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.
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.
Welcome back, gamers! A week ago, I wrote a Note here with the goal of crowdsourcing reader and expert knowledge in order to come up with a game-theory-based understanding of climate policy that could be used to find some insights about how states and countries might implement different policies. So far, I’ve received dozens of emails and tweets from students, economists, game theorists, climate change scientists, and some field-leading experts with some great questions, ideas, and resources. I’m currently sifting through them all and working to gain a better idea of what questions might be answered and how.
I thought it might be a good time to whittle down just what we’re trying to do here based on feedback. First, just what actors and climate policies are we examining? Originally, I had the idea to just think about a kitchen sink of international actors or states. Obviously, that’s not a very good setup for any kind of modeling, so I’ve been thinking about three separate problems. The first is taking a look at West Virginia and Kentucky, two neighboring states that are among the worst in per capita greenhouse emissions. What might a regional emissions-cap agreement look like for them? What are the costs of mitigation for each state? What are the risks involved? Using simple models, what could payoffs could we predict from their decisions?
The second problem I’m considering is perhaps the classic climate-change “game” between the United States and China. Given that these countries make up 44 percent of all greenhouse gas emissions, this game provides a decent enough understanding of global climate policy and the inputs and considerations required. Here, let’s just consider a very loose hypothetical: cutting total combined emissions from fossil fuels in both countries by half over the next ten years. Would each country be responsible for only its current share, or would the United States pick up some of China’s slack? How much would the reduction cost? How could we estimate the climate gains and externalities of these decisions? What unique benefits and drawbacks might climate change mitigation have for each country? Given all these variables, we should be able to roughly model basic climate decisions between the two.
The third and most ambitious problem that might be worth examining is modeling the long-term outcomes of the Paris Agreement, given its stated objective of limiting climate increase to 1.5 degrees Celsius and the different policy levers involved. This would be an addition to work done to model the Paris framework and previously the Copenhagen framework. Instead of modeling negotiations, though, we’d be exploring long-range decisions and payoffs for a range of set policies. Granted, tracking over 100 signatories is impossible work, but we can take a look at the United States, China, the European Union, India, and the Russian Federation. Modeling this problem may prove too ambitious for the scope of an article here, but I’m hoping that by discussing it we can understand some of the complicated considerations of climate policies.
Thanks to readers from last week for providing some vital context and understanding. Last week, I discussed climate change as a prisoner’s dilemma, but depending on how much it costs to fix and how much averting climate change may help, that may not be the case. I will include some graphics to illustrate in the next Note, but basically a prisoner’s dilemma tends towards a scenario where both players defect (or choose the option to not cooperate) because the risk of choosing to cooperate while the opponent exploits you (in the prisoner’s dilemma, the opponent snitching and sending you to prison), is just too great. So although cooperating is the best option, both players tend towards not cooperating. This is how I envisioned climate-change policy working, but through email, reader Chris Lambert challenged my idea with the idea of a game of chicken––or a game that tends towards “swerving,” or one party embracing climate policy efforts with the other party encouraging it, but not helping:
Just to elaborate a little: based on preliminary outcomes, actors given reasonable ranges of uncertainty for the number and nature of the costs and benefits of abatement have been more likely to conclude that the sum costs of defection (fighting for the other nation to do more abatement) exceed the benefits of the target global abatement level. This causes a lot of "swerving," rather than defection by both parties. One or the other state decides to unilaterally commit to more abatement than their "fair share" under a cooperative outcome. As a climate game this might not make much sense, but it does predict some of the behavior.
Lambert and I discussed the difference in marginal benefit of abatement between China and the United States. That concept is a bit dense for this space, but essentially, there is a “sweet spot” between the value of abatement and the value of keeping pollution where it is, and it’s different for different states. Thus, one country may be keen on exploiting another state into doing the work of abatement—which has global impacts—another may be especially predisposed to doing that work. There’s more on the idea of marginal benefit of abatement here.
That’s all for now. Check back later on this week for some basic matrices and payoff analyses, and please let me know if you have any questions, comments, input, or any idea for how to tackle the games we’ve come up with. As always, feel free to email me.
Let the game begin! I was very excited by my colleague Andrew McGill’s work to bring game theory into the context of the election. Long story short, the weird three-sided game of chicken between GOP #NeverTrump leaders, voters, and candidates can be explained by game theory, which uses mathematical concepts to model and predict interactions between multiple decision-makers. Essentially, the game of endorsements and counter-endorsements, the dance of pledges, and the calculus of electability are all based on complex webs of predictive decisions that can actually be modeled.
I’ve long been a fan of game theory, even though I’m not an expert in it. I studied the related, but infinitely less interesting field of decision theory in graduate school, and I’ve always been interested in modeling how to solve complex global problems. Andrew’s article gave me an excuse to revive my old fascination with game theory and global catastrophe.
The very first game theory concept I became familiar with was the prisoner’s dilemma in the context of nuclear war and mutually assured destruction. In this particular game, two nuclear-armed adversarial sides that aren’t diplomatically engaged tend towards an arms race and an eventual mutual strike, even when the obvious best solution is both sides disarming. Luckily for the world, we had just enough diplomacy, luck, and influential free-radical actors to defuse that situation. So far. Here’s a little more on that.
Both the Bulletin of Atomic Scientists and President Barack Obama identify climate change as one of the key looming catastrophes of today. My colleagues here have been doing great work on the issue of climate change and the war-like mobilization that might be necessary to confront it. I’m concerned with the political and diplomatic nuts and bolts required to implement climate policies, and my guess is that game theory can help. My limited sense is that both are informed by the prisoner’s dilemma, but this “game” is much more complex than the two-sided dilemma I’m familiar with. I still think the concepts hold up well enough to use game theory to help provide workable policy ideas to try to stop some of the worst future effects of climate change, hopefully in ways that could fit some bipartisan sensibilities. In this case, what’s the equivalent of nuclear disarmament in climate policy and how can the costs and benefits be balanced?
So here’s the reason I’m writing this note: I think it would be interesting to work with readers and experts to provide a nuanced game-theory-based understanding of climate policy. Generally, journalists keep their ideas quiet and call up big-name experts until a workable article arrives. But that often leads them to talk to the same narrow cast of experts, even if other academics are doing more interesting work. And the fields of game theory and decision theory are full of enthusiastic basement forecasters—and I’d like to get their input, too.
Here’s the ask: If you are working on game-theory-based climate policy forecasting, if you're involved in the field and have ideas, or if you’re simply intrigued and have any input or questions, send me an email. Let me know what you’re working on, show me your models if you have any, send me resources that might be useful, or just ask questions!
I’ll provide updates and share input from contributors in Notes as the project coalesces. Thanks, y’all!
