The Rational Statesmen: Donald Trump and Kim Jong Un

By: Tsahi Halyo

Though tensions are high between the United States and North Korea, through an analysis using game theory, the potential for a nuclear fallout may not nearly be as high as made out to be.

It is a commonly held assumption by those in the media that the recent war of words between President Trump and Kim Jong Un represents a dangerous turn away from diplomacy that vastly increases the chances of nuclear war. However, a game theory analysis of the current situation can show how the threat of nuclear war is exaggerated and why North Korea’s acquisition of nuclear weapons may stabilize the situation in the Korean peninsula. A full analysis is beyond the purview of this article; this article will restrict itself to merely analyzing the reason behind North Korea’s nuclear programme, why nuclear weapons act to stabilize a situation and the introduction of anti-missile technology works to undermine it, and why fears of a nuclear war are overblown.

Quick Game Theory Introduction:

To illustrate key concepts in game theory that will make the rest of the piece clearer, let us begin with a famous problem in game theory known as The Prisoner’s Dilemma. Consider the following scenario: two men are arrested at the scene of a murder (punishable by life in prison); however, the district attorney lacks the evidence to convict them of murder and instead only has enough evidence to convict them of trespassing (punishable by 1 year in prison). In an attempt to get at least one murder conviction the DA offers each prisoner a plea deal: if he confesses and betrays the other prisoner then he’ll walk free. If both accept the plea deal then they’ll both be sentenced to 10 years in prison. The two prisoners can’t communicate. What should each prisoner do?

(Player 1, Player 2)

Accept Deal Refuse Deal

Accept Deal

(10, 10)

(0, Life)

Refuse Deal (Life, 0)

(1, 1)

The above table represents the game, with the vertical axis representing Player 1 and the horizontal representing Player 2. In the parentheses the results are written as:  (Player 1 sentence, Player 2 sentence).

To find the optimal strategy for each player let us consider a Nash Equilibrium, the situation in which any unilateral change of strategy (changing from refusing the deal to accepting it) will impact the player negatively. In this case there is only one equilibrium point at which both prisoners confess. If either player decides to unilaterally refuse the deal he’ll be sentenced to life in prison. This is the optimal strategy despite the fact that if both prisoners were to cooperate they would both have lighter sentences.

The Rationale Behind North Korea Acquiring Nuclear Weapons:

The rationale behind North Korea’s nuclear programme is simple. Only by creating a nuclear arsenal will Kim Jong Un be assured that the U.S. will not invade and depose him or launch any nuclear strike against him.

This behavior can be explained using a game called Nuclear War. In this game we will make a few assumptions. First, that if a nuclear strike is launched at any one of the players a retaliatory strike will be ordered launched back. Second, that both players are rational in that both will pick the optimal strategy. If both players choose to launch their nuke then both players are destroyed; if either player chooses to nuke his opponent, given the surety of the retaliatory strike, both players are destroyed; if both players choose to not nuke the other the status quo remains.

U.S.        \       North Korea

Nuke

Doesn’t Nuke

Nuke

Nuclear Annihilation

Nuclear Annihilation

Doesn’t Nuke

Nuclear Annihilation

Status Quo

Once again, to find the optimal strategy for both players let us consider the Nash Equilibrium. In this game, the Nash Equilibrium is in the case that neither player chooses to fire his missiles. As seen in the table above, a player’s deciding to preemptively fire missiles dooms both to nuclear annihilation. Since firing first causes one’s own destruction, it’s never advantageous to fire first. Consequently, the winning strategy for both players is to hold off and allow the favorable outcome of the status quo.

A nuclear armed North Korea is rightly denounced as a danger to the West. Their government may sell nuclear material to hostile actors (e.g: terrorists) and their successful acquisition of atomic bombs in the face sanctions may embolden other rogue powers to develop nuclear weaponry as well. Nevertheless, the threat of nuclear war is blown out of proportion in the public discourse. As shown above, both rational players will choose to maintain the status quo.

Why ICBMs are better for peace than anti-missile technology:

Given the development of the THAAD and Patriot anti-missile systems it is natural to ask whether these systems increase the chances of peace or whether both sides increasing their nuclear stockpiles would prove better. Common sense would dictate that defensive weaponry should help the cause of peace while the construction of ICBMs should cause the opposite; however, game theory can show that the reverse is actually true. Much like how a knight’s armour gives him an advantage over an armed peasant in allowing him to attack the peasant with impunity (the armour protects the knight from the peasant’s sword); defensive weaponry allows the nation possessing it to attack countries that lack it without any fear of consequences. By taking the danger out of war, defensive weaponry makes war a much more palatable, and in effect, probable option.

Let us now recreate the Nuclear War game shown above with the additional caveat that THAAD is capable of intercepting all North Korean missiles, meaning that the U.S. has a successful nuclear defensive shield. The game would now appear as so:

U.S.        \       North Korea

Nuke

Doesn’t Nuke

Nuke

North Korea Annihilated

North Korea Annihilated

Doesn’t Nuke

North Korea Annihilated

Status Quo

Where in the original game both parties would be annihilated in the case either party launched their missiles, in the modified game only North Korea would be destroyed. In this game there are two Nash equilibria, both being the case that U.S. chooses to nuke North Korea. The optimal strategy would then be to destabilize the peninsula and launch a first strike. If the U.S. were to only build additional ICBMs, the original balance of power created by the original game would remain unchanged. It is then clear that developing anti-missile technology is more destabilizing than increasing one’s nuclear stockpiles.

Conclusions:

The threat of nuclear war is much exaggerated despite the recent spike in North Korean-American tensions. Using Game Theory, it is possible to show that given that the leaders of the U.S. and North Korea are rational, both nations will inevitably choose to de-escalate rather than cause a devastating nuclear war. In addition, it is possible to demonstrate that an arms race is safer than the development of anti-missile technology. If you’ve been staying up at night because the North Korean threat you should get some rest.

Sources:

  1. Nuclear Weapons and Proliferation: A Cheat Sheet. (n.d.). Retrieved October 15, 2017, from https://web.stanford.edu/~imalone/NuclearWeaponCheatSheet.pdf
  2. Manea, M. (2016). Game Theory. Retrieved October 15, 2017, from https://ocw.mit.edu/courses/economics/14-126-game-theory-spring-2016/lecture-notes/MIT14_126S16_gametheory.pdf
  3. Game Theory and Nuclear Weapons. (n.d.). Retrieved October 14, 2017, from http://www.umsl.edu/~naumannj/Geography%20PowerPoint%20Slides/russia%20-%20former%20USSR/Game%2520Theory%2520and%2520Nuclear%2520Warfare%2520condensed.pdf