policy can be achieved when environmental policies are formulated together. Some scholars introduced a spatial dimension into a differential game for transboundary pollution to explore the temporal and spatial dynamics of pollutant stock (de Frutos and Martín‐Herrán, 2019; de Frutos et al, 2021). Chang et al (2018) used cooperative and noncooperative games to study the optimal emission reduction strategy in transboundary pollution.…”