# Game theory, sanctions, and Ukraine

*Epistemic status: I am doing a master's degree in Economics and know quite a lot about game theory but have no expertise in war. I can recommend Bret Devereaux's blog on* [*nuclear deterrence 101*](https://acoup.blog/2022/03/11/collections-nuclear-deterrence-101/) *for a perspective from someone who does have more military knowledge than me.*

Most discussion around the war in Ukraine, and the Western response, including Zvi's [otherwise excellent post](https://www.lesswrong.com/posts/jeaaeDTyj2xmbkxqz/ukraine-post-2-options), misses what I think one of the most important goals the West should have.\[1\] (For the rest of this post, I will use 'we' and 'the West' loosely to mean the US/EU/UK/NATO and allies.) That goal is **deterring the next war. **

There is a concept in game theory called backward induction. You look at possible future decision nodes, and ask what is the expected value of being at that decision node. For example, imagine that China invades Taiwan tomorrow. What should the West do then? 1) Fight to defend Taiwan, with extremely high risk of escalation and causing World War Three? 2) Let millions of people fall to tyranny, demonstrate that the value of Western protection is worthless, encourage even more future invasions, and watch as every medium-sized country scrambles to build nukes to defend itself?\[2\] *If we get to the point that someone has to make this decision, we have already lost.* There are no positive-expected-value choices left.

You can make the same argument for a world where Russia invades a NATO member like the Baltic states. What do we do then? Start World War Three? Abandon huge parts of Europe to be invaded until Russian tanks are rolling through Germany?

We do not ever want to end up in these scenarios. Therefore the main goal of Western strategy should be to never get to that point. That means that our response to the Russian invasion of Ukraine must credibly signal to Russia, China and any other potential invaders that the cost of invading another country is too high. Remember that their leaders are making comparable calculations: what is the best strategy for China/Russia to take given the expected response of the West.\[3\]  If China thinks that invading Taiwan will result in World War Three - or even that there is a 50:50 chance of World War Three - then it is not in their interests. If they think that invading Taiwan will result in a slap on the wrist then they will do it, and the West faces its terrible choice.

What does this mean for our response to the Russian invasion of Ukraine? Primarily the importance of keeping the pressure on Russia, for as long as Russia is attempting to occupy Ukraine. (We should be willing to end sanctions iff Russia calls off the invasion and brings its soldiers home, presumably in the context of regime change.) The West have been doing a good job so far at signalling resolve and a willingness to inflict costs on Russia. We need to maintain our resolve, even as the costs of sanctions - be that rising food prices in poor countries or incentivising China to build its own replacement for SWIFT - become more apparent. The benefit of deterring World War Three is worth substantial pain. 

Specifically, we must be ready to keep sanctions going for the long-haul. If the war ends with Russia still occupying all or some of Ukraine, there will be pressure in the West to normalise relations and cut our losses, especially as we see more of the cost of sanctions to innocent people both inside and outside Russia. Ending sanctions would absolutely be the wrong action. If Putin or Xi Jinping or some other dictator thinks that the cost of invading an innocent country is only a few months or a year or pain before things go back to normal, then they will decide that cost is worth it. That is a terrible outcome if they're right, and even worse if they miscalculate the West's response to the next outrage and trigger World War Three.

I don't have specific recommendations for readers' personal actions, beyond what Zvi has [already suggested](https://www.lesswrong.com/posts/jeaaeDTyj2xmbkxqz/ukraine-post-2-options#I_indeed_strongly_prefer_such_outcomes_), so I will add my voice to encourage readers to provide what aid they can to Ukraine, and support maximum sanctions on Russia, and to maintain that support even if it becomes clear that the occupation of Ukraine is a fait accompli.

\[1\] To be clear, I wholeheartedly support Ukraine and I want the Russian invasion to be defeated. I just think that with so much focus on the short-term goal of helping Ukraine we are at risk of forgetting longer-term strategic goals which are also vitally important.

\[2\] Evidence from the response to the Russian invasion of Ukraine suggests that we'd go with option 2 and take major economic damage trying to throw China out of the world trade system while still failing to save Taiwan.

\[3\] This does assume at least moderately rational leadership, which is likely true for China. I am aware of doubts about Putin's rationality.