Applying game theory to the Israeli-Palestinian war.

Applying game theory to the Israeli-Palestinian war.

Applying game theory to the Israeli-Palestinian war.

Science, evolution, and politics explained.
May 15 2002 4:52 PM

Both Sides Now

Nearly 300 million people live in America, and about 6 million people live in Israel proper. So when 15 Israelis were killed in a pool-hall bombing last week, that felt to Israelis roughly the way it would feel for 50 times that many American civilians—750—to die in a single bombing.


About 3 million people live in the occupied territories. So a few days before the pool-hall bombing, when Israeli soldiers mistakenly killed a Palestinian woman and two children, that felt to Palestinians roughly the way it would feel for 300 American civilians to die.

These conveniently round conversion factors—50 for Israel proper, 100 for the occupied territories—make it easy to see that both sides of this conflict have endured trauma well beyond the recent experience of Americans. Since the beginning of this Intifada, in September of 2000, about 350 Israelis have been killed—think 17,500 Americans, or six 9/11's. About 1,200 Palestinians have been killed—think 120,000 Americans, or two Vietnams. 

In theory, all of this could be cause for hope. People think of armed conflict as a zero-sum game—a game with a winner and a loser, a game in which the players' fates are inversely correlated. But the game theorist Thomas Schelling has long stressed that war typically has a non-zero-sum dynamic, and the Middle East is now illustrating his point. Continued fighting is massively lose-lose, so peace would be win-win.

Yet peace never comes. How does a game theorist account for this wanton irrationality? There's no shortage of possible explanations. And collectively they point toward the most plausible path to peace.


Explanation No. 1: The seeming irrationality of human nature. People are driven by their emotions—vengeance, pride, etc.—to do things that aren't necessarily in their interest. They thus fall into downward spirals of mutual retaliation. (Actually, impulses such as retribution were more consistently functional in the environment for which natural selection designed them. In a modern environment, they sometimes come in handy but often don't.)

Explanation No. 2: Diverging interests between people and their leaders. In war, even people on the "winning" side die—which is why Schelling says wars are at some level lose-lose. But the winning political leader doesn't die, so from the leaders' point of view, conflict may seem purely zero-sum; when the fighting is over, one leader will stand triumphant and the other will be disgraced. Both Yasser Arafat and Ariel Sharon seem to be looking at things that way, focused largely on annihilating the other guy.

Explanation No. 3:Ironic twist on Explanation No. 2. Actually, in the short run, Arafat and Sharon are playing a non-zero-sum game—and, oddly, it's been more win-win than lose-lose. The last few months of conflict, which have brought such suffering to their people, did wonders for their approval ratings, as the "rally-round-the-flag" effect (itself rooted in emotions that figure in Explanation No. 1) kicked in on both sides. So short-run political incentives encourage both leaders to stick with a tough, uncompromising posture; and this policy in turn feeds the conflict, which intensifies the rally-round-the-flag effect, and so on. Indeed, it was after both leaders finally engaged in small-scale compromise—to resolve the standoffs in Ramallah and Bethlehem—that their groundswell of popular support started to recede; now both suddenly face dissent from more hawkish domestic elements. In the short run, at least, this is the Skinner box that Arafat and Sharon are in: You get a food pellet for making war and an electrical shock for making peace. (Arafat also faces dissent because of the Palestinian Authority's long-standing corruption and governmental ineptness.)

Explanation No. 4: Lack of trust. Often players in a non-zero-sum game can't get to the win-win outcome unless they trust each other. In the Middle East, trust is famously lacking on both sides. Israelis feel that any concessions will be greeted by more bombings, and Palestinians feel all "interim arrangements" are designed to allow the construction of more Israeli settlements in the West Bank. Both sides have good grounds in recent history for mistrusting the other. In game theory, when there is no basis for trust, the endless retaliation that is deemed irrational under Explanation No. 1 can actually be rational. In the classic non-zero-sum game the prisoner's dilemma, you get more points for just refusing to cooperate than for trusting the other player and then getting burned.


Explanation No. 5: Escalating conflict as bargaining. In real life, non-zero-sum games usually have a zero-sum dimension. When you buy a car, there is a price range—say, between $20,000 and $21,000—in which the deal makes sense for both you and the dealer: win-win. Still, once you're inside that range, both of you want the best deal you can get, and your interests are exactly opposed. So, you bargain. There are two basic ways to bargain. You can convince the other party that you have alternatives to the deal. (When buying my Honda Odyssey, I signaled that I knew the Isuzu Oasis was the exact same car, only cheaper.) Or you can raise the costs to the other party of not making a deal with you. (The dealer didn't retaliate by destroying all nearby Isuzu dealerships, but that would have increased his leverage.) Maybe the Palestinians and the Israelis, in exchanging violence, are just doing the second kind of bargaining—a little last-minute jockeying before striking a deal. (This possibility is neglected by those who say that Arafat's apparent support of terrorism, coupled with his rejection of the famous Camp David offer implies that he doesn't want a two-state solution.)

Of these five explanations, the last is the most hopeful, as it suggests the prospect of a deal after a bit more tactical posturing. And this bargaining may indeed be a factor. Unfortunately, it's not the only factor. The first four explanations—the less hopeful ones—have a dismaying compatibility with the evidence at hand. 1) On both sides, people clearly are driven by raw feelings of retribution, sometimes with limited reflection on whether retribution is a good idea (and with the certainty of their own rightness that is characteristic of our species). 2) On both sides, the leaders seem to see themselves in a long-term zero-sum-game with the other leader; Sharon has expressed his wish that Arafat die, and Arafat has never advocated a long and happy life for Sharon. 3) In the short run, Sharon and Arafat seem indeed to be in a non-zero-sum game, getting rewarded for mutual belligerence. 4) On both sides, trust is essentially nonexistent—and not without reason.

All of this is dispiriting. But it does explain the basic irony: Continued conflict is, for both the Israelis and the Palestinians, lose-lose, yet conflict is what both sides seem bent on sustaining. It also explains why the only near-term hope lies with outside intervention—with the United States and other powers stepping in and essentially imposing a settlement, as well as helping to enforce it. (This means going beyond just convening an international conference; it means actually outlining a detailed two-state solution, ideally based on both the recent Arab League initiative and the January 2001 negotiations in Taba, Egypt.)

An externally imposed settlement would bypass the warped motivations and incentives that have guided Sharon and Arafat so far. It could also address the trust problem. In a non-zero-sum game, third-party policing (which, admittedly, would be dicey in this particular game) can be a surrogate for trust—and a way of creating an environment in which actual trust can slowly be rebuilt. It's increasingly clear that, absent some such jump-start, trust may never exist in the Middle East, so continued lose-lose conflict may remain the "rational" option from both points of view.


To say that the Israelis and Palestinians need adult supervision isn't to patronize them. If we were in their shoes—recall those huge conversion factors, 50 and 100—we'd be as out of control as they are. Remember how Americans felt right after 9/11? Now imagine enduring an endless series of 9/11's. Our ratio of rage to trust would be approaching infinity.

In selling Sharon and Arafat on the idea of adult supervision, President Bush might make a simple point to them: even though mutual militancy has been, in political terms, win-win for them, in the long run it will be lose-lose. Endless fighting won't finally earn them a warm place in their people's hearts. And it won't do much for their legacy. There are only two ways that either man is likely to wind up in the history books: Make a lasting peace deal with the other, or combine with the other to lead the region, and maybe even the world, into a great conflagration. Go down in history as the hero or as the goat—but, either way, if you go down in history at all, you're probably going down together.

This is a hard thing for both Arafat and Sharon to accept: They share their fate with someone they hate; they are in the same boat with a mortal enemy. So, their behavior is understandable. But it's not acceptable, because we're all in the boat with them.

P.S.: Earthling's Uncanny Predictive Powers Demonstrated Again! On April 5, I wrote in this space:

In fact, I predict that, in the short run, the current incursion will subdue the rate of suicide bombings. ... If terrorist bombings indeed abate after the current incursion, prepare yourself for the inevitable Charles Krauthammer column touting the success of Sharon's iron-fist policy. It's a natural sequel to Krauthammer's column belittling the significance of the "Arab Street" after the Street failed to boil over and depose any Arab regimes in the wake of the Afghanistan war. In both cases, the fallacy is the same: failing to see 1) that metastasizing hatred can work slowly, beneath the surface; 2) that, increasingly, hatred needn't be mediated by a regime (or a quasi-regime, like the Palestinian Authority) to be lethal; and 3) that the lethal leveraging of hatred—the hatred-death conversion factor—will probably grow exponentially over the next five to 10 years, as lethal technologies advance and spread.

Today Krauthammer graciously complied with my expectations.