Nuclear Game Theory

Let's talk about game theory and nukes for a second. Consider the relatively simple game that exists between two nuclear-capable states: each side can either use their nukes or not at any given time. In game theoretic terms, the payout matrix would look something like what's at right. To get into the swing of things, imagine that its your country versus another, much more evil country. Your payouts are in virtuous green, meanwhile theirs are in evil red. Anyway, as you can see from the graph, if both sides choose "no nuke", everyone is slightly better off (we didn't die!), but things are more or less the same as they were before. Meanwhile, if both sides choose to nuke, everyone dies and suffers a massive -10 points - each. Sad times all around. However, if one side chooses to nuke first, they gain moderately (their evil enemy is destroyed!) while the other side suffers massively - as reflected in the numbers, I consider this an even more massive -11 points: -10 from being nuked, and a further -1 from knowing that your enemy got away with it, too. So while one side celebrates its victory, the other side can treat its radiation sickness.

The astute among you would recognize this payoff matrix as the same as that for the classic prisoner's dilemma game. And as we all know, in a single iteration of the prisoner's dilemma, the only Nash equilibrium is mutual defection - both sides nuke, and both sides puke. From radiation sickness, from the bombs. And then they die. The ones who die in the initial blast are the lucky ones. Anyway... the even more astute among you will wonder - if game theory predicts that everyone nukes the frack out of each other, then why aren't we living in a nuclear winter wonderland? Is game theory wrong?

Ha ha - don't fool yourself! Game theory, like any mathematical science, can't be wrong - it can simply be applied incorrectly by people. Notice how mutual defection is only a Nash equilibrium in the single iteration case. Assuming that both countries can exchange multiple nukes in an iterated version of "nuke or be nuked", we can suddenly see how when iterated over several hundred missiles each capable of delivering thousand megaton payloads, all those little "+1 we didn't die!" points really can add up. Alternatively, a single defection will result in a final score that's way lower than what you would have gotten if you had simply not launched nukes. So the sensible thing to do here then is simply never launch at all - unless your opponent launches, in which case you launch back and let the holy fire of justice rain down from the sky. But, assuming that each player in the game is at least pursuing their own self interest and wants to maximize their points, mutual cooperation suddenly becomes the name of the game here, especially if we make mutual defection both assured and costly. And this, my friends, is precisely the current state of affairs between modern nuclear equipped states, more or less: each has arsenals large enough to ensure complete destruction of their opponent should they need to use it. In terms of points, that's like a kraken-sized -100 - and, since world leaders generally would rather keep their jobs, everyone avoids nuking each other and we all live together peacefully. A bit uneasy, sure, but peacefully.

This simple breakdown of nuclear strategy is known as mutually assured destruction (MAD), and although I know quite a number of you may balk at its Machiavellian efficiency ("Why can't we all just disarm?!" you may ask), but the fact remains that MAD's cold calculus has proven effective - humanity has not used a single nuclear weapon in over 60 years, despite the rapid proliferation of its capability to do so. Hell, even Pakistan has nuclear arms, now! So how does MAD keep the peace so well?

Well, like any stable, sustainable treaty between multiple parties, MAD has a couple key qualities: 1) it is individually beneficial for both parties to participate regardless of what the other side does, and 2) it is enforceable - any involved party will suffer consequences for renigging on the deal. Specifically, as I argued earlier, in an iterated nuclear game, the individually optimal thing is to not initiate global thermonuclear war. You can always react to one - its the same outcome for you either way, and since this type of logic applies for all players, everyone concludes that its better not to launch, 2) unless they are launched upon first. This is the enforcement part of MAD - by publicly being known to have nuclear arms, participant states readily communicate to each other the consequences of renigging and launching first.

Now, this isn't rocket science, nor is this crazy shaman magickry - this is cold hard game theory here. It is for this reason that I think the Nuclear Nonproliferation treaty will fail. Its not that I want it to fail - quite the contrary; I want it to succeed, and that's why I'm so quick to point out its one major flaw: it is not mutually enforceable. Yes, the current nuclear states are more than capable of enforcing it should other states deviate - both with forced inspections, embargos, political pressure, and eventually invasion. From the United State's point of view, the treaty is definitely enforceable. However, who's going to force us to hold up our end of the bargain?

Think about it from a non-nuclear state's perspective. Specifically, imagine if you're some poor modern state that doesn't have nuclear arms yet, and someone big who's words are backed with NUCLEAR WEAPONS (like Russia or China) comes along and asks you to sign their Red version of the Nuclear Nonproliferation treaty - essentially, they'll agree never to nuke you first, as long as you agree to not build nuclear weapons (and prove it to them). Now, you don't really trust this weird Russia/China hybrid state, but you want to play nice to try to get along with them, so you decide to go along with it and agree to their demands. What else can you do? They were just going to invade you if you didn't agree, so what could you do?

But now, let's go back to our good old friend, the payoff matrix (at left). This time, because you didn't build nukes, you don't have the option to build nukes. Do you see what can happen now? You have no choice in the matter - you have to pick "no nuke". However, the other side has a choice to either nuke or not nuke. If they hold up their end of the bargain, they can collect an easy, assured +1 points each round. However, they could just as easily go "nuke" and get +5 points - and honestly, what can you do to stop them? You're going to be too busy watching your insides melt from radiation sickness. I mean seriously, did you ever see Battlestar Galactica? You know how it opens up with the evil Cylon robots nuking the fuck out of the entire human race, with humanity essentially sitting by, impotent to stop them? Yeah, that would be you here - should Russia/China/The Cylons choose to renig on their end of the bargain and nuke you anyway.

Now, obviously a deal like is just extremely poorly disguised bullying - no reasonable, self interested state would every agree to something like that, nor would they expect anyone else to either. So there's a extra sweetener added to the deal - should you be nuclearly attacked by someone else, Cylon Russia-China will come to your aid and nuke the bajeezus out of them for you. Thus, against everyone else you get all the best elements of MAD without having to build a nuclear stockpile of your own. Isn't that just great?! Even better, The CRC agrees the less severe attacks like some biological weapons and crippling cyberattacks will not count as being worth nuclear retaliation - essentially, you can agree to this agreement and still fight the Evil Red Cylons should it be necessary! You just have to make sure you use the right biological agents - perhaps you there's a committee you need to clear your attack with?

Of course, if you're the type of country who would never ever want to attack Cylon Russia China, then this deal is great - you save on having to build your own nuclear program while still getting nuclear protection, plus you get that nice warm fuzzy feeling of playing nice with everyone. Or perhaps you're a country that doesn't feel all that great about the CRC, but fears being nuked by someone else - if you don't have any hope of acquiring your own nuclear arsenal within sufficient time to adequately deter such an attack, it would probably still be in your best interest to sign a nonproliferation treaty. In these cases, fact that the treaty isn't mutually enforceable isn't a huge concern - in each case, you benefit by trusting the CRC, so its in your best interest to pursue the treaty regardless of what decision the CRC makes - literally, no matter what the Cylon's advanced Bayesian networks compute to be optimal, you're always acting in your best interests.

However, let's say that you're a country who's main enemy is Cylon Russia China. What happens then? Well, suddenly you stand little to gain from getting MAD insurance - the country who you most fear will attack you is precisely the same one vowing to defend you. Can you say conflict of interest here? Without that extra bit of incentive, the deal effectively becomes political bullying, and as we've clearly seen before, no country in their right minds would accept such a deal. Worse, its insulting to think that they even would.

Now, I've avoided using any real country's names in this article (well, Russia and China, but I meant it more like the countries that exist as vague "enemies" to the USA in seasons of 24, not the real countries we have to deal with in our daily lives - plus, I called it Russia/China, which is clearly some alternate history creation and not a real country. Yet). However, we can't help but draw metaphors and parallels between what we read and what we see happening around us in our daily lives - which countries did you project onto this article? When you thought about being a country who's main enemy is the CRC, which real world country's shoes did you put yourself into? Just think about it for now, and try to ruminate on the truth behind the basic game theory here - I want to let it sink in before using it to argue a very controversial but also very correct conclusion.

Any thoughts or opinions about what I've said before we go further?