The Palestine Dilemma: Game Theory and the Middle East, Part II
[Part I is the post immediately preceding this one.]
The issue gets still more interesting when you consider the main third party players, the US and the Arab world. Both the US and the Arabs have some vested interest in the Palestinian conflict. The US generally supports Israel and would like to avoid harming them. They also want, but less strongly, to avoid harming the Palestinians. The US would also like to see a negotiated solution, to keep the situation stable and keep it from causing future trouble. Finally, the most direct US interest is in the effect that the conflict has on our relations with the Arab world. Right now, while trying to build support for an attack on Iraq, the US would like to keep the larger Arab world friendly to us or at least neutral. So, if the rows represent the Israeli actions and the columns represent the Palestinian actions, the US payoff matrix looks something like:
Having them both fight is the worst solution—both sides are hurt and the Arab world is mad. Having just the Israelis fight is better, but the Arab world is still mad, which in the short term is bad for the US. Having the Israelis negotiate and the Palestinians fight is also bad, since the Israelis are getting screwed, but at least in that case the Arabs would be happy. Finally, the best possible solution for the US is for both sides to negotiate, since no-one gets hurt, the Arabs are quiet, and it could lead to a lasting peace.
Now, it’s debatable which of the two off-diagonal terms should actually be better for the US—which side they’d prefer to negotiate while the other keeps fighting. But either way, the key feature of the matrix is that, whatever the Palestinians do, the US is better off (in the short term) if the Israelis negotiate. This, then, explains why the US is pressuring Israel to negotiate. Because that is in the US interest, even if it isn’t in theirs.
The last interested party is the wider Arab world. Their interest in the conflict is mainly that they hate Israel and want to cause damage to her. And if you were a trusting soul, you could even argue that they care for the welfare of the Palestinians. I’m not sure the governments really do, but at this point because they have used the situation in their proaganda for so long, the populace probably does care somewhat for the Palestinian welfare. So we can estimate their payoff matrix as equal to the negative of the Israeli payoff matrix (what’s bad for Israel is preferred by the Arabs) plus half of the Palestinian payoff matrix (they care half-heartedly for the Palestinians.) When you put that together, you get the following payoff matrix for the Arab states:
Again, you can argue about the fine details of the payoff values, but the important thing is their relative magnitudes. And looking at this payoff matrix, two things stand out. The first, and most important, is that no matter what the Israelis do, it’s in the interests of the Arab states for the Palestinians to keep fighting. This is why Saudi Arabia and Iran provide aid and arms to Arafat, and why they fund and encourage the suicide bombers. Second, no matter what the Palestinians do, the Arabs would prefer for the Israelis to negotiate. Hence the second thrust of Arab diplomatic efforts—trying to get the US to force Israel to the negotiating table.
Even with this simple treatment, the broad outlines of the problem are clear, and the dilemma that Israel faces comes through. The Arab states are doing everything in their power to exacerbate the conflict and to keep the Palestinians fighting—to keep the suicide bombings coming. Meanwhile, their pressure on the US in turn makes the US pressure Israel to take the destructive path of negotiation, something that will never work as long as the Palestinians continue to fight. And with the Arab support and their own belief that it can be a winning strategy, they show no signs of stopping the terrorism.
From this discussion it’s also clear that a big, big part of the problem is the attitude of the wider Arab world. And in my opinion, a key to breaking the deadlock of violence and moving towards a solution is to change the Arabs' attitude. Either by actually overthrowing their governments militarily or by the threat of doing so, the US needs to change their payoff matrix so that support of Palestinian terrorism is no longer in their interest. Just as the US war on terrorism consists both of direct military confrontation and of broad action to try and cut off terrorist funding, so a solution to Palestinian terrorism must deal both with the Palestinians themselves and with their sources of funding—Iran, Iraq, Syria, and Saudi Arabia.
For Part III, my plan is to add a little more nuance to the strategies available, splitting up the negotiation option into negotiating in good faith (really working towards a solution) and negotiating in bad faith (without any intention of making any concessions, just hoping to gain an advantage.) My thought is that this might shed some light on the value of the “peace process” in and of itself, and why the US (and Europe) keep pushing this despite its failures.
The Palestine Dilemma: Game Theory and the Middle East, Part I
As a general rule, I’m skeptical of articles claiming to use game theory to assist in analysis of policy issues. Mainly because those claims are rarely backed up by substance. Most often, game theory is invoked in the opening paragraph to try and lend an air of scientific rigor to the article, but in the body of analysis, there’s not a scrap of game theory to be found. Robert Wright is the main culprit, of course, having dismounted from the evolutionary psychology hobby horse and mounted up with game theory. Hardly a column of his goes by where he doesn’t mention game theory or non-zero sum games, but I have yet to see any actual game theory in any of his articles. (Which doesn’t necessarily make them bad, just lacking in actual math.)
Nevertheless, I thought I would try to apply a little game theory to the Israeli-Palestinian conflict. I don’t claim that any blinding new insights will result, something that has never been written or thought about before. But I think there is some value since it provides a different framework to think about the conflict, the options, and the motives of the various players. Payoff matrices also are a very clean and terse way to present a lot of data, in a more or less (in this case less) quantitative way, which is how I like to think of things.
For this first take on the problem, I’m reducing it to its simplest form, to see if any conclusions can be drawn. Then, in future installments, I will add more wrinkles (assuming I find anything more of interest to say.) So, for a first, attempt, I’ll assume that both sides have only two strategy choices—to fight or to negotiate. Further, for simplicity I’ll assume that the payoffs are symmetric—that the Israeli payoff if they fight and the Palestinians negotiate is the same as the payoff for the Palestinians if they fight and the Israelis negotiate. Then, only one payoff matrix needs to be written. Looking at the short term results, this is how I see it:
If both sides choose to fight, both suffer some cost. However, this cost is less than that of trying to negotiate and making concessions while the other side continues to fight. Similarly, the best situation for either side is for they themselves to continue fighting while the opponent tries to negotiate. Finally, both sides choosing to negotiate results in a net gain to both sides. But since negotiations involve making compromises and concessions, you don’t get as much out of that as you do out of fighting if the other side doesn’t resist.
This situation is now similar to that of the famous prisoner’s dilemma. For each side, regardless of what the other side does, their payoff is better if they choose to fight. However, if both sides follow this “rational strategy,” the result is worse for both than if they had both cooperated. Further, the situation is really a repeating game, since negotiations don’t solve the problem instantaneously. So both sides have to keep playing the game over and over.
A famous series of experiments were done to analyze this situation and find out what the best strategy was. It turned out that the best approach was “tit-for-tat.” You start out trusting your opponent (negotiating) but then responded to what they did in kind. If they continued to negotiate, you would too. But if they started to fight, you’d respond by fighting. It seems to me that this is the strategy Israel has pursued. They have negotiated in good faith and have made and were willing to make concessions. However, when the Palestinians continued to launch terrorist attacks against them, they responded by using force themselves.
The Palestinians, on the other hand, started out negotiating, but it seems to me that they were not negotiating in good faith. Rather, they were trying to get some concessions and then betray the process, jumping into the “we fight, they negotiate” cell of the matrix, hoping to get the best of both worlds there. Israel then responded with force, which takes us to where we are now, stuck in the upper left corner. The problem is, for either side to unilaterally compromise at this point involves a cost with no gain to themselves. The Israelis certainly, and maybe the Palestinians, would prefer to be down in the lower right instead of the upper left, but there’s no way to get there from here. Neither side wants to blink, because that would give the opposition an advantage in the short term.
Further, as I mentioned, the game is really run repeatedly. And the Palestinians seem to think that if they continue to fight long enough, then the Israelis will just give in unilaterally, and switch to a negotiating strategy. In other words, the Palestinians think they can win, that staying in the upper left, paying the cost for long enough, will get them over into the upper right, where they can maximize their payoff. The Israelis may also believe this—that they can win a military victory, although this is less certain.
Coming soon, Part II: The US and Arab perspectives
In my previous post I discussed the difference between liquid fuel and solid fuel rockets; the type of fuel used is one way to divide missiles, although not the most interesting from an operational standpoint. There are two other big divisions, which describe how a missile flies rather than what is used to propel it. These are:
cruise missiles vs. ballistic missiles
guided missiles vs. unguided missiles
The second split is pretty self-explanatory—does the missile have an internal guidance system to adjust its course in-flight and allow it to hit close(r) to where you’re aiming it? The simplest missiles, like the old V-2’s, did not. You just pointed them in the general direction of where you wanted them to hit, and launched away. Older tactical missile systems, like the Russian “Stalin’s Organ” (Katyusha—now used by Hizbollah) during WWII, or the US MLRS systems, were also unguided. These types of missiles are just rocket-propelled artillery. They were designed for saturation fire, to get a lot of munitions in the general area of the target.
Other systems, and most modern missiles, do have internal guidance. This can take a number of forms. For ground attack missiles, the job is to get the missile to a particular aimpoint on the ground. GPS makes this relatively easy; if you can get accurate target coordinates, then you just use a GPS receiver in the missile to tell it where it is, and bring it to the target coordinates.
Before GPS, missile guidance relied on internal inertial navigation. Inertial systems measure the acceleration of the missile; if you know all the accelerations undergone by the missile, you can calculate how far it has traveled, and how fast it is currently traveling. Unlike GPS systems, which give an absolute position (a Lat-Long position), inertial systems give you a relative position—how far away you from where you started—which changes the problem somewhat, but that’s neither here nor there.
Surface to air missiles are also guided, but they are designed to home in to a moving target, rather than to fly to a fixed point on the ground. Surface to air missiles hence use a different sort of guidance, focused on the relative position of the target to the missile. This information is provided either by a seeker head on the missile itself, or by transmissions from a ground radar station.
The second split in types of missile is between cruise missiles and ballistic missiles. The Tomahawk is a cruise missile; SCUDs are ballistic; ICBMs, as the name implies, are also ballistic. What’s the difference? The difference is, cruise missiles are fly under power for the duration of their flight. The engine is running the entire time. Ballistic missiles, in contrast, use a short boost phase at the beginning of the flight to accelerate the missile, and then it “coasts” the rest of the way.
Throwing a baseball is like a ballistic missile—you give it impulse with your arm while it’s in your hand (the boost phase) and once you let it go, it flies the rest of the way with no more power. A “ballistic trajectory” is the path of an object under the earth's gravitational pull, but without any other accelerations; hence the name ballistic missile. (Gravity’s Rainbow, for the Pynchon fans in the audience.) An airplane landing is like a cruise missile, while the space shuttle landing is like a ballistic missile.
The advantage of cruise missiles is that they can do much more complicated things during flight. A ballistic missile is pretty much limited to a big, arcing flight along a straight-line to target trajectory. A cruise missile can fly close to the earth, can make turns and course adjustments during flight, and do other neat things. The disadvantage is that you need fancy electronics and guidance packages in order to take advantage of the cool things that cruise missiles can do, which is why countries just developing their missile technology go for ballistic missiles rather than cruise missiles.
Steven Den Beste recently posted a good discussion of the different problems in the manufacture of liquid versus solid fuel rockets. But after reading his discussion, you might come away wondering why anyone bothers with solid fuel rockets to begin with. If the fuel is both more dangerous and tougher to manufacture, then what’s the draw?
The answer is the discussion at the USS Clueless focused only on the manufacture of the missiles, rather than their operation and storage. First, while it’s trickier to manufacture the solid fuel for a rocket than liquid fuel, designing the rocket motor itself is much easier for a solid fuel missile. Because they have a simpler design, solid fuel missiles are somewhat more reliable (meaning they blow up or fall out of the air less often.) Also, once you have cast it, the solid fuel motor is much less trouble than a liquid fuel tank, since the liquid fuels used (and the oxidizer needed—more on that later) usually need to be stored at a very low temperature. The liquid fuels are also more volatile, in general, than the soldi fuels. So while it might be more dangerous to manufacture the solid fuel rockets, it's more dangerous to store the liquid fuel rockets.
To explain these difference in reliability and simplicity of design, it’s necessary to take a brief digression into rocket design. Rockets work by burning a fuel and blowing the exhaust out the back, which pushes the rocket itself forward. The key to this is creating a fuel mixture that will burn very quickly, to give you a lot of thrust, without actually exploding, which would be bad. To achieve this combustion, you need both a fuel source—something to burn—and an oxidizer to enable the combustion. Just as a candle needs oxygen to burn, the rocket fuel also needs oxygen or some other oxidizer to burn.
In a solid fuel, the oxidizer is mixed in with the fuel. You light it on fire, and it starts burning, continuing to burn until the fuel is all used up. This is one of the disadvantages of a solid fuel rocket—once it’s started burning, there’s no way to stop it until the fuel is used up. The engine basically consists of a solid tube of fuel with the outlet nozzle on the back, and a payload on the front. Very simple, with no moving parts in the engine. This is how the engines on model rockets work, if you've ever seen one of those.
A liquid fuel rocket, on the other hand, is pretty complex. The liquid fuel is stored in one tank, while the oxidizing agent is stored in a separate tank. You need piping and pumps and valves to mix these two materials together in the correct ratio in a combustion chamber to burn. As a result, there are a lot of moving parts and a lot of potential points of failure. On the plus side, the more complex liquid fuel rockets are more controllable, since you can adjust the fuel flow to the motor, and so control their thrust during flight.
So there are pluses and minuses for both types of fuel, and which type you choose to use will depend on the details of what you are trying to do and how you will be using the rocket.
About a week ago, Steven den Beste posted an interesting item over on the USS Clueless about the importance of maintaining the initiative, specifically not letting the situation in the West Bank distract the US from more pressing concerns in the Middle East—namely Iraq, Iran, and (maybe) Saudi Arabia. In this he was absolutely correct (as is most often the case), but it occurred to me that the reverse was also equally true.
That is, just as it is possible for the US to be distracted by the conflict between Israel and the PLO, it is also possible for the Arab states to become equally distracted by it. So much of their day to day diplomacy and foreign policy is directed towards Israel, that it seems very possible that the current unrest there could draw all of their attention, and serve as a smoke screen for the preparations in the area for US action. Israel is a lightning rod, drawing all of the Arab world’s attention, distracting them from ongoing US action.
According to reports, the US is slowly increasing its military presence in Kuwait, they are looking at alternative basing options to Saudi Arabia, and generally going on about the business of preparing for action against Iraq. Yet beyond some formal expressions of solidarity and disapproval, none of the Arab states seems to be focusing much on this front—they are expending their efforts to try and get the US to lean on Israel.
So in many ways, the Israeli offensive in the West Bank is a win-in situation. The Israelis get to attack and hopefully do serious damage to the Palestinian Authority’s terror network. The US gets to mouth pious platitudes and, maybe, look good by “reining in” Israel, once Israel is done doing what they wanted to do. And the US gets diplomatic cover for its maneuverings preparatory to an assault on Iraq.
A week or so ago, there was a report that one of the September 11th hijackers had received medical treatment for skin lesions possibly consistent with cutaneous anthrax. Unfortunately, the records for that case were inconclusive, so the report was suggestive at best. At the least, it reinforced suspicions that the anthrax attacks might have been connected in some way with the September 11 attacks--one coming so soon after the other seemed like a remarkable coincidence for them to be unrelated, as the FBI was publicly claiming.
Now, a new report in Newsweek says that an analysis of the anthrax from one of the letters shows it to be remarkably sophisticated--more advanced than anything the US has produced. If true, this would blow the FBI's "one germ-man" theory out of the water. It is simply impossible for an individual, no matter how gifted, to have produced such advanced specimens on his own, in a lab in the basement.
The linked article spins this result as a setback to the FBI investigation, which it is, in a way. On the other hand, if the report is true, the advanced milling and unique coating of the anthrax is actually a fantastic lead. It might prove that the FBI's current theory was wrong, but it is nonetheless a critical piece of evidence which should be enough to conclusively identify the source of the anthrax. It's as if an investigation found a set of fingerprints that didn't match the police's current suspect. On the one hand, it's a setback, but on the other hand, the fingerprints are a great piece of evidence.
Similarly, the job now (probably for the CIA rather than the FBI) is to identify what weapons labs in the world are producing this highly advanced, weaponized form of anthrax. If we can find a lab producing such finely milled anthrax, with this unique coating, then the source of the powder will be known. It could be from a weapons lab in the former Soviet Union--if so, hopefully we can ferret that out via diplomacy or espionage. Or it could come from Iraq, which could be proven once we get investigators in the country, either before, or more likely after, the Army.
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