Beauty of Gray

Wednesday, May 08, 2002

Game Theory and the Middle East, Part III

Parts I and II can be found here and here. In those I took a very rough look at the options and payoffs of different Israeli and Palestinian strategies for them and for the third parties of the Arab world and the US. At the time, I promised a third installment adding one or more additional strategies for the combatants, to get a more nuanced analysis. I did that, but it didn’t add anything new or interesting to the original work, so I never bothered to write it up. Now, however, I’d like to change the framework a little and look at the conflict in a different way, as a war of attrition. I think this is an accurate description of the low level conflict that was ongoing in the region, with periodic terrorist attacks on Israel and retaliatory strikes by Israel.

In game theory, you can express a war of attrition in a relatively simple form. Imagine two competitors. Their only choice of strategy is a waiting time (T). While they are waiting, they are enduring a constant cost per unit time (w). Whichever one wins gets a payoff utility (U), while the loser suffers an additional cost of defeat (D).Whichever side is willing to wait longer wins the game. (For a good overview of the game theory treatment of wars of attrition see this link.)

If we use the label i for Israeli and p for Palestinian, the Israeli payoff matrix looks like:

Ti > Tp_____Ui – wi*Tp
Ti < Tp_____-Di – wi*Ti

The Palestinian matrix is similar, with the i and p labels switched.

Above, I said that the only choice of strategy was in how long each side was willing to wait. Actually, this isn’t true. Each side also can control their own level of attacks, which alters the enemy’s unit time cost, w (as well as their own, more weakly.) Further, their diplomatic efforts and demands control what the returns are for victory and defeat.

In the academic version of the game, it turns out that the best strategy for a player is to randomly select an amount of time to wait, with an exponential distribution. (That is, the probability of waiting a time t is proportional to exp-kt.) The prefactor in the exponential is proportional to (U+D), and is chosen so that the cost of the average duration of a contest, wt, is equal to half the reward of victory (U+D). That is, the bigger the difference in payoff between winning and losing, the longer a competator is willing to wait in order to achieve victory. Which makes sense.

Given this framework, it’s possible to see what the two sides’ strategies are. Each side would like to make the other side quit first—make them less willing to continue the war of attrition. There are three ways of doing this:

1. You can increase the cost of the war, w
2. You can make victory less rewarding for the opposition (decrease U)
3. You can make defeat less costly for the opposition (decrease D)

The Israelis have adopted a two tiered approach. On the one hand, they have tied their own retaliations to Palestinian attacks, which serves a twofold purpose. First, it is intended to deter attacks, and so keep their own cost (wI) down as low as possible. Second, in the event of an attack, it is intended to cause equal or greater harm to Palestine so that they gain no advantage via terrorist assaults. Second, Israel’s diplomacy has been geared towards a relative compromise solution. It doesn’t give the Palestinians everything they want, but it gives them a lot of it. In the game theory framework, this can be seen as an attempt to minimize the cost of defeat for the Palestinians. If the Palestinians would end the terrorism and negotiate in good faith (defeat for them), Israel is still willing to give them most of what they want.

The Palestinians clearly (assuming rational action on their part, which might not be a valid assumption—more on this later) adopted the first course of action, by increasing the severity and frequency of the suicide bombings. However, they have completely undercut this strategy by their stated goal of wiping Israel off the map. In doing so, they have made the cost of defeat much higher for Israel. By refusing to allow for the possibility of peaceful coexistence, they have made it clear that Israel granting them a state would not end the attacks, and set up a condition where the ultimate cost of defeat for Israel will be its destruction, a cost they cannot pay.

Furthermore, the Palestinian strategy of maximizing the number of attacks also illustrated a failure of strategic thinking, because it assumed that the past form of the game (terrorist attacks followed by limited Israeli attacks) was the only form it could take. They didn’t see that Israel had a second option open to it, which was the large scale military assault on the territories. And the Palestinians foolishly escalated their attacks to the point that, even in a short term analysis, it was less costly to the Israelis to mount a full scale assault than it was for them to maintain the status quo.

I don’t have the numbers in front of me, but during the weeks of the recent Israeli military action, I think they lost something on the order of 50 soldiers killed, with only one smaller terrorist attack occurring during this period. In contrast, in the weeks leading up to the assault, the Israelis were suffering a deadly terrorist attack almost every day. So, amazingly, the Israelis were actually suffering fewer casualties during a full scale assault on well armed guerillas operating in fortified and booby trapped urban terrain than they were by remaining on the defensive. And this is just looking at it from the short term and ignoring the hoped for disruption of the Palestinians ability to plan and execute attacks in the future.

So where does this all lead? I’m not sure, because for game theory to have any predictive power, the players have to behave in a rational manner. And there’s pretty strong evidence that the Palestinians are no longer behaving rationally. Their goal is no longer to maximize their own utility, but instead to inflict maximum damage on the Jews, regardless of the cost. What started out as a possibly rational, if evil, strategy of terrorist attacks, has devolved. The ends that were being pursued (a Palestinian state) have been lost, and the means to achieve that end have become elevated into ends in themselves. The terrorism now serves no outside purpose—it has become its own justification.

Addendum: The above analysis becomes more complicated when you factor in the idea of information transfer and signaling of intentions--actions have value not just in their direct payoff, but also in their ability to influece the other player by showing them your intentions, in this case your willingness to pay a high price for victory. But that's not worth getting into right now.

Link posted by Doug Turnbull at 10:04 AM

The wisdom of defeat?

There have been a number of hopeful articles recently speculating that the recent Israeli incursions into the West Bank might teach the Palestinians the error of their way, and show them that terrorism doesn’t pay. Their economy is in shambles and Israel has just demonstrated its ability to exert its will over the occupied territories, so this line of thinking goes, and the Palestinians will, having thus tasted defeat, recognize the Intifadah as a failed attempt and will adopt new leaders and new strategies. The attack will, in essence, shock them out of their complacency and belief in their own ability, teaching them that they are defeated and need to alter their strategy. This line of argument then goes on to refer to Germany and Japan, both of which were fierce and implacable enemies during WWII, but which were taught a lesson by their crushing defeat and were able to radically reform their societies and join the civilized world within a decade after the end of the war. The South in the Civil War is another historical example of defeat affecting a fundamental change in a society.

I wish I could be this optimistic, but I think these analyses are guilty of wishful thinking, for a number of reasons. To begin with, I’m skeptical of the WWII comparisons. Both Germany and Japan suffered devastation on a scale far, far exceeding anything the Palestinians experienced. The major cities of both countries were essentially reduced to rubble. In Germany’s case, armies of hundreds of thousands of men fought throuhg the countryside and towns, leaving a trail of destruction. By comparison, the Palestinians have suffered nothing other than a minor inconvenience from the Israeli attacks. You may have seen the satellite picture of the small razed area in Jenin. By comparison, in WWII the entire city would have been burned to the ground.

A second failure of the WWII comparison is in the psychology of the eneimies. Both Germany and Japan preached doctrines of national and/or racial superiority. They believed they were superior to their opponents, and superiority which was proven by their military successes. The reverse, then, was also true. Their crushing and total defeats inescapably refuted their claims of superiority, and hence produced a great psychic shock to their populations and assisted in a break with their failed tyrannical policies. The Palestinians don’t have the same idea of individual superiority, and so a demonstration of Israel’s far greater power does not clash with their basic mindset. Indeed, many commentators have analyzed the Islamicist movement as precisely a reaction to feelings of inferiority to Israel and the West. Conspiracies are then invented to explain these shortcomings. It’s hard to see how one more in a long line of military defeats will create a similar shock of cognitive dissonance to that experienced by the Germans and Japanese. Such a defeat does not strike at the heart of their world view and justification the way it did for the Axis powers in WWII.

A second objection, and another criticism of the WWII parallels, is that the Palestinians have been brainwashed now to the point that for many the goal is not so much victory for the Palestinians or a self-governed state as it is the killing and ejection of the Jews from the Holy Land. I think the hopeful analysis of the Palestinians outlined above fails because it assumes their goals are the same as those of the author—peace and stability in the region and a prosperous, well governed Palestinian state. But for many, and particularly for the militant groups, those aren’t the goals at all. The goal is to kill the Jews, and as the most recent suicide attack shows, that objective remains, despite the Israeli incursion.

I hope I’m wrong, and I hope the Palestinians do wake up and realize their current path simply leads to death and destruction, but as of now I see no evidence that this is likely to happen any time soon.

Link posted by Doug Turnbull at 7:49 AM

Tuesday, May 07, 2002
The Social Construction of Poverty

Instapundit has gleefully pounced on this study that the Swedes are actually poorer, on average, than blacks in America, contrary to what pretty much everyone’s expectation would be. This is certainly telling evidence against the strong democratic socialism practiced in Sweden, as I assume Glenn meant it to be. (As well as a nice tweek to Europhiles.) Although, it must be pointed out, it could also be a hopeful sign for the US—that blacks are moving into the middle class in substantial enough numbers that their median income is now equal to that of the Swedish. There were two other points that occurred to me, however.

First, while strictly speaking poverty is a matter of not having enough money, just as important as purchasing power are other, less quantifiable quality of life issues. What makes many inner city blacks’ lives miserable is not just lack of money, it’s the inner city environment they live in. High crime, from robbery to drive by shootings, neglected public roads and services, terrible schools, etc. It’s these environmental factors that make inner city life today so bad, and they are something that a simple economic analysis will miss. I think this explains the view of the Swedish as comfortably middle class.

These factors are somewhat mysterious. Any city dweller is probably familiar with areas that are nice but only a few blocks away from bad areas. In DC the prime example is the Capitol Hill neighborhood, with million dollar mansions on one end and 6 or 8 blocks away, areas where it’s not safe to walk at night, with drug addicts shooting up in the alleyways. But it’s the same neighborhood—the same basic location, houses that are nearly identical from the outside; logically the neighborhood should be a single entity, but it most certainly is not.

Second, when reading history, it’s struck me to what an extent our definition of what being poor actually is, is conditioned by our environment, and how flexible of a concept poverty is. I wrote in a previous item how wealth is at least partially judged comparatively—it’s not just having some amount of money, it’s having more than most other people. Similarly, poverty is felt not so much at some absolute level of purchasing power as it is at a level that’s enough lower than most other people.

So as a result of our wealth, the US has defined poverty up, radically. Even very poor residents of the US lead lives of great luxury compared to most throughout history, or even in the present for that matter. Almost every facet of our lives is tremendously improved in ways that we have come to take for granted but which would have been unimaginable not too long ago.

In the late Middle Ages, even fairly wealthy squires had little furniture in their houses and probably not any chairs. They’d sleep on a mattress made of straw, the same straw which also covered their floors and which was replaced once every year. Heating was via fire and was smoky and inefficient, which limited winter habitation to the single room with a fireplace. There was no artificial light. Their service plates would be a precious heirloom that was guarded jealously and passed down from one generation to the next. (See this book for a wonderful glimpse into the everyday life of upper middle class England during the Wars of the Roses.)

It’s even more fundamental than that, though. During the roughly four hundred years from 1370 to 1790, Florence, a wealthy city and one of the most glorious leaders of the Italian Renaissance, experienced 111 famine years, compared to only 6 years of plentiful harvests. This doesn’t mean that people were dying in the streets every year, but in 1 out of every 4 years for much of modern history, food was scarce enough that merely getting enough to eat was a constant worry. Scarcity of food was a dominating factor, a looming feature of everyday life. Peasants up until the industrial revolution were living on diets that today would be seen as near starvation level. They almost never ate bread from wheat, much less white bread.

Fighting back to some semblance of a point, the “poverty” experienced by even the poorest citizens of the US is, relatively speaking, great plenty. Poor families now have televisions and video games. Many have cars. Poverty now is less a matter of lack of the basics of life (although I’m sure some are in this boat) than it is a lack of sufficient luxury. In this sense, poverty has become a matter of perception rather than reality, a perception that is at least partially punctured by this most recent study.

Together, both of these points (the misery from environmental causes and the relative well off nature of most who now are considered poor) also show how futile it is to try and end poverty with simple welfare—just by giving money to those in need.

Link posted by Doug Turnbull at 2:47 PM

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