Category Archives: Game Theory

(Paper here.)

Earlier this month, I wrote about Iranian nuclear intransigence. In this post, I want to generalize the argument: war exhaustion sabotages long-term arms treaties.

This is part of my dissertation plan, so some background is in order. My main theoretical chapter shows that if declining states can’t threaten preventive war to stop rising states from proliferating, they can buy them off instead. The idea is that weapons are costly to develop. Rising states don’t have any reason to proliferate if they are already receiving most of the concessions they wish to obtain. Meanwhile, the declining state is happy to offer those concessions to deter the rising state from proliferating.

Let’s boil it down to the simplest version of the game possible. The United States has two options: bribe or not bribe. Iran sees the US’s move and decides whether to build a nuclear bomb. American preferences (from top to bottom) are as follows: not bribe/not build, bribe/not build, not bribe/build, bribe/build. Iranian preferences are as follows: bribe/not build, bribe/build, not bribe/build, not bribe/not build.

(I derive these utilities from a more general bargaining setup, so I suggest you look at the paper if you think these seem a little off. I personally wouldn’t blame you, since it seems strange that Iran prefers accepting bribes to taking bribes and proliferating anyway.)

Given that, we have the following game:

By backward induction, Iran builds if the US does not bribe but does not build if the US bribes. In turn, the US bribes to avoid having Iran build.

Great! Iran should not proliferate. But…yeah…that’s not happening at the moment. Why?

One problem is the reason why Iran prefers not building if the United States is bribing. The idea here is that bribes are permanent. By continuing to receive these bribes for the rest of time, Iran sees no need to proliferate since it is already raking in the concessions and nuclear weapons will only waste money.

But what if the United States had the power to renege on the concessions? In the future, the US will no longer be suffering from war exhaustion from Afghanistan and Iraq and will force Iran not to proliferate by threat of preventive war. At that point, the US can renege on the bribe without any sort of repercussions.

Again, boiling the argument down to the simplest game possible, we have this:

Backward induction gives us that the US will renege (why give when you don’t have to?). So Iran builds regardless of whether the US offers a bribe (it’s a ruse!). Proliferation results today because the United States can treat Iran as essentially nuclear incapable in the future. Iran has a window of opportunity and must take it while it can.

This is neat because a commitment problem sabotages negotiations. Recovering from war exhaustion makes the United States stronger in the sense that it will be more willing to fight as time progresses. Yet, this additional strength causes bargaining to fail, since Iran fears that the United States will cut off concessions at some point down the line. More power isn’t always better.

In addition to discussing Iran, the chapter also talks about the Soviet nuclear program circa 1948, which is fascinating. We often take Moscow’s decision to proliferate as a given. Of course the Soviet Union wanted nuclear weapons–there was a cold war going on! But this doesn’t explain why the United States didn’t just buy off the Soviet Union and avoid the mess of the Cold War. Certainly both sides would have been better off without the nuclear arms race.

Again, war exhaustion sabotaged the bargaining process. The United States was not about to invade Russia immediately after World War II ended. Thus, the Soviets had a window of opportunity to proliferate unimpeded and chose to jump through that window. The U.S. was helpless to stop the Soviet Union–we had zero (ZERO!) spies on the ground at the end of WWII and thus had no clue where to begin even if we wanted to prevent. The same causal mechanism led to intransigence in two cases separated by about 60 years.

If this argument sounds interesting to you, I suggest reading my chapter on it. (Apologies that some of the internal links will fail, since the attachment contains only one chapter of a larger project.) I give a much richer version of the model that removes the hokeyness. Feel free to let me know what you think.

Apparently “Iran threatens attack” is the top trending search on Yahoo right now. Here’s a news story of what is going on. Apparently some general in the Iranian air force (Amir Ali Hajizadeh) said that if Israel strikes Iran, Iran will retaliate by attacking American bases in the region.

Umm. Okay.

Iran will do no such thing. The American public does not have the will to engage Iran at the moment. If someone will launch a preventive strike on the Iranian nuclear program, it will be Israel, not the United States. (And, as Israeli officials are finally conceding, this is an unlikely outcome.) But do you know what would give the American public the will to fight? I don’t know, how about an attack on American bases? If Iran initiates on the United States, it undoubtedly ends badly for the Iranians. In turn, anyone who has spent two minutes learning backward induction (see video below) knows how preposterous Iran’s original threat is.

This news story reflects a curious and disturbing trend in American news media. Whenever some crazy person from another country says something inflammatory, it gets reported as though it is serious business, even if it is in no way the actual policy of the regime in charge. Then rhetoric explodes for no particular reason.

The only thing Americans should take away from this news story is that Amir Ali Hajizadeh is a complete idiot.

(Of course, we have some silly people in our country who say silly things, and I am sure that the Iranian media also reports them as though they are serious. This goes both ways.)

At the insistence of many of my friends, I started watching Avatar: The Last Airbender (the TV series, not the dreadful film). The show appears to take place on a post-apocalyptic Earth, where humans have been divided into four tribes (fire, water, earth, and air), which can “bend” their particular element as a means of weaponization.

The world is constantly at war. The show’s narration blames this on the disappearance of the disappearance of the Avatar, the traditional peacekeeper and only person capable of wielding all four elements.

However, the lack of the Avatar fails to explain the underlying incentive for war. Today’s pre-apocalyptic world does not have an avatar, and yet most countries most of the time are not at war with most other countries. Moreover, the Avatar theory does not address war’s inefficiency puzzle, i.e. how the costs of fighting imply the existence of negotiated settlements that are mutually preferable to war. Why not reach such an agreement and end the war that has completely devastated the world economy? The Avatar might be sufficient for peace but is by no means necessary.

In contrast, I propose that the underlying cause of war is the presence of rapid, exogenous power shifts. As described in the episode The Library, the fire tribe’s ability to bend fire disappears during a solar eclipse. Likewise, the water tribe’s ability to water bend disappears during a lunar eclipse. These rare events leave their respective tribes temporarily powerless. In turn, that tribe faces a commitment problem. For example, on the eve of a solar eclipse, the fire tribe would much enjoy reaching a peaceful settlement. In fact, they would be willing to promise virtually everything to achieve a resolution, since they will certainly be destroyed if a war is fought on the solar eclipse.

But such an agreement is inherently incredible. Suppose the other tribes accepted the fire tribe’s surrender. The solar eclipse passes uneventfully. Suddenly, the fire tribe has no incentive to abide by the terms of the peace treaty. After all, their power is fully restored, and they no longer face the threat of a solar eclipse. They will therefore demand an equitable share of the world’s bargaining pie.

Now consider the incentives the other tribes face. If they fail to destroy the fire tribe during the solar eclipse, the fire tribe will demand that equitable stake. But the other tribes could destroy the fire tribe during the eclipse and steal their share. That is a tempting proposition. Indeed, the other tribes likely cannot credibly commit to not taking advantage of the fire tribe’s temporary weakness.

Finally, think one further step back, once again from the perspective of the fire tribe. If the fire tribe does not successfully destroy the other tribes before the solar eclipse, they run the risk of being destroyed on that day. From that perspective, it is perfectly understandable why the fire tribe fights.

Thus, there are commitment problems abound in the world of Avatar. The fire tribe cannot credibly commit to remaining enfeebled after the solar eclipse. The other tribes cannot credibly commit to not attack the fire nation during the eclipse. War seems perfectly rational.

Interestingly, one way out of the problem is for the fire and water tribes to agree to protect one another during their eclipses. Given that, neither side has incentive to attack during the eclipse; if that tribe did join the other tribes in an attack, then it would be left without any protection during the next eclipse. (This resembles a trual–a dual with three people.) Yet, in the series, the fire and water tribes appear to be the most bitter enemies.

One wonders if the library contained a copy of Fearon 1995 or In the Shadow of Power. In any case, you can read more about preventive war in the third chapter of The Rationality of War or watch the below video: