Pollution Games: Environmental externalities meet Economic analysis

April 25, 2023

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The economic discipline has a long tradition on micro- and macroeconomics which aid the policy debates regarding contemporary issues. These days, besides governments having to deal with rising inflation, increasing wealth inequality or high levels of unemployment, the economics of climate change has been steadily rising to the agenda. However, I will highlight examples of economic literature that show that environmental and ecological issues have been discussed for a long time. The papers I discuss are examples of theoretical studies on transboundary pollution control; there are spill overs between countries as pollution is a global phenomena from which everyone suffers.

The Original Pollution Game

In 1993, Dockner and Van Long published a paper that set the stage for the analysis of pollution interaction between countries. This is a nice problem for economists as it has many attractive modelling features. The authors consider a mathematical model with two countries that have to choose at each instant in time how much emissions to produce. On the one hand, emissions have a positive side as it yields economic activity, which in turn yields welfare (e.g. in order to produce and enjoy the benefits of a car you need to produce the car first). On the other hand, emissions increase the total global pollution stock, which is a public bad as both countries suffer from the pollution. For instance, if the Netherlands starts burning coal at a rapid rate, across the border (and also worldwide, but at a less intense rate) the consequences (e.g. bad air quality) will be felt. This is also the tricky feature of the pollution games, as the benefits of emissions are felt locally, but the costs are felt globally.

The authors consider two outcomes of the game. First, they show how a social planner, who can perfectly internalize the negative effect each region has on the other region, maximizes welfare. This is an ideal scenario, but of course in practice it is difficult to enforce environmental treaties as there are incentives for both countries to deviate from treaties. Thus, the authors also consider what happens when both players only maximize their own welfare. The model then transforms to a so-called differential game, which is a dynamic game in continuous time. In order to arrive at a solution of the game, the authors consider Markovian Strategies. This means that at each moment in time each player sets their strategy given the pollution level they observe. As such, their strategies are subgame perfect (a term you might recognize from your Game Theory course).

This was all a lot of terminology, but what do the authors actually show? For one, the competitive case in which each player only maximizes their own welfare will yield higher pollution levels (technically, I slightly abuse the notation here but if you are interested in the technicalities you can read the paper). Second, the social planner outcome is the most attractive one as it is Pareto efficient, but it does not possess the equilibrium property as both countries have an incentive to deviate. What I like about this paper is that the model is simple but very attractive as it can showcase how much welfare gain there can be when we switch from the optimal scenario to a competitive scenario.

A nice extension of the classic pollution game is a paper by Nkuiya published in 2015. The author studies the same model as Dockner and Van Long, but asks an additional question. Suppose that pollution has another side effect, namely that more pollution increases the risk of an irreversible tipping point, after which there will be more damage from pollution, taking place. How does the behaviour of agents that anticipate this transition and the risk associated with this change, and how does the behaviour change when the transition risk becomes larger or the damages that are anticipated become higher?

The Acid Rain Differential Game

The second paper I discuss is one by Mäler and De Zeeuw. In 1998, they published a paper that discussed a different kind of pollution problem. Each country has interest in minimizing the cost and damages it incurs from acid rain, a phenomena that occurs due to sulphur emissions which end up in the soil. The soil has a carrying capacity (or critical load), which loosely speaking means that when the concentration of sulphur exceeds this threshold, the soil gets destroyed. It can also be interpreted as the amount a country can pollute before the soil starts to get acidic. In short, each country has a trade-off between reducing emissions (which is costly) and the acid buffers destroying the soil. 

The authors then apply their model to an empirical situation, namely an acid rain differential game between Ireland and Great Britain. They highlight that cooperation yields higher benefits than a Markov equilibrium. Heterogeneity in the costs and damages that countries incur implies that most countries have to lower their emissions severely, which induces free-riding chances for other countries. It remains a challenge for policymakers to enforce environmental treaties, as countries need to be properly incentivized to keep their word and not disregard the effect they have on other countries.

This was my last article for De Econometrist. Whoever is reading this, I wish you best of luck with the rest of your studies!


Dockner, E.J. and Van Long, N., 1993. International pollution control: cooperative versus noncooperative strategies. Journal of environmental economics and management, 25(1), pp.13-29.

Mäler, K.G. and De Zeeuw, A., 1998. The acid rain differential game. Environmental and Resource Economics, 12, pp.167-184
Nkuiya, B., 2015. Transboundary pollution game with potential shift in damages. Journal of Environmental Economics and Management, 72, pp.1-14.

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