Game theory and the climate

One way to view the climate crisis is through the lens of game theory. There are simplifications to be sure but I think it really does allow us to see the pros and cons of a number of different approaches to trying to solve the problem. If we were to formalise the issue in a game it would most likely look something like a prisoners dilemma where we have the rest of the (W)orld on one axis and a particular (C)ountry on the other axis.

One simplification to note right away is that the table here suggests that (C) is small enough that whatever action they take won’t actually determine the final state the world ends up in, e.g whatever New Zealand does if the rest of the world all pollute or all don’t pollute NZ’s individual actions won’t really change the outcome. This is obviously less true for countries like the USA or China but is still largely true even for them. For any one country, no matter the size, if the rest of the world is all doing a particular action that action will dominate.

The second simplification is that the rest of the world will be magically coordinated on a particular action. The reason this assumption has been put in at the moment is to reflect that most countries have a somewhat symmetric decision making systems. Often what is better for one country will also be better for most other countries and so we can imagine all countries being faced with this same matrix. If it makes sense for the USA to pollute for the sake of growth it probably also makes sense for India to.

So what is the matrix (with my admittedly somewhat arbitrarily chosen numbers) saying? It is saying that if the rest of the world is all going to continue polluting it’s going to end in disaster no matter what you do but you’ll be a bit less poor along the way if you also pollute. If the rest of the world isn’t polluting then things will likely be fine in the end but as a country you will probably be a bit better off if you just free ride on everyone else’s lack of polluting and continue with business as usual.

Overall then polluting is what would be called a dominant strategy, your best response regardless of what the rest of the world is doing. And if all the other countries have a similar payoff matrix then we would have all countries polluting as a Nash equilibrium, that is, even if you can see the actions of all the other countries you will have no incentive to change your behaviour.

This is a simplification but in many ways it does seem to describe the situation we have in the real world. Countries really do seem to have short run benefits from allowing pollution to occur for growth reasons, individually therefore they often will prefer to pollute and if they don’t then other countries really do get to somewhat free ride off their efforts. Most importantly we really do seem to be stuck in a Nash equilibrium of not changing our behaviour enough (We seem to only be on track to get to 1% reduction of greenhouse gasses by 2030, way below target).

So what can game theory and real life tell us about how to break out of the notoriously difficult prisoners dilemma? Below are a few theoretical and more practical ways prisoners dilemmas have been solved and we can see how they correspond to different strategies to address climate change.

Iterated game

Let’s start by relaxing the one shot nature of the game and making it iterated. This is actually how the prisoners dilemma is often gotten around in real life. You don’t all that frequently interact with someone once and then never see them again, instead you often go back to the same restaurants or do business with the same people. Now if the duration of doing business is not explicitly known or is sufficiently long you can find that you now have a Nash equilibrium to cooperate or in our climate setting not pollute. i.e Let’s all pollute a bit less this year and then as time goes on you can establish trust that the other party is truly going to cooperate with you. You now find yourself in the payoff square (4,4) and live happily ever after.

This does kind of work, although there is an issue that what I said isn’t strictly true. Moving to (Don’t, Don’t) is not actually a Nash equilibrium. It can be if you add something like, I will not pollute in the first period and then after that I will do whatever action you do and if the timeline is long/fuzzy enough (as it is in the case of our planet will be around for a really long time) then this does become a dominant strategy. You may have realised the problem. In strict logical terms this requires our credible commitment to switch back to polluting if you deviate. That would be like saying, we’ll massively roll out renewable energy projects across our country but if you don’t do the same we’ll burn a forest. Not very credible.

The other way that iterated games work is through reputation, over time you get known as a country that doesn’t pollute and this makes others more likely to do business with you, and so it can then be in your best interests to gain this reputation premium. This I think makes more sense apart from at the moment there are no international rules that would make this occur. It’s not like the WTO says there are 5% climate tariffs to countries who don’t meet their targets. This isn’t really enforceable and would also likely be massively regressive towards developing countries.

Multistage game

We could change the nature of the game from being simultaneous to being multistage. Imagine the following set up, country A sets a conditional binding climate goal, country B gets to see this goal and then set their own goal. If the two goals are similar (e.g if both goals are to reduce pollution) then that is the end and we are bound to our courses of action. If however our goals differ country A gets to go back and change their goal. The idea here is to de-risk choosing don’t pollute by allowing you to change your mind if it would lead to a worse payoff but not change your mind if it leads to globally better outcomes.

This again makes a fair amount of sense in theory but faces similar issues to iterated games in practice. How can you make a binding commitment. Would the USA really go back on its climate policy just because the UK didn’t follow along?


Another option is to add punishment, here if our punishment term (p) is large enough then we can change the best course of action for countries to take.

This is how a fair number of prisoners dilemmas are solved in the real world. When you interact with a random seller on the internet they might well have the incentive to ship a product of lower than advertised quality. After all they have the funds now why give you somethings as expensive? This though is called fraud and is punished, in fact it has a whole industry dedicated to detecting and punishing it.

The issue in our example is that there is nothing above countries that has this capability. Yes there are things like the UN and such that do fine countries if they fail to meet climate targets but these punishments are in some ways a voluntary payment by the country to save face and far too small to really matter. If the payments were large enough to actually address the behaviour it would be much more likely that they they would also be too large for countries to want to comply with.

This is also where reputation comes in again, if your reputation gets damaged from breaking the “agreed upon” action then you can basically get punished by losing business. In our world example though again this doesn’t seem that likely to happen.


One way the PD is solved in the real world is something that economic models don’t really get along with which is “people can just be nice”. I know, how would the maths work for that one? This really is though how a lot of interactions go.

*(we just end up here because we’re good, nice, non ‘rational agent’ people)

This works a lot in real life, people feel bad or have a sense of honour or guilt or whatever. People just take altruistic actions that others better off while potentially getting a little bit worse off themselves and the world is all the better for it.

The above might sounds sarcastic but I do actually think peoples propensity to act like this is one of the foundational building blocks of civilisation and one of the greatest credits of human kind. People can break out of the inextricable logic of payoff matrix’s and just be nice.

This seems to work well and often on the level of individuals and maybe even small groups. It does not seem to work particularly well at the scale of entire countries or large scale anonymous networks of international trade. The other thing is that in settings where you need resources to survive if you do too much of this you’ll just die to the people who are not as nice as you.

A counter to the above is that this is actually somewhat happening, many businesses are voluntarily taking greater action for climate at the cost of their short term ‘bottom line’. This is amazing to see and will undoubtedly be crucial, my point here though is that the actual short run incentives haven’t really changed. It is somewhat blindly hoping that the goodness of those in positions of responsibility and power will do the right thing, and so far that hope does not seem to have paid off very well.

Changing the payoff matrix

One of the methods I believe holds the most hope is changing the payoff matrix itself. This isn’t typically an option if you’re reading through a book about game theory but what if we managed to turn the payoff matrix to this:

Here we have a weakly dominant strategy of not polluting (weak because if everyone carries on polluting you’re still pretty screwed regardless of what you do). We got here by basically making the act of polluting more costly. The reason this is different to the punishment method though is that here we would be attempting methods that do it endogenously. This can include things like carbon pricing and taxes and the like. The idea is to actually change the incentives for the ‘man on the ground’ to move away from polluting.

I think this holds a lot of promise, carbon taxes seem to be a great idea that would genuinely distort market incentives towards better behaviour. There is an issue with this approach though and it is that it is a ‘permisionful’ one. You still basically need the permission of governments to make it happen. It’s not much good to the world if India has a carbon tax but China and the USA don’t.

That brings us to this matrix. Here instead of making polluting more costly, we make not polluting less costly (okay this does make polluting more costly on a relative basis but you get the idea). The reason this would seem to be so powerful is that in a lot of way this can be permissionless. We could to a large extent endogenously change incentives in a way that make people want to pollute less out of their own self interest.

Make solar power the cheapest way to reliably get energy, people, I’m sure, would love to stop burning fossil fuels. Make reliably good synthetic meat alternatives better value than actual meat and I’m sure, after a bit of an adjustment period, huge numbers of people would gladly make the change.

This may seem like somewhat of a panacea but in many ways it is already coming true. Solar has been on an exponentially decreasing cost curve for 40 years that has just in the past year or two made it cheaper than fossil fuels. The great thing about this is that unlike our ability to reduce the price of fossil fuels solars price can likely still fall a long way. Firstly the fixed cost is drastically different, you might have to build factories to make the panels but you don’t have to buy any energy input, like coal, that puts a price floor on things. Therefore, almost all of the cost of solar energy is in the transformation stage where we turn one form of energy another, and in the case of solar this seems like something we are getting much much better at over time the more we build.

Price of electricity new renewables vs new fossil no geo
The most hope inspiring chart in the world?

It is probably getting ahead of ourselves to imagine anything close to a Moores law but renewable energy really does seem to be scale exponentially in terms of price reductions and efficiently and now that we have reached the tipping point of getting cheaper than fossil fuels this can lead to a virtuous circle.

A similar thing is occurring with meat. At the moment synthetic meat is incredibly expensive and difficult to grow thus massively limiting the use of it. However, as a technology it is one that also seems to be experiences leaps and bounds in its cost curve, and it also benefits from many of the same thing solar does. You can ignore the fixed cost (in this case instead of coal or oil it is needing to actually buy and raise a cow or chicken) and instead the cost comes from the transformation of one cheap thing (animal cells) into something useful and this technology is rapidly getting cheaper and more efficient.


None of the above is meant to suggest that things like international agreements or similar are not necessary or needed. It is mainly here to do two things

Present a framework to explain why these things seem to have been failing us over and over again by considering the effects on the short term incentives of agents actually doing the polluting.

Present a potential scheme, within the same framework, that offers hope and is much newer to our struggle, that of endogenous technological innovation.

Extra notes:

Below are some links to things that have really shaped my thinking in this area