Faculty & Research -The irreversible pollution game

The irreversible pollution game

Irreversible environmental change is the top existential issue nowadays, and as such, it’s the subject of numerous research programs in many scientific disciplines, theoretical and applied, to found proper environmental policies. See more references below.

Irreversible environmental change is probably the hottest topic nowadays as the ecological crisis originating in global warming is getting increasingly acute. An already abundant scientific literature points at unequivocal signals of irreversible climate change. An example of such a literature is in the growing evidence on the weakening of the AMOC (Atlantic Meridian Overturning Circulation), a key  climate regulation system of the Atlantic ocean currents bringing warm waters to the North where it cools, sinks and returns to the South. See Bonnet et al (2021) for example. The main idea behind irreversibility is that continuous accumulation of pollutants (GHG in the case of global warming) can at a certain point in time reach a threshold level beyond which key regulating and vital global or local regulation mechanisms become permanently partially or totally defective.

At the local level, a well-known case of irreversible pollution is the so-called shallow lake problem where small variations in phosphorus loads lead to the emergence of tipping points in the lake ecosystem dynamics resulting in huge losses in ecosystem services, often through eutrophication. In the case of climate change, this generally translates into specific destabilizing temperature-based mechanisms. Consider for example the AMOC case. AMOC strength is indeed driven by a sophisticated water salinity-based mechanism that is tightly dependent upon temperatures. If temperature goes up leading to less salty and dense surface water (say through the melting of glaciers), then the latter cannot sink to form the so-called  North Atlantic Deep Waters (NADW) that return to the South, and AMOC ceases to work with the paradoxical global warming consequence that Western Europe would experience much colder winters.


The economics of irreversible pollution and environmental change

Economists have been concerned by irreversible pollution for a while, specific elements inherent in global warming have been more recently introduced. A key question turns out to be to which extent irreversible environmental regimes can be avoided. This question has been studied in very different frames since the 90s. A seminal approach considers pollution control problems in which irreversibility occurs if pollution reaches a critical level above which the decay rate of pollution drops permanently to zero leading to rapidly ascending pollution patterns. In such a context, even a close optimal control approach monitored by a benevolent central planner cannot always avoid crossing the critical pollution level. This still holds even though optimal pollution abatement policies are introduced. This negative result may arise at the optimum as the joint outcome of the natural pollution accumulation process (especially if the pollution level is initially high) and the absence of a radical enough change in consumption and production. The latter derives from governments’ arbitrage between pro-consumption/production policies and pollution negative externalities, which in turn generally also reflects the strength of  pro-environmental attitudes and intergenerational altruism in society.

Another aspect appears to be potentially important for the ultimate impact of irreversible pollution: uncertainty. Indeed: for example, the irreversibility threshold levels are not known with certainty. As to the potential collapse of AMOC, this uncertainty is still huge: for Ditlevsen and Ditlevsen (2023), this may occur between 2025 and 2095. Uncertainty bears also on the extent of damages caused when the irreversibility thresholds are reached. There is a strong research line which associates irreversibility thresholds crossing with catastrophic damage zeroing or infinitely reducing human welfare. Alternatively one could assume that reaching the irreversible regime will produce a permanent sharp drop in welfare, not necessarily to zero or minus infinity.

A subsequent very interesting question is whether the perception of this risk, catastrophic or not, will induce a more prudent economic behavior (thus less pollution) ultimately allowing to avoid the irreversibility thresholds. Quite counter-intuitively, economics agents and governments may also be even more aggressive than without the risk if they believe it’s too late to avoid crossing the irreversibility thresholds so that reducing drastically current living standards are useless. This is more than corroborated by the most recent reports of UN Climate Change, the latest on November 14th, 2023: while greenhouse gas emissions need to be cut 43% by 2030, compared to 2019 levels according to the Paris agreement, extrapolation of the current trends deliver at best a reduction of 2% in 2030 compared to 2019, thus calling for further much more severe adjustments in the next years to hit the target.

A key concept here is free-riding, that’s in our transboundary pollution context, the tendency of certain individuals/countries to rely on others efforts to reduce the common stock of pollution. Boucekkine et al (2023) precisely provide with a game-theoretic extension of the seminal irreversible pollution economic model in order to characterize the free-riding behavior in such a context and to identify ways to at least partially circumvent it to more robust international environmental agreements.  Countries play Markovian in this theory: they do not adjust to any past observation or circumstance (like a past commitment), only to the current state of the world to which they respond optimally according to their own interest. If all countries play the same, what would be the aggregate outcome? Beside the technical contribution, the authors identify a key factor determining the aggregate impact of free-riding compared to the ideal situation of full cooperation (zero free-riding): the degree of heterogeneity of countries involved. If for example countries do not face the same pollution unit cost (asymmetric case), would the aggregate cost of free-riding be larger or lower? The authors find that within the generic irreversible pollution economic model, the player who faces the higher unit cost will make more efforts to reduce the pollution than any other player facing a lower unit cost. Much more importantly, the long-run pollution stock will be lower in such an asymmetric case than if the countries face the same pollution cost (symmetry). In other words, the global burden of free-riding is larger under symmetry.

Concluding: Implications for the design of international environmental agreements

The latter result is new, and it may be important for the design of international environmental agreements. The traditional approach to the conceptual design of international environmental agreements (or coalitions) only consider identical countries, the so-called symmetric game frame (see for example Carraro and Siniscalco, 1993). In such a case, the key parameter is the size of the coalition. Boucekkine et al’s results indicate that cost heterogeneity (or may be other heterogeneity types) might be also very important. Combining size and crucial heterogeneity characteristics should be indeed the more relevant approach to construct more robust pro-environmental coalitions in a few steps.


This is a conceptual paper making intensive use of game theory. More precisely, as the decisions taken within this frame (consumption, abatement…) have intertemporal consequences, the authors solve differential (non-cooperative) symmetric and asymmetric games. A strong technical contribution of this paper is the analytical solution to so-called Markovian game equilibria in a non-convex context due to irreversibility.

Applications and beneficiaries

This paper studies the determinants of free-riding in environmental policy, and identifies a new factor that should be accounted for in the design of pro-environmental coalitions. It’s therefore of interest to policymakers at any level concerned with these critical issues. The paper also develops a new mathematical methodology to broaden the analysis of irreversible pollution problems that should be of interest to researchers in this area.

Reference to the research:

Boucekkine, R., W. Ruan and B. Zou (2023). The irreversible pollution game. Journal of Environmental Economics and Management, 120, Article 102841.

Consult the research paper

Related useful references (cited above)

Bonnet, R., Swingedouw, D., Gastineau, G. et al (2021). Increased risk of near term global warming due to a recent AMOC weakening. Nature Communications, 12, 6108. 

Carraro, C., Siniscalco, D. (1993). Strategies for the international protection of the environment. Journal of Public Economics, 52 (3), 309-328.

Ditlevsen, P., and S. Ditlevsen (2023). Warning of a forthcoming collapse of the Atlantic meridional overturning circulation. Nature Communications, 14, 4254.