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Game theory is the study of probabilities within situations where the results of one side depend on the actions of others.
if I'm playing tennis against someone who is mid-court, do I lob or play a drop shot? Is he going one way or the other? If he's coming to the net and I lob, my chances of victory are better, but if he knows that, maybe he's about to change course for the back court, in which case a dropshot will be the smart play. But if he knows that, maybe he'll be there waiting for me at the net regardless...
It's a complex area of study that is based in applied mathematics and fuels debate in every area from politics to sports to video games to courtroom battles to biological research, engineering... and war.
North Korea right now is talking about engaging in a "holy war" against the south, should their southern neighbours get too close with their current 'war games' training runs. The south, in turn, is threatening "merciless counterattack" should the North get uppity again and decided to lob mortars (or worse) at the border. The two sides are set to launch a battle that will claim many thousands of lives, cost much treasure, and set the region back a long time. Of course, they could also just put their guns down and shake hands, but whoever tries to do this first leaves themselves open to attack and defeat...
This, my friends, is the Prisoner's Dilemma.
For the uninitiated, this is how Wikipedia demonstrates the PD:
Two suspects are arrested by the police. The police have insufficient evidence for a conviction, and, having separated the prisoners, visit each of them to offer the same deal. If one testifies for the prosecution against the other (defects) and the other remains silent (cooperates), the defector goes free and the silent accomplice receives the full 10-year sentence. If both remain silent, both prisoners are sentenced to only six months in jail for a minor charge. If each betrays the other, each receives a five-year sentence. Each prisoner must choose to betray the other or to remain silent. Each one is assured that the other would not know about the betrayal before the end of the investigation. How should the prisoners act?
This dilemma is at the core of just about all competition. For example, if the Republicans and Democrats cooperate with each other, they could pass some seriously groundbreaking laws that would set their country on a strong course for world domination. But, should one party decide to leave the other hanging and instead filibuster all legislation, they get to say their opponents have failed, earning themselves a better shot at victory. Should both 'defect', they get in the trenches for long wars of PR, investigation, lies and betrayal that position them both in a way that everyone gets worked over, the country stalls, and neither side gets anything done.
Players of RISK know all about the Prisoner's Dilemma. Decide not to attack the biggest guy on the board and you'll do well, as long as he thinks the same way as you. but the moment he decides to throw down on you, if you're not expecting it, you're done for. But if you're both constantly guarding against that attack or, worse, constantly beating on each other, you limit your options. Cooperate and you destroy all, but eventually someone doesn't coooperate and everything goes to heck.
In the Koreas, mutual cooperation would be a great thing. Families would be reunited. The North would receive aid and maybe even investment. The South would save money that they currently spend preparing for an attack against them. The area would, in all likelihood, be seen as the next economic giant, were it to suddenly work together.
But in order for that to happen, one side needs to commit to it, even in the face of an attack by the other. Take the hit, demonstrate that you're not the enemy of your opponent and maybe they stop and start real peace talks. The downside of this is, in this case, taking the hit may mean taking a nuclear blast.
The US and Russia were engaged in the Prisoner's Dilemma for decades. In a tit-for-tat game of brinkmanship, they wasted billions loading up on nuclear weapons that, really, were unlikely to ever be needed, hoping that the other would flinch and leave themselves open to domination. But both sides also knew, should one side launch, retaliation was unlikely to bring about victory OR peace. You'd simply be blowing up their cities ten minutes after yours went down. You were likely dead anyway, so you could just as easily not launch and, at least, part of the world lives on.
Or you could just launch everything and blow the world up eight times over.
Eventually, both sides figured out that mutual cooperation was of more benefit that claiming the ashes of a nuclear wasteland and agreements were made to stand down. But it took a lot to get there.
If Israel or Palestine could follow the Prisoner's Dilemma, there might be a chance for peace in the Middle East, but neither side will commit to 'cooperation' in the face of 'defection', let alone engage in mutual cooperation. They're just too far gone. Both sides want the other side dead, or at least enough elements on each side do that cooperation is actively sabotaged at every turn.
Game theory thinking says, eventually, Israel and Palestine will figure out that there's no victory in eternal war, because they are, at heart, not insane. In the Korean situation, that's not the case, and it's why war between the two sides is inevitable.
North Korea will always run to the knife, betting that the knifeholder will throw it down and run away before North Korea gets to him. South Korea knows that, and was okay with it as long as the North didn't have the nuke. But now it's a better than fair bet that they do, so the rules change. Since mutual cooperation can't happen, the advantage goes to the side that attacks first.
North Korea, in all likelihood, has one or two nukes that may or may not work. The South, through their alliances with the western world and Japan, have enough attack capability to level the North many times over.
According to game theory, they should use it. But modern diplomacy says they can't unless provoked. North Korea knows this, and so keeps a lid on their provocation while they work on growing their nuclear arsenal.
If you take emotion out of the equation and rely on simple math, South Korea should level the North and do so now. They should probably have done so five years ago, when the chances of actual retaliation were minimal and the south had a genuine advantage. What prevents them from doing so is morality, ethics and the greater good. North Korea doesn't factor in those things when making national decisions.
The irony is, the south's dedication to doing the right thing will ultimately cost many more lives than if they did the 'wrong' thing and struck first when they had a clear strategic advantage.
Game theory says, when dealing with an opponent set on 'defection', your only victory can come from attacking first. Attacking second means, in reality, mutual defeat.
And that's why pacifists (like me) hate game theory... because it actually explains why war, on occasion, is the greater good