Game Theory and Nuclear War

What a wonderfully cheerful topic with which to get back to work, eh?

But then again, we’ve to live up to our billing of being the dismal science, and what could be more fitting than trying to analyze the chances of nukes going off sometime this year?


Timothy Taylor kicks things off, by reminding us of the canoe and the rowboat:

For those of you who have not experienced the pleasure of gliding across a northwoods lake or river in a canoe, I’ll just note that a canoe has a point at both ends, which make it maneuverable but also potentially tippy. In contrast, a rowboat has a point at one end but is flat on the other end, which makes it more stable. From this standpoint, are small conflicts between great powers “better” in some sense than larger ones? Yes. But if there is too great a willingness to engage in many smaller conflicts, then the chance that one of them will escalate in the tippy canoe to a larger conflict is worrisome. Is a fight more likely to dump you into the water in a canoe or a rowboat? Once the fight starts, a canoe is tippier. But if neither party wants to end up in the water (in this case, a metaphor for a much broader war or a nuclear exchange), then they might be less likely to start a fight in a canoe than in a rowboat in the first place.

https://conversableeconomist.com/2022/03/06/fighting-in-a-canoe-thomas-schelling-redux/

Read, as always, the entire post. But one point in particular stood out in that post:

There are too many imponderables that could be affecting Vladimir Putin’s decision process to make any definite claims, but one wonders if his decision to invade Ukraine might have been affected by earlier western actions. For example, what if there had been a stronger western reaction when Soviet troops essentially levelled the city of Grozny in Chechnya about 20 years ago? What if the countries of western Europe had been more willing to keep their promises to commit 2% of GDP to military spending over the last two decades? What if Germany had not been so extraordinarily eager to become dependent on inflows of Russian-exported oil and gas? What if various assassinations that appeared to be engineered by Russia had been met with greater pushback? What if the Winter Olympics in 2014 had not been held in Sochi? What if the Russia-Ukraine conflict of 2014, which ended with Russia annexing Crimea and other areas, had received greater pushback when Joe Biden was vice-president?

https://conversableeconomist.com/2022/03/06/fighting-in-a-canoe-thomas-schelling-redux/

Timothy Taylor’s point in the excerpt above is that “saving face” isn’t so much about pride and honor in the present instance (whatever that instance may be), but rather about sending a message about our likely actions in the future. And that the west, because of their earlier actions and decisions, may well have signaled to Putin that they weren’t quite as decisive as they would have been in the past.

Which is a useful segue into reading an NYT profile of Putin:

An important moment in this development appears to have come with Mr. Obama’s last-minute decision in 2013 not to bomb Syria after Bashar al-Assad, the Syrian president, crossed an American “red line” against using chemical weapons. Mr. Obama took the case for war to a reluctant Congress instead, and under the lingering American threat and pressure from Moscow, Mr. al-Assad agreed to the destruction of the weapons.
The hesitation appears to have left an impression on Mr. Putin. “It was decisive, I think,” said Mr. Hollande, the former French president, who had readied warplanes to take part in the planned military strike. “Decisive for American credibility, and that had consequences. After that, I believe, Mr. Putin considered Mr. Obama weak.”

https://www.nytimes.com/2022/03/26/world/europe/vladimir-putin-russia.html

Basic game theory is actually – to use a strong word – useless. And the reason it is useless is because basic game theory assumes two things:

  1. Rationality on part of the actors
  2. Some prior knowledge about the payoffs associated with a game.

But as Noah Smith points out on his substack (the post, alas, is paywalled):

The first is that game theory fundamentally assumes that the players are rational. You have to be a cold calculating machine to think through all the strategies and pick the one that yields the greatest payoff. But it’s not clear that real actors are always rational. Putin might simply be nuts.
In fact, there’s a whole theory called “madman theory”, in which it makes sense to try to fool your opponent into thinking you’re crazier than you really are. If your opponent thinks you’re a madman, they are likely to give you more concessions than if you were rational, simply because they’re less sure about what would push you over the edge into a mutually destructive war. Nixon is said to have used this strategy intentionally by acting unhinged in order to scare the USSR, and Putin might be using it right now.

https://noahpinion.substack.com/p/nuclear-game-theory-and-its-limitations

Is Putin rational? Who knows? Does Putin? Authors have been trying to figure out Vladimir Putin for a very long time, says The Economist:

In “The Man Without a Face” (2012), for instance, Masha Gessen characterised Mr Putin, then set to reclaim the presidency after a pro-forma stint as prime minister, as a killer and extortionist. This version of him—a kgb thug turned mafia godfather—had been “hidden in plain sight”, but obscured by wishful thinking and that grey veneer. Death and terror were politically useful to Mr Putin, the author wrote. He made no distinction between the state’s interests and his own.

https://www.economist.com/culture/writers-have-grappled-with-vladimir-putin-for-two-decades/21808311

Does that sound rational to you? And regardless of your answer, how does it help one think of what Putin will do when it comes to deploying a nuke?

By the way, speaking of Masha Gessen, listen to or read her conversation with Tyler Cowen. Here’s a cheerful tidbit about Russia:

I think that there’s a kind of grumpy and dark culture in Russia. Russians certainly have a lot of discernment in the fine shades of misery. If you ask a Russian how they are, they will not cheerfully respond by saying they’re great. If they’re miserable, they might actually share that with you in some detail.
There’s no shame in being miserable in Russia. There’s, in fact, a lot of validation. Read a Russian novel. You’ll find it all in there. We really are connoisseurs of depression.

https://conversationswithtyler.com/episodes/masha-gessen/

But back to game theory and nukes.

The Economist tells us that using game theory to study the topic isn’t all that simple:

As a showdown between nuclear powers becomes more intense, Schelling observed, the risk that unexpected and perhaps undesired developments cause the situation to spiral out of control rises. (When nuclear forces are on high alert, for instance, false alarms become far more dangerous.) The upper hand, in such a situation, is thus maintained by the side that is more willing to tolerate this heightened risk of all-out nuclear war.
This is the essence of brinkmanship. It is not merely a matter of ratcheting up the tension in the hope of outbluffing the other side. It is also a test of resolve—where resolve is defined as a willingness to bear the risk of a catastrophe. Mr Putin’s move to increase the readiness of his nuclear forces may represent an attempt to demonstrate such resolve (over and above the message sent by the invasion itself). President Joe Biden’s refusal to escalate in kind could be seen as an acknowledgment of the conspicuous fact that an autocrat embroiled in a pointless war has less to lose than the rich democracy to which Mr Biden is accountable.

https://www.economist.com/finance-and-economics/2022/03/19/the-disturbing-new-relevance-of-theories-of-nuclear-deterrence

So is Putin, bizzare though it may sound, being rational by getting some folks to think that he is a madman? That is, if he anticipates that Biden is thinking along the lines outlined in this excerpt above, does it actually make sense for Putin to push this line of thinking in a calculated manner, increasing the chances that Biden will blink first.

Ah, but should Biden see through this and therefore discount the whole thing?

Of course you could model trickery attempts as their own strategies, with some (unknown) probability of success. But when you start introducing more and more options like this, you run into the second limitation of game theory — real-life strategic interactions are hellishly complex. This puts them beyond the modeling power of human theorists — perhaps the A.I. from War Games could handle this, but not even the most piteously overworked grad student is going to draw you a game tree that incorporates every possible feint and misdirection and signal. There are whole scholarly books that try to think about every possible nuclear move and countermove; they’re intellectually interesting, but they end up giving you a near-infinite menu of models to choose from, and thus they’re not very useful in real life.

https://noahpinion.substack.com/p/nuclear-game-theory-and-its-limitations?s=r

Here’s where we are then, after reading all those excerpts:

  1. There is (and there is no sugarcoating this) an increased chance that a nuke will be launched this year.
  2. It helps to try and think through this problem, because the phrase “skin in the game” is applicable for all humanity where this problem is concerned
  3. Game theory is a good place to start, because it seems to be the best, most appropriate tool in our toolkit
  4. Who better to tell us how to think about the game theoretic aspects of a nuclear war than Thomas Schelling? He won a Nobel Prize for it, and his book is the book to read about the topic!

… except it ain’t really about game theory!

But as subsequent writers have pointed out, Schelling’s work wasn’t really a work of game theory. Game theory, as an economist knows it, is an exercise in pure rationality — two rational actors, each knowing that the other knows they’re rational (and knowing that the other knows, and so on) think through the possible set of strategies that they and their opponent(s) might take. This process of thinking through all of the possible moves causes them to arrive at some kind of strategic equilibrium (usually some kind of Nash equilibrium, although there are other kinds that people think about). At that point, playing out the moves of the game is simply pro forma; what people will do is either predetermined, or randomized.
Schelling’s concept of deterrence, in contrast, is full of signaling, misdirection, and guesswork about the opponent’s motives and thoughts. It’s the kind of thing that could only be rationally calculated in its entirety by a supercomputer like the one in War Games. Schelling’s ideas are more like the way real people play most games — feints, blunders, deception, and looking for tells.

https://noahpinion.substack.com/p/nuclear-game-theory-and-its-limitations?s=r

But if you ask me, that is exactly why you should read Schelling about this topic! Precisely because it isn’t just about basic game theory, and because it takes into account signaling, misdirection and guesswork.

Or, if you’d like the same thought expressed in more popular, and less highfalutin’ words, this is a game in which you have to play the man and the cards. And the stakes are ridiculously, scarily high.

As my favorite blogger sometimes says, have a nice day.

Author: Ashish

Hi there! Thanks for choosing to visit this page, and my blog. My name is Ashish, and I'm a bit of a wanderer when it comes to vocations. I'm not quite sure what I want to do with my life, and I'm not even sure that it is any one single thing. But I know I like knowing about a lot of things, as many as possible. I know I like bike rides, I know I like the city I was born (Pune) and I know I like reading and writing. Feel free to drop me a line if you feel like a chat - I'll look forward to it. Cheers!

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