More Game Theoretic Analysis for the Middle East

One of my favorite classes when teaching my game theory course is on so-called judo economics. The classic example has a small firm entering an incumbent firm's market. Think of a discount airline entering an existing airline's market. The judo arises from the following economics: If the entrant is small, threatening to take only a small part of the incumbent's market, then the incumbent firm will be tempted to not retaliate (cut price) against the new competition, playing instead a strategy of accommodation. The basic tradeoff occurs if retaliation requires some price cut on all of the incumbent firm’s sales; if that is the case, it might be better to just lose a small portion of sales to the entrant rather than cutting price on the entire market.

The mathematical form of the model is great, in that it allows you to calculate just how much of the incumbent firm’s sales the entrant can take and still not induce retaliation. I like to think of the model as showing us “how far you can push someone.” It applies really well to business, but I always try to extend it to general life as well. If someone just bugs me a bit, I might let them get away with it – but when they contest my principles, I will fight back.

So a couple thoughts on applying this to the current Israel/Hezbollah conflict.

First, judo economics requires the entrant (Hezbollah) to not bite off too much, or it will incite retaliation. That some reports have Hezbollah being surprised at Israel’s reaction suggest that Hezbollah went a bit too far.

But it gets even more interesting when you start putting the judo economics ideas into a multiperiod context, where the incumbent (think Israel) is worried about what might happen in future situations if it accommodates in the current situation. There are several game theoretic ways to think about the value of retaliating even when it might not be in your “short run” interest. One approach I really like is the reputation model originally constructed by the “gang of four ” (Kreps, Milgrom, Roberts and Wilson). In this model of reputation, the incumbent will sometimes want to mimic an “irrational” player and retaliate against even a small entrant. The idea is that other potential entrants believe that there are some truly irrational players out there, and if you don’t play irrationally, you remove all doubt in the minds of future entrants and they will act accordingly. (By the way, I think the best reference for the model is Kreps, D., Milgrom, P., Roberts, J., and Wilson, R., "Rational Cooperation in the Finitely Repeated Prisoneers' Dilemma," Journal of Economic Theory 1982.)

I find this a pretty attractive way of thinking of much of what we do in life. I tell my students that as a manager I am often trying to make people think I am crazy, so they won’t think I am going to be a pushover. If you give in once, people know you are not crazy, that you look at the world like the rest of us, and then people can play judo economics against you till the cows come home.

So for the Israeli situation, application of the model is quite straightforward. Certainly when we are dealing with the Middle East, we have to be willing to accept the possibility of truly irrational players (I use irrational pretty broadly here – acting consistent with strongly held religious beliefs would certainly qualify, and I say that without any moral judgment implied). So Israel acted in a way that surprised Hezbollah, who were not expecting a large scale war after what they might have viewed as a relatively minor violation of Israel’s border and the death and kidnapping of small numbers of Israeli soldiers. But now what do future players think about future reactions by Israel to possible future incursions and violations? A bit more fog of war, no? And sometimes, that is just what is required in order to reduce the likelihood of future incidents.