The war against Iran: a game theoretical perspective

If Israel goes solo, expect the US to get dragged in anyway
For Iran, escalation might actually work

For Iran, escalation might actually work

With the world still slugging through the second act of the Great Recession, few scenarios cause more chills to run down the spines of Washington policymakers than a potential war with Iran. Although it is difficult to envision Iran emerging victorious from such a conflict, the outcome would be all but pyrrhic for the US: oil prices (potentially reaching $200 per barrel) would grind the economy to a halt, and the only hole bigger than the ones made by the USAF’s bunker-busting bombs, would be the budget hole caused by another hot war in the Middle East, one which in the worst case scenario would be bigger, longer and bloodier than those being waged in Iraq or Afghanistan. But perhaps what scares the pants off the Obama administration is the war’s total unpredictability: it only takes one surprise attack by Israel to launch a series of events which could lead into an unmitigated disaster. Many people have wondered whether such a scenario could be “contained”; that is, leave Israel and Iran slugging it out among themselves. Certainly that would limit the diplomatic fallout, and leave the US to worry on more important domestic matters during a crucial election year.

But as I will show in this post, such a scenario appears unrealistic. Once the first bomb falls, the US will be sucked in it, just like a limited tactical nuclear strike during the Cold War would have inevitably escalated into all out exchange. My analysis will be capped by a simple game theoretical model which will make the outcome clearer for those of you who are more numerically inclined.

How an Israel-Iran attack would look like

The prevailing scenario of a war with Iran involves an initial air strike by Israel in order to cripple Iran’s nuclear weapons program. Israel certainly has the means to do so, and it would likely mirror a similar strike against the Iraqi Osirak reactor back in 1981. Although over three decades have passed since then, the hardware would be almost identical: a package of IAF F-15 and F-16 aircraft would fly low over either Iraqi, Saudi or Turkish airspace in order to avoid radar detection, strike the suspected nuclear sites, and hastily fly back. The surprise factor would be crucial, Israel would hope that the main nuclear sites be crippled in the initial wave, with follow-up waves mopping up any unfinished business as well as striking at Iran’s command, control and communications (“C3”) networks to weaken their capability of responding.

The distances involved however, are significant and this represents the major logistical challenge for the IAF: although supersonic fighter jets flying low could escape detection over hostile territory, the large, slow and bulky tankers (which the IAF would need to make the weapons-laden fighters reach Iran and fly back to Israel) wouldn’t. This could force an even longer oversea route around the Arabian peninsula. Although difficult, this is not impossible: the IAF has previously struck terrorist targets as far away as Tunisia, and the daring raid on Entebbe back in 1961 shows that if any military makes the seemingly impossible possible, it’s Israel’s. The second major problem facing Israel is that, unlike Osirak, Iran’s nuclear facilities are well hidden in deep, concrete shelters which would be all but impenetrable by normal missiles or bombs. Enter the GBU-28, better known as the bunker-buster, a laser-guided bomb which can supposedly penetrate more than 6m of reinforced concrete. As far as we know, at least 55 of these were known to have been sold to Israel in 2009 and you can pretty much guess what they were intended for. Even then, there is no guarantee that Iran’s facilities, buried deep in the ground, would be destroyed.

Against this strike, Iran has pitifully little. On paper, its Soviet-style air-defence network might appear formidable but experience over Iraq and Yugoslavia has showed how these have melted away in the face of a determined Western air onslaught. Iran’s air force is large but increasingly obsolescent. It’s most modern aircraft are a handful of (recently upgraded) MiG-29s, but most of its other warplanes are a legacy of 1970s US and French arms sales to the Shah and it is unlikely that they could reliably sustain a major air campaign. Perhaps the most illustrative of Iran’s weakness in air power is its fleet of F-14 Tomcats, the only other country which ever purchased the fighter that Tom Cruise made famous in Top Gun (and with the Tomcats now retired from US Navy service, Iran is the only user). It is estimated that Iran still retains 44 Tomcats of which perhaps only two dozen are operational and would probably not put up much of a fight against the nearly 400 modern fighters in the Israeli arsenal (entirely F-15s and F-16s), flown by some of the most well-trained and experienced pilots of any air force in the world.

Assuming the war remains a purely Israeli-Iranian affair, it’s easy to see how meagre Iran’s powers of retaliation would be in comparison. Air strikes on Israel are out of the question: the IAF would knock out anything in the sky well before it even approached its territory (plus, the Iranian air force is defensive in nature, and does not have the capabilities for deep strike). The only option left would be to use ballistic missile attacks, similar to the Scuds launched by Iraq during the first Gulf War. These would not be terribly accurate and Israel has some anti-ballistic missile capability of its own (such as Patriot missile batteries), but you only need a few to fall on densely populated areas of Tel Aviv or Jerusalem to get dozens, and possibly hundreds of civilians killed. This, in turn, would probably make Israel’s follow-up response even more violent. Having attacked the suspected weapons sites in those crucial first waves, the IAF would follow up with further precision strikes on key Iranian political, military and C3 targets, doing as much damage as it can before the inevitable arises: those terribly expensive bombs and missiles run out.

This is one of the most embarrassingly common features of high-intensity modern war and it is particularly acute for second-tier military powers such as Israel which largely depend on the US for its logistical support. The French and British, for example, had nearly run out of weapons after just a few weeks of combat in Libya despite using only a fraction of their air power in what was essentially a low-intensity conflict. A high-intensity war would make the logistical crisis even worse which means that unless the US restocks Israel with an endless supply of weaponry, one can easily envision the war gradually winding down after a few weeks at which time a negotiated cease fire could be found. At the expense of low civilian casualties, Israel would have set back Iran’s weapons program at least for a year or more and caused moderate-to-significant physical damage to its military and civilian infrastructure. Despite its formidable domestic propaganda machine, it’s hard to see Iran claiming victory in this scenario, which would put huge political pressure on the government in the face of a mounting pro-democracy opposition.

…which is why Iran needs to strike at the US

A vulnerable giant

A vulnerable giant

Iran cannot damage Israel enough to claim victory, but it can – ironically – do much more damage against an even mightier opponent: the US. There are two fundamental benefits for Iran in drawing the US into a conflict: 1) the economic fallout that a rise in oil prices would have on the US and Europe, added to the extra military expense that would cripple the US budget and 2) the political benefits to the Iranian regime which can claim that it went up against not just one, but its two hated enemies. Of course, number two is only a viable benefit if the regime is not threatened by extinction, as was the case of Saddam’s Iraq in 2003. But to eliminate the Iranian regime, you’d have to topple it by force and this would invariably necessitate an invasion.

Would the Obama administration invade Iran? One can easily imagine the US bombing the country back into the stone age but putting US troops on the ground facing a long, and protracted ground war followed by an occupation is another thing entirely. Unlike Iraq, Iran is a larger, more mountainous country. Its 79 million people is well over twice that of Iraq (30 million). The open desert of the Mesopotamian plain which runs across Iraq makes it perfect terrain for mechanized warfare but any quick look at a topographical map of Iran would give any tank commander nightmares. The last thing an American politician wants is a long, hard Afghanistan-style infantry slog. Invasion and regime change are therefore out of the question.

So now we have a variation of the initial scenario, in which Iran responds to an Israeli aggression by attacking US naval forces or shipping in general along the Persian Gulf, particularly through the Straits of Hormuz (the choke point that separates the Persian Gulf with the Indian Ocean and is less than 40 km wide). In an election year, the US would have no choice but to respond, let the Obama administration give any hint of weakness. Such a response would be quick and vigorous, by clearing the seas of Iran’s minuscule navy, and bombing the daylights out of any naval and military installation along the coast. Iran’s “closing” of the Straits would therefore be a very short and temporary affair, but markets have already begun considering the implications of such a scenario and an oil price of $200 per barrel (and perhaps $150 or more while the war drags on) is a real possibility. Of course, having now been drawn in, the US is unlikely to just limit itself to local attacks, it might as well finish what Israel started by attempting to destroy whatever remains of Iran’s suspected weapons sites, and by attacking Iran’s political, military and C3 infrastructure on a scale well beyond what Israel could have managed with its air power alone.

But although air power has brought many a foe to the negotiation table, but it has yet to topple a regime alone. For this you need either troops on the ground, or a rebellious military force already in the country ready to do the dirty work for you (like the Northern Alliance did in Afghanistan, or the Libyan rebels overthrowing Gaddafi’s loyalists). So it is conceivable to imagine that even after a brutal air campaign, the Iranian regime would survive, as both sides eventually realize that a negotiated end to the conflict is in each other’s interests. For the US, it would mean that a financially costlier escalation of the conflict would be avoided, while for Iran, the regime could at least claim “victory” (however lopsided in the military sense) in order to quell its rising domestic opponents and retain its legitimacy for the better part of the decade. And although the Iranian nuclear program would inevitably have been set back, this end result (essentially a victory by virtue of not losing) still gives the regime the option of pursuing it again in the near future.

A game theoretical model

Game theory was used extensively by the superpowers during the Cold War to model the potential responses of its adversaries (perhaps the best and most comically frightening example is Dr. Strangelove’s explanation of why a nuclear doomsday machine cannot be turned off in Stanley Kubrick’s classic film of the same name). A simple sequential game can show why the equilibrium solution is in fact, for Iran to drag the US into the conflict. The game has two branches, with the first player (Iran) choosing whether to attack the US or not, following an initial Israeli strike. The next branch shows the second player (the US) choosing whether respond by bombing, by invasion or to remain uninvolved. The payoffs for each move will be quantified from -2 (worst outcome) to +2 (best outcome) and will involve a political and financial cost dimension for both players, which will be added up. So, for example, an outcome which implies a modest political gain (+1) and a major financial cost (-2) will have a payoff of -1. The financial cost for Iran will be represented by the physical damage caused by air bombardment, while for the US it will be the fiscal burden of war. There are six different outcomes which are described as follows:

  • Iran doesn’t attack, US doesn’t attack (N, N’)
    Iran suffers a -1 political cost by “losing to Israel”, and a -1 financial cost from Israeli bombing. Iran payoff: -2. US gets no gain or loss from keeping the war an Israel-Iran affair. US payoff: 0.

  • Iran doesn’t attack, US bombs (N, A-B’)
    Iran gets a +2 political gain for receiving an unprovoked US attack, but a -2 financial cost from more intense US bombing. Iran payoff: 0. US suffers a -1 political cost from going to war unprovoked, and a -1 financial cost from the bombing campaign. US payoff: -2.

  • Iran doesn’t attack, US invades (N, A-I’)
    Iran gets a -2 political loss since the regime would be ousted, and a -2 financial cost from the US invasion. Iran payoff: -4. US suffers a -2 political cost from the unpopularity of another ground war/occupation which was unprovoked, and a -2 financial cost from the massive expenses incurred. US payoff: -4.

  • Iran attacks, US doesn’t attack (A, N’)
    Iran gets a +2 political gain for having the US not respond to its aggression, offsetting any humiliation from “losing to Israel” and the -1 financial cost of Israeli bombing. Iran payoff: +1. The US would suffer a -2 political cost for not standing up to an Iranian attack, and a -1 financial cost from a surge in oil prices caused by the unwillingness to defend the Straits. US payoff: -3.

  • Iran attacks, US bombs (A, A-B’)
    Iran gets a +1 political gain for going to war against its US enemy, but a -2 financial cost from more intense US bombing. Iran payoff: -1. The US would get a +1 political gain for responding to aggression but a -1 financial cost from the bombing campaign. US payoff: 0.

  • Iran attacks, US invades (A, A-I’)
    Iran gets a -2 political loss since the regime would be ousted, and a -2 financial cost from the US invasion. Iran payoff: -4. US suffers a -1 political cost from the unpopularity of another ground war/occupation despite having been provoked, and a -2 financial cost from the massive expenses incurred. US payoff: -3.

Playing the game.

Sequential games are played backwards, that is, the lower branches play first and from there you move up. The best payoffs for the US player would be to not attack Iran if Iran doesn’t attack first (0 vs. -2 or -4), and to bomb Iran if Iran indeed attacks (0 vs -3 or -3). Eliminating all the other scenarios, the best payoff for Iran under these two remaining ones is to attack the US (-1 vs -2). In mathematical terms, this is known as the subgame perfect equilibrium. So, under this simple game theoretical model, it’s impossible to imagine the US not ultimately getting dragged into a war against Iran since Iran has all the incentives to lure it in. An expanded-form representation of this model is shown below:



I am hardly suggesting that this is the way a potential war with Iran would play out but clearly it shows that assuming all players are rational, there is a big incentive for Iran to take the risk and drag the US into the conflict. First and foremost, short of invasion, the regime can expect to survive even a sustained US bombing campaign – no regime has yet been toppled by air power alone. And although it would have seen its nuclear program set back various years, and have suffered enormous physical destruction from the bombing, its political legitimacy from having taken on both the US and Israel would give it a huge boost in the eyes of certain segments of the Arab world. The US would not gain much from this, but would have little choice but to respond particularly given the fact that it is an election year, and a government which appears spineless in the face of military aggression (particularly from Islamic fundamentalists) can pretty much start counting the days before it will get kicked out of the White House.

Now just cross your fingers Kim Jong-un doesn’t have any crazy plans of his own…

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