The game theory of the Israeli-Hezbollah conflict

Matthew Yglesias has as good an explanation as any I’ve seen advanced for the actions of Israel, Hezbollah, and France in the Israeli-Hezbollah hostilities and the current tenuous ceasefire:

The war in Lebanon, as wars so often are, was the result of a serious double miscalculation. First, Hezbollah clearly failed to anticipate how Israel would respond to their cross-border raid. In turn, Israel clearly failed to anticipate how difficult it would be to mount a major anti-Hezbollah operation in Lebanon. And, indeed, the miscalculations were surely interlinked. Hezbollah correctly assessed how difficult it would be for Israel to mount a massive retaliation and therefore banked on Israel not retaliating massively.

The resulting war was a disaster for both sides. Israel really was significantly hurting Hezbollah. But it was doing so at a massive cost to itself in terms of lives lost and money spent. Hezbollah was bound to start running low on rockets and Israel running low on things to bomb. The situation was heading in the direction of grinding, endless guerilla conflict that would have been exceedingly costly and essentially hopeless from the Israeli perspective while also imperiling everything Hezbollah’s built itself into in southern Lebanon.

Each side had reason to regret the conflict’s existence. Both sides would have been made better off by calling “do over” and returning to the status quo ante. But neither side wanted to back down. Nor would it have been easy for either side to do so since the coalition Hezbollah/Syria/Iran team won’t negotiate with the Israel/USA coalition and vice versa.

France’s objective in the negotiations was a return to the status quo ante.

In essence, through two consecutive bait-and-switches — first over the wording of a UN resolution, and second over the deployment of French troops to Lebanon — France managed to get both parties to agree to a return to the status quo ante, which is better for both sides (that’s why the tricks worked), but that neither side could admit to wanting. That’s a pretty good result, especially considering that Chirac spent essentially none of France’s resources achieving it.

To put it into game-theoretical terminology both Israel and Hezbollah were treating their mutual relationship as though it were a “zero sum game of perfect information” (a set of transactions in which, when one side wins, the other loses and each side knows what the other is doing) whereas, clearly, that was far from the case.