Israel/Lebanon ceasefire

Clausewitz tells us that war is politics continued by other means. If this is true, in a very simplified manner, war as politics exists on a continuum with a hierarchy of possibilities. This hierarchy looks like this:

1. Objectives achieved, no effort
2. (or 3) Objectives achieved, with effort
3. (or 2) Objectives not achieved, no effort
4. Objectives not achieved, with effort
   

The first preference is to achieve your objectives with no effort (and effort, in this case, means military expenditures, deaths and casualties, political capital, etc.)

The last preference is to fail to achieve your objectives at considerable effort.

In reality, most geopolitical contests will fall somewhere in between these two poles. And this entails a calculus. Is achieving your goals worth the effort this will take? Can you know the cost before you embark on a given course? And at what point does “cutting and running” become the least worst available solution?

I ask this because it has relevance both to Israel/Hezbollah and the U.S./Iraq. In the Israeli/Hezbollah case, so far we have an unstable ceasefire in place. What was Israel’s calculus in this matter, and what was Hezbollah’s? Did either achieve their objectives? And what was the cost they paid? (Both clearly have paid a cost, but it is not at all clear that the cost for both is equal. It is conceivable that Israel decided that it did not achieve its objectives but that additional effort was not worth the additional benefit. The same could be said of Hezbollah, or, for that matter Iran. Or they could have achieved their objectives and look at the cease fire as a way to keep the cost of this achievement from escalating).