Byrne's Eye View

I'm in the middle of Thomas Schelling's The Strategy of Conflict, a collection of essays on Game Theory. One thing he points out is that negotiators can get better results if they have less freedom: if you're buying a house and you would be willing to pay $500,000, but have signed some sort of binding pledge not to pay more than $400,000, you're in a great bargaining position (as long as your binding pledge puts you somewhere above the minimum price at which the other party sells).[1]

What I wonder about is why this isn't more popular. Imagine if a buyout shop took control of some union-dominated company in a debt-finance acquisition, and explained to the negotiators that because of the interest payments on debt, the company would have to cut labor costs 20% or go under. Suddenly, by weakening their capital structure, they've strengthened their bargaining position. Of course, the benefit here goes straight to the former shareholders, rather than the new owners. One possibility would be a situation in which the new owners bid, say, $1 billion for a company they own 20% of, but finance that transaction mostly with debt. They only get a small fraction of the total benefit, but they do benefit, and someone owes them a favor. My question is:

a) Why is this not the most popular justification and strategy for LBOs -- that by depriving companies of capital, they force unions to capitulate to any reasonable demand?

or

b) Is this how people made money borrowing at double-digit rates to pay a 30% premium for an assortment of companies in declining businesses? Hm.

[1] Schelling uses this example, but his book was written in the 60's, so the prices he uses are $16,000 and $20,000. Even if he ended up paying the $20K, I sure hope for his sake that he got the house.