Is Climate Change a Prisoner's Dilemma or a Stag Hunt?

Toby Melville / Reuters
Editor’s Note: This article previously appeared in a different format as part of The Atlantic’s Notes section, retired in 2021.

Welcome back, gamers! This installment of the project on game theory and climate change will take some time to outline basic concepts about game theory and apply them to the three “games” described in the previous Note. To recap, we’ll be considering scenarios involving a hypothetical negotiation between West Virginia and Kentucky to curb emissions, a similar negotiation between the United States and China, and finally the future actions of the major expected signatories of the Paris climate agreement.

In each scenario there are a collection of actions that each actor can take. We’ll need to simplify a lot of these actions in the early going into approving and enacting a climate policy or deciding to continue business as usual. Here, in the context of the game, it makes sense to label the two strategies coordination and defection. There are, of course, infinite other possible strategies that may only differ by a dollar amount of spending or a single ton of emissions reduced. As the project goes on, hopefully we’ll be able to model these more accurately using some fancy statistics, but for now the two strategies are to coordinate or defect. The conjunction of each of these strategies with another actor’s corresponding strategy will produce an outcome for each actor.

In all scenarios, the five main considerations are the value of environmental resources, the future costs of climate change, the degree to which emissions policies can affect those future costs, how much those policies cost, and how much each actor can actually afford to spend or lose. There are some other considerations that can act as minor variables, such as the often considerable “inertia” involved in adopting new technologies and policies, the externalities of emissions policies (i.e. reducing smog in China or water pollution in West Virginia), elections and shifting public opinion, and the changing immediacy of the costs of climate change. But in all, each of these considerations can be collapsed into two categories that revolve around a set of outputs: costs and payoffs.

Max Malikov

Reader Max Malikov shared with me some useful examples for visualizing the climate game. The first figure shows what a short-term assessment of climate policy might look like if there was no real threat to the environment. Acting to protect the environment is costly and has a limited benefit that is far outweighed by the benefit of simply using the environmental resources at maximum efficiency. So, in the example of Kentucky and West Virginia defection would mean both states opening up as many coal plants as possible to maximize energy output and profits. Neither state has an incentive to help protect the environment, especially in a market where the two neighbors compete against each other for jobs and productivity.

Max Malikov

However, in the tragedy of the commons, exploitation of a resource inevitably makes the resource scarcer. In this case, the resource is not land or coal, but the sum of the ecosystem itself, which degrades in time as it is exploited and polluted. The payoff of exploitation diminishes to zero and protection becomes increasingly attractive. So eventually there will be a point—near environmental collapse—where every actor will get it together and actually protect the environment. In game theory, this scenario where coordination is clearly dominant over defection is called a “stag hunt.” Only, in this absurd scenario, that point would come fairly close to when the environment was already gone.

This simplification misses out on some things, and ideally a game could collapse some of the benefits and drawbacks of the environment in the present and future into a single model, even though risks will still change as we get closer to the environmental cliff, a concept that will itself take much time to define if it even exists.  Also, it appears that some damage to the climate and environment is likely inevitable, and policies are only working at this point to mitigate future global temperature rise or emissions. Additionally, emissions policies have real cost in terms of direct investments and productivity losses.

Given these considerations, we might be able to make some adjustments to the matrix. Let’s say that right now, we estimate present and future costs of runaway climate change to be a ten on some arbitrary scale for each country. Using the example of the United States and China, let’s also assume that each country’s emissions policy can only mitigate the costs of climate change by three points that apply globally. So if the United States or China cuts emissions independently, the costs of climate change are reduced to seven. If both act, the costs are reduced to four. But emissions policies are also costly, and given the global nature of climate change, if one actor acts alone, generally the returns are diffuse compared to the costs. So let’s say the policy costs more than the benefit of one state’s contribution, or four points. The matrix now looks like this:

So the best option overall is for the two countries to work together. But the prospect of being faked out and the lure of gaining the benefits as a free rider with no investment (both the top right and the bottom left cells) mean that both sides will tend towards defecting, or continuing to exploit the environment at the rate they are currently going. This is the dominating strategy in a Prisoner’s Dilemma, which we discussed before. This scenario might become a stag hunt as the costs of climate change become more immediate, clear, and relatively high and the benefits of even small amounts of mitigation gain a higher relative payoff. The goal of much of diplomacy, green technology, and climate education is to turn the game into a stag hunt before the world gets too close to destruction. This involves increasing the payoff and reducing the cost of emissions mitigation and increasing the understanding—and thus, the inherent risk and relative costs—of climate change.

Did I miss anything or get anything wrong? Are there any assumptions that I missed that might change the nature of the game? Are there any questions or ideas on how to make this more sophisticated and better understand the examples? I am sifting through some reader feedback and research from experts to add to the analysis and get closer. As always, feel free to email me.