After an exhausting decade-long standoff over the Iranian nuclear program, Iran's moderate new President Hassan Rouhani seems like a breath of fresh air. "Iran poses absolutely no threat to the world or the regions," Rouhani said in his recent speech to the United Nations in which he declared that his country is now prepared to engage in renewed negotiations over the nuclear issue. [1] Many observers have found President Rouhani's conciliatory tone to be a welcome change from the hardline stance of his Holocaust-denying predecessor Mahmoud Ahmadinejad.
But Israeli Prime Minister Benjamin Netanyahu quickly warned the international community not to fall for the new Iranian President's charm offensive. In his rebuttal to Rouhani's speech at the UN, Netanyahu accused Rouhani of disingenuously using the prospect of more negotiations to buy time for Iran to build a nuclear weapon. In the opinion of the Israeli Prime Minister, Rouhani is even more dangerous than the previous Iranian President, because Ahmadinejad was at least honest about the fact that he was your enemy: "Ahmadinejad was a wolf in wolf's clothing. Rouhani is a wolf in sheep's clothing." [2]
Should the U.S. trust the new Iranian President? Or are the Israelis right that Rouhani is pulling the wool over our eyes? America had better figure it out quickly because very soon we'll have to decide whether to continue negotiating with Iran, or launch a military strike before they have a chance to build a nuclear bomb.
Today we'll construct a simple game theory model between two players: the U.S. and Iran. The U.S. must choose whether to negotiate with Iran or launch a military strike to take out their nuclear facilities. If the U.S. opts to negotiate, then Iran will have to decide whether or not to give up its nuclear program.
The tricky part of this game is that the U.S. doesn't know whether or not to trust Iran's new President. We'll go ahead and adopt Netanyahu's metaphor, and say that President Rouhani is either a "sheep" or a "wolf." If Rouhani genuinely wants to negotiate in good faith to find a way to end Iran's nuclear weapons program, then we'll call him a "sheep." But if Iran's new openness to negotiations are just a cynical ploy to distract the West while they get closer to the bomb, then Rouhani is a "wolf" ...who just happens to have one helluva convincing sheep costume. If Iran's President is secretly a wolf, then their government's number one goal is to get a nuclear weapon. If he's a sheep, then Iran would prefer to give up their nuclear program in exchange for the international community lifting trade sanctions, which have crippled the Iranian economy.
Obviously Rouhani and the Iranian government know the whole time whether he's actually a wolf or a sheep. But the U.S. has no way to know with absolute certainty what Iran's real intentions are. Therefore, this type of game theory model is referred to as a game of asymmetric information.
If Rouhani is a sheep, then it's definitely in America's best interests to negotiate with Iran in order to disarm them peacefully rather than start a war. However, US and Israeli officials believe that Iran is somewhere between a few months to a year away from developing a nuclear weapon. [3] So if the U.S. decides to engage in a new round of negotiations with Iran, but Rouhani turns out to be a wolf in sheep's clothing, then there's a big risk that Iran will be able to use these negotiations to stall for time until after they've finished building a nuclear weapon.
Outline of the Game
In the game outline below, I've assigned both sides theoretical "payoffs" to represent how much they benefit from each possible outcome (the higher the number the better.) I will argue that these payoffs are *ranked* according to the U.S. and Iran's real world preferences. The precise *magnitudes* of these payoffs, however, were made up simply for the sake of concreteness.
Note for Game Theory Nerds: The traditional way to model this game would be to introduce a third player called "Nature" that determines whether Iran is a wolf or a sheep. But that would make things more confusing, especially as we make this game more complex in the next post. The important thing to remember is simply that Iran knows whether it's a wolf or a sheep before the game begins; its only the U.S. that isn't sure of Iran's true intentions.
First, the United States must decide whether to launch military strikes on Iran or to negotiate with them.
We will assume that if the U.S. went with the military option, they would successfully take out all of Iran's nuclear facilities. America has recently upgraded their "bunker buster" bombs that were specifically constructed and tested to evade Iranian air defenses and destroy uranium enrichment facilities, even those buried deep underground. [4]
President Obama has stated time and time again that he will not tolerate a nuclear Iran and is willing to take military action if he believes it's the only way to stop them from getting the bomb. [5] Therefore, we'll also assume that although the U.S. would like to avoid another war in the Middle East, they would rather conduct a military operation than allow Iran to develop a nuclear weapon. (Moreover, if the U.S. thought a military strike would fail or they weren't willing to go through with it, then there would be no point in gaming this situation out. So for the sake of argument, we'll just take President Obama at his word.) If the U.S. launches a military strike, then their payoff will be -2, because war is still costly even if you win, and Iran's payoff is -5.
Instead of going to war, the U.S. could take Rouhani up on his offer to sit down at the negotiating table. If the U.S. chooses this diplomatic route, then Iran must decide whether to secretly keep proliferating nukes or to disarm.
The problem is, the U.S. can't be sure beforehand if Rouhani is just saying he wants to negotiate in order to keep America from attacking or if Iran is actually willing to compromise. On the game tree, this uncertainty is represented by the two dotted lines: one for the possibility that the U.S. would be negotiating with a vicious wolf, and the other for the possibility that the U.S. would be negotiating with a peace-loving sheep. Let's say the U.S. believes there is a probability of p that Rouhani is a wolf. This implies there's a probability of 1 - p that Rouhani is a sheep.
If Rouhani is a wolf, and the United States is tricked into negotiating with him, then the diplomatic talks will give Iran enough time to develop a bomb. Our definition of a wolf was that their number one goal is to get a nuclear bomb, so if Rouhani's a wolf, then Iran gets a payoff of +5 if they choose to keep proliferating and a payoff of 0 if they disarm.
However, if Rouhani is telling the truth that he's a sheep, then he doesn't care about obtaining a nuclear weapon and would be willing to give it up in order to get the sanctions lifted. So if he's a sheep, Iran gets a payoff of 0 if they keep proliferating and a payoff of +5 if they disarm.
To Bomb or Not To Bomb?
The United States will launch military strikes if and only if their expected payoff from striking Iran is greater than their expected payoff from negotiating. We know from the game tree that if the U.S.'s payoff from striking will be -2. To find their expected payoff from negotiating, we take the U.S.'s payoff if Iran is a sheep and the U.S.'s payoff if Iran is a wolf, weighted by the probability that Iran is a wolf. This works out to be the U.S.'s payoff if Iran is a wolf (-3) times the probability that Iran is a wolf (p), plus the U.S.'s payoff if Iran is a sheep (+5) times the probability that Iran is a sheep (1 - p). So the U.S.'s expected payoff from negotiating is:
-3p + 5(1-p)
The U.S. will launch a strike if their payoff from striking (-2) is greater than this expected payoff from negotiating. So the U.S. will strike if:
-2 > -3p + 5(1-p)
If you solve for p, you will find that this implies the U.S. will strike if:
p > 7/8
Conclusion
The U.S. will negotiate as long as they believe there is at least a 1/8 chance that Rouhani is a sheep and is actually willing to negotiate in good faith. Since the U.S. has a huge incentive to work this whole thing out peacefully, even if they think it's more likely than not that Rouhani is lying, as long as there's a 1/8 chance that he's telling the truth, the U.S. will give negotiations a chance.
I wrote this post before the recent (short-term) nuclear deal with Iran. This provides a great opportunity to see whether policy-makers were able to navigate the tricky game I just outlined. In my next post, I'll explain why this new agreement President Obama just signed is brilliant -- this thing completely changes the game
Read Part Two >>
Read Part Two >>
