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Volume 16: Game Theory and the Nuclear Age: Part II

How About a Nice Game of Chess?

“Gentlemen, you can’t fight in here! This is the War Room!” – President Merkin Muffley, Dr. Strangelove

The 1960s were perhaps the most dangerous period in our history. At the height of the Cold War, the United States and Soviet Union fought for influence on five continents. The Berlin Crisis, Bay of Pigs, and Cuban Missile Crisis flowed to escalation in Vietnam and the bellicose leaderships of Richard Nixon and Leonid Brezhnev.

The world of the Sixties existed every day in the shadow of nuclear weapons. Increasingly powerful and reliable, ready to launch from airplanes, missile silos and submarines. By the end of the decade, the superpowers felt obligated to possess nearly 40,000 bombs, enough to destroy the world many times over.

Somehow – and sometimes despite our best efforts – there was no nuclear holocaust. This is the story of how we avoided it and of whether we’ll be able to in the future.

  • What is Mutually Assured Destruction?

  • What are the problems with MAD?

  • Will this game work in the modern nuclear paradigm?

Your author cautions you (same as in Volume 14):

Nuclear weapons are terrible things. This is true in all of the word’s meanings. Terrible: extremely bad, as in “a terrible movie.” Terrible: formidable in nature, as in “a terrible responsibility.” Terrible: extreme or great, as in “a terrible disappointment.” Nuclear weapons are not to be trifled with, joked about or handled except with extreme care.

Which is all to say – this Volume will prominently feature death, destruction, fallout, nuclear winters and the end of the human race. We will flippantly talk about the gruesome deaths of millions and even billions. We will explicitly do this through the lens of a game, winning and losing, keeping score of the destruction. We will not modify our usual style of writing or the ongoing attempts at mild humor. We are not focused on the morality of these weapons, their development or their use. Except in the paragraphs immediately following.

The previous five hundred years have been a period of steady human advancement with no major steps back. It was inevitable that we would learn about the power of the atom. Every man, woman and child is innately aware of this power. It stares you in the face every day, from sunrise to sunset. We were going to learn about radioactivity, fission and fusion and chain reactions. It necessarily follows that we would try to harness this power. Even with knowledge of their destructive potential, we were eventually going to develop nuclear weapons capabilities. They are a by-product of these five centuries of discoveries about the Universe we live in.

Morality comes only after development: how can these weapons be controlled to prevent their use? The two decades after the Trinity Test were not just a scramble to build bigger bombs, but also to develop these controls. Game theory contains the most effective controls we’ve found. And we can only learn the game theory of nuclear weapons by repeatedly simulating the destruction of the world.

Only by understanding these weapons can we prevent their use.

-NC

What is Mutually Assured Destruction?

We left off in Volume 14 discussing the classic problems of game theory and this is where we will pick up. Recall that in game theory, Players (two of them, in our examples) make decisions from a set of choices, each called a “Strategy.” All the Players try to maximize their “Utility,” a generic measure of value, usually represented by a single number. Players in game theory are always assumed to act rationally. In some games, Players are allowed to communicate before choosing their Strategies. If you need a longer refresher on game theory basics, I encourage you to look back at Part I.

In game theory, Global Thermonuclear War is closest to Chicken, so we will start there. In classical Chicken, two drivers are headed towards a cliff and each must decide to Swerve First or Swerve Last. If both Swerve First, the game is a draw. If both Swerve Last, they drive off the cliff and are killed.(1) Table 1 shows the outcomes for our first game of Chicken:

The most important feature of Chicken is that the “Crash” outcome is far worse than the “Lose” outcome. This makes sense: the slight embarrassment you feel from swerving First is a better than the death you feel from driving off the cliff. Therefore, if you think that your opponent will swerve Last, you should swerve First. Even if you aren’t certain what he(2) will do, a significant likelihood of his choosing Swerve Last should make you cautious. Using the game theoretic terminology, the Nash Equilibriums of Chicken are where exactly one player swerves.(3)

Strategic Deterrence has been an element of warfare for most of history, long before the term was coined. The idea is simple: your nation-state tells all the others that, if attacked, you will respond disproportionally – usually against their homeland as well as their military forces. Knowing the losses they would experience, anyone thinking of attacking you will think twice. If this potential response is deadly enough, it will not be in their best interests to begin a war. Therefore, if they are rational Players, they will not attack you and peace is preserved.

Strategic Deterrence only works if the threat is credible. Napoleon couldn’t keep England off the European continent because he couldn’t credibly threaten a crossing of the English Channel.(4) Imperial Japan was forced to open its borders to Matthew Perry’s Black Ships. Japan’s Navy of the 1850s was archaic, making Perry’s threat credible. In World War II, strategic bombing took deterrence to new heights. The firebombing of Dresden on February 14/15, 1945 killed at least 22,700 people, rendered at least 100,000 homeless and destroyed the entire city. The Allies lost only eight of the more than 2,000 warplanes sent against Dresden.(5)

But the disparate damage caused by raids in 1945 obscures the experience in World War II up to that point. When Germany (or, for that matter, England) had active fighter defenses, the bombers did not always get through.(6) In the British Bomber Command, 55,573 of around 125,000 total aircrew were killed by the end of the war. The American Eighth Air Force, also primarily tasked with bombing Nazi territory, suffered 47,000 casualties, 26,000 fatal.(7) It was not unusual for almost 10% of the crews to be lost in a single raid. In addition, the bombing campaign involved massive investments in ground crews, war materiel and critical aviation fuel. In short, it isn’t clear that Allied bombing campaign was actually successful, given the cost.(8) Conventional bombing would not be a credible strategic deterrence in the post-war era.

The limits of this threat were known by the Superpowers. Counterintuitively, the prevention of war relied on the ability to create credible deterrence. This need for credibility led to the development of Inter-Continental Ballistic Missiles, or ICBMs. ICBMs could be stationed in North Dakota and still reach central Russia. Flying at many multiples of the speed of sound, and with a tiny cross section, ICBMs could not be destroyed in flight.(9) To increase threat credibility, each ICBM came to contain Multiple Independent Re-Entry Vehicles, or “MIRVs.” Above the top of the atmosphere, an ICBM could release perhaps a dozen MIRVs, along with decoys and who knows what else. Each individual MIRV carried massive destructive power, enough to destroy a city.(10) The difficulty of intercepting the incoming attack thus became an order of magnitude greater.

Land-based ICBMs were, however, still vulnerable to attack. If you know where your opponent kept their missiles, you might try to destroy them using your ICBMs, a so-called “first strike.” So, everybody started looking for hiding places. Maybe keep them underground, or put them on trucks so they are mobile. But, the best hiding spot is below water; nuclear submarines are the key to credible deterrence. By 1961, ICBMs were on both American and Soviet submarines. Destroying one submarine was challenging enough; destroying a fleet impossible. Simultaneously destroying your opponent’s bomber force, submarine force and land-based ICBMs would be far too risky to try. Hence, the threat was completely credible. This arrangement became known as the Nuclear Triad.

Nuclear Triad

By 1965, both sides had thousands of missiles arranged in their Nuclear Triads. A successful attack from the other side would be certain to draw a response. This is called “second strike” capability. American planners considered that nuclear weapons equivalent to 400 million tons of TNT would be enough to destroy the Soviet Union’s capability to make war; the Soviet Union probably had a similar number in mind.(11) Given that each side possessed around 10,000 million tons of bombs by the end of the 1960s,(12) any second strike would be on a massive scale. Both sides had a highly credible threat; a successful nuclear strike would return a strike in kind. This is Mutually Assured Destruction, also known by its acronym, “MAD.” Game theory tells us MAD should prevent nuclear war. In theory.

What are the problems with MAD?

We’ve talked a lot about the “D”, Destruction. There is little doubt that both Superpowers had the ability to annihilate the other in a successful strike, hence the “M”, Mutual. Which leaves us with the trickiest letter: “A” for Assured. To consider it, we’ll leave the historical-technical path and return to game theory.

Let’s go back to our game of Chicken, in Table 1 above. We can translate Swerve Last to Fire First and Swerve First to Fire Second – but there is a problem. In Table 1, the situation where you Swerve First is not such a terrible outcome. You are the Chicken, but you will survive. In Global Thermonuclear War, the situation where your opponent Fires First and you Fire Second is really bad. We need to modify the table; maybe to something like this:

We can quibble about the exact values here. For example, I assume you would prefer to be attacked by a second-strike rather than a first, but it could easily be the other way.(13) What really matters – and should make you feel a bit better – is that the outcome where neither side fires its Nukes is stable. Deterrence has worked. The prospect of nuclear war is so terrible that neither side will start one. This is what we hoped MAD would do, so QED.(14)

Unfortunately, there is a problem. In the real world, both sides have a third option, “do not retaliate.” There are many reasons why a Superpower might not actually conduct a second strike. They could be unable to or could choose not to. Maybe their weapons don’t work; after all, 400 million tons of TNT just exploded somewhere. Even launch detection was a real question in the 1960s. If you don’t know whether the other guy fired his missiles, how can you be sure you’ll strike back?

Let’s look at our game again, including the option not to retaliate.

Our first three-choice game, it looks confusing, but it’s not so difficult. The four outcomes in the bottom-right represent situations where nobody fires their bombs first. If nobody fires first, there is never a nuclear war and everybody wins. The other outcomes show what happens with the three possible responses to an attack. If you retaliate, you end up in the same situation as in Table 2. But if you hold your fire, it is worse. On the other hand, your opponent is even better than if the war never happened. If you get nuked and don’t fire back, the other guy dominates the world.

Fortunately, when both sides play “Retaliate” the game is still stable. However, the situation changes if your opponent plays Never. If you know he is doing this, you could fire your missiles immediately, winning the war. Recall that in game theory, players are always rational. In Table 3, Retaliate always performs as well or better than Never. Therefore, no player will ever choose Never and we are safe.(15)

But is our game truly descriptive of the real-world? Consider the situation where you are facing an imminent incoming strike and must decide what to do. The attack will destroy your entire country, probably killing half of your population and rendering your land uninhabitable for a long time. Given that this will happen no matter what – are you sure you would fire back? If you hold fire, your country will be destroyed, but your opponents’ will survive. Not a great situation, but a retaliation would kill hundreds of millions more and possibly result in the extinction of humanity. Not so easy to pull the trigger. If you think you might be better off not retaliating, it leads to a new game:

The key point to notice is that {First, Never} is now, unfortunately, a Nash Equilibrium, while neither {Retaliate, Never} nor {Never, Never} is stable. Therefore, game theory tells us that, if one player chooses Never, the other will immediately launch a full strike. This means that even if you aren’t sure you will Retaliate, you must make your opponent think you will. And, if you suspect your opponent of weakness, you must consider Firing First.

Let’s leave game theory and go back to the Sixties. Put yourself in the seat of President Kennedy or Chairman Khrushchev. In both countries, power to fire nuclear weapons sits with one person. If either Kennedy or Khrushchev chooses Fire First, no Congress, Presidium or military leadership can stop them.(16) And there is plenty of mutual distrust. Kennedy used the CIA to sponsor a coup in a Soviet-aligned nation ninety miles south of Florida. Khrushchev attempted to force the capitulation of West Berlin by provoking another crisis at that flashpoint. They sit, at the White House and at the Kremlin, buffered by military, political, domestic and foreign policy advisors, each with their own agenda. They have met in person only once, a tense one-day summit in Vienna. To keep the world safe (or at least stable), each must convince the other of their willingness to end the human race, should the situation arise.

Brinksmanship is the strategy of pushing conflicts to the edge of disaster without quite crossing the line into nuclear war. It became de facto American policy under President Eisenhower’s Secretary of State, John Foster Dulles, who said, “The ability to get to the verge without getting into the war is the necessary art.” President Truman intervened in the Korean War, but specifically prohibited the use of nuclear bombs. In 1961, American and Soviet tanks stared each other down over Checkpoint Charlie. A false move by a private manning a turret could have led to nuclear holocaust. And the most dangerous – ballistic missiles in Cuba were unacceptable to U.S. security interests. Kennedy had to find some way to eliminate this threat.

Brinksmanship, Explained

Brinksmanship was dangerous, but it did serve a purpose: communication. Defending your interests in the most far-flung parts of the world left little doubt that you would defend your own homeland to the hilt. If you are crazy enough to fly in every morsel of food and pound of coal to supply the entire city of Berlin for fifteen months, clearly you are not to be trifled with.(17) On the other hand, actual attacks directly on the personnel or materiel of the other Superpower were likely to lead to escalation. So, the Soviets shot down not a single one of the 200,000 highly vulnerable supply flights during the Berlin Airlift. Similarly, the American quarantine of Cuba went to great length to avoid firing a deadly shot.

Of course, any good brinksmanship player would play the game far from home. Both Superpowers had plenty of proxies around the world to use in these battles. Like most games of chess, it usually didn’t work out well for the pawns. Upwards of 2 million Vietnamese lost their lives during twenty years of American involvement in southeast Asia. Perhaps just as many Afghans were killed during nine years of Soviet incursion there; we don’t really know. Fully one third of the Afghan population became refugees, and the Taliban came to rule after the Soviets pulled out of the Bear Trap.(18)

Will this game work with in the modern nuclear paradigm?

Mutually-assured destruction worked when it was two superpowers facing off. Worked well enough, at least.(19) Never before in human history have nations possessing the best and the biggest weapons refrained from using them for such a time.

As we have seen, MAD requires any number of prerequisites to be effective. Each of the Players must have the ability to destroy their opponent. Each Player must know that his opponent is able – and willing – to produce a devastating retaliation. Having clear and consistent lines of communication is important; you need to convince the other guy that you are not playing