Even More Thoughts on North Korea Through the Lens of Game Theory

Given that a military confrontation between the United States and North Korea has all the makings of the second most dangerous post-WWII American air and naval operation short of the Cuban Missile Crisis, I can’t resist further application of game theory to this evolving situation.

Skeptics of game theory might dismiss my analysis, and game theory generally, with the old saw that no plan survives contact with the enemy.

True.

To a degree.

But some plans are better than others.  The point of using game theory in warfare, or any other competitive endeavor, is to create an informative strategic map.  An informative map outlining the points where success and failure are most likely to occur; and even whether war should occur.  All these considerations and more are clearer when thought through the perspective of game theory.

I will walk you through these three game theory concepts and apply them to events on the Korean Peninsula.

Sequential Games – Any game where the move of one competitor is dependent on the move of another and everyone’s move is visible to all players.

Examples are most classic board games such as chess.

Simultaneous Games – Any game where the actions of both competitors are made without knowledge of what the other side’s actions are.

An example of this is a submarine sent on a search and destroy mission against another sub when neither sub has spotted the other.  As soon as at least one submarine detects its opponent this simultaneous game becomes at least partially sequential.

Real life military situations almost always combine elements of sequential and simultaneous games.

Rationality and Irrationality – The game theory terms of “rationality” and “irrationality” are often used wrongly by media pundits to mean “logical” and “illogical”.

What real mathematicians and statisticians mean by “rational” is not “logical”.

In game theory rational actions are actions that an actor in a game takes to achieve a preferred outcome, even if that outcome is objectively illogical.  Actions taken by irrational actors are actions that deliberately do not lead to their preferred outcome.

As far as game theory is concerned the actions of Jeffrey Dahmer – selecting targets, luring victims, hiding evidence of his activities – were rational despite being illogical because he valued cannibalizing other humans above all his other preferences.  Dahmer’s actions would have been irrational only if he preferred cannibalism above all else but did not take actions that led to his preference.

Now to apply all three concepts to North Korea.

Is Kim a rational actor to pursue nuclear weapons despite the fact he is arguably better off giving up his weapons in exchange for diplomatic normalization with the rest of the world?

Game theory says yes if he values nuclear weapons over economic prosperity.

If he valued prosperity over nukes he would have already given them up as Ghadaffi did (Btw, the destruction of Ghadaffi’s regime likely taught Kim not to give them up, but that is a different subject).

Kim’s seemingly crazy threats to counter attack and the occasional, limited, military provocation by him are in fact very rational because they serve to deter a preemptive attack against his nuclear facilities.  This deterrence buys him time until his nuclear weapons are capable of reaching US soil.  Once that capability is reached he will be in a much better position to either blackmail the United States or use them in war.

Because a North Korea armed with ICBMs is much more dangerous in American risk-reward calculations than a North Korean nuclear program with only regional capacities, America’s preference calculations are escalating to damaging or destroying his nuclear capacity before America comes within range of Kim’s missiles.

This conflict would have a sequential nature because each move by one side would influence the next move of the other.

As discussed previously, the conflict would open with America striking Kim’s nuclear sites in a combined air and naval strike.

From there, how the conflict would unfold would depend on how Kim’s preferences lead him to respond.

There are three main decisions for Kim to choose from, all of which would be met sequentially by equivalent American and allied responses:

  • Kim decides against serious retaliation – America does not attack again
  • Kim starts a conventional war by firing artillery at Seoul – America and South Korea fight a conventional war
  • Kim uses whatever remaining WMDs he has – America retaliates with nuclear weapons

In America’s view the optimal military result is that our strikes severely damage the North’s nuclear program and the North does not significantly retaliate.  But whether this favored result turns out to be the real life result depends on Kim.

And what Kim will do depends heavily on his rationality immediately following the strike.

After the air strike, a rational Kim’s first action would be to assess how much damage his nuclear program suffered and decide whether to retaliate.

It is because either a conventional or nuclear confrontation would be very costly to North Korea that a rational Kim may decide against retaliation.  Especially if his nuclear weapons, already prone to test failures, have been rendered inoperable by the opening American attack.

I’ve mapped out sequential events after the initial airstrike assuming Kim is rational.

But what if Kim is not rational at that moment?  Suppose he panics if bombs fall near him and he orders artillery strikes without knowing what state his nuclear arsenal is in?

Or, what if he is killed/incapacited early and the decision falls to a second in command with different preferences?

It may be that we would be better off if Kim is healthy and rational in the aftermath of our attack because he is more likely to choose America’s desired outcome (no post-strike retaliation) if he is able to rationally assess the unfavorable risk-reward calculations of retaliation.

Therefore, game theory suggests our preemptive airstrike should intentionally avoid hitting Kim in order to statistically maximize the odds of our preferred outcome happening.

Of course, it is possible we might kill him anyway by accident.  Kim and his commanders could be touring their nuclear facilities at the time without our knowledge.  This is part of what makes the nature of military action against North Korea partly simultaneous.

But if he is irrational due to fright, or if he is incapacitated and the decision falls to someone else, we have no way to guess how North Korea would react.

What lessons game theory’s concepts of rationality, sequentiality, and simultaneity have to teach.

Will game theory statisticians try to quantify the likelihood of each counter-move in each scenario?

Yes.

They will normally provide odds of such and such a result occurring.  This makes many suspicious – how do they know there is a 55% chance of the North retaliating?  Are the real chances 50%?  70%?  etc, etc…

But this is to miss game theory’s advantages.

What is most valuable to the decision maker is the broad perspective game theory gives and where the crucial steps in the game are.

From just the three concepts discussed in this article we learn:

The key moment will be if and how Kim decides to retaliate.

Therefore America must make the most of its first mover advantage because how strong the first move is will heavily influence the North’s move.

The extent to which North Korea’s nuclear program is damaged will greatly factor into whether Kim decides to counter with a full scale land assault against South Korea IF he is rational.

These lessons are useful because they map out, in their proper context, the most likely route the conflict would take.

They are also intuitive conclusions.

What is counter-intuitive is that it may be optimal for the United States to not target Kim himself in the opening because North Korea might not act rationally according to its own risk-reward calculations when they decide whether and how to retaliate.

It is game theory’s ability to come to surprisingly counter-intuitive recommendations about seemingly straight-forward military questions as well as its broad strategic overview that make it a field well worth studying.

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