Senator Ben Nelson was the 60th vote in the Senate on healthcare reform.  He held out for what is now called the “Nebraska purchase,” a side-payment from the federal government to Nebraska to extend Medicaid.  He also got rid of the public option.  He compromised a bit on abortion so he did not get all his cake. In an interview, he says:

NELSON: Well, I gave a little – a half-way in between and then you ask for it all.

So, compromise was short-term stance and he was going ask for the whole cake later on. How?  Nelson planned to bargain hard for more in conference in the (now-hypothetical) scenario where the Senate and House bills were merged (my emphasis) as he preferred the House bill to his own language in the Senate bill:

NELSON: To get it there.  Right.  I know – with my language which was better than the language in the bill.  But, once it went to conference, as part of the conference, there was still another 60 vote threshold, and that is when I would have insisted and that is what Christy was talking about when I mentioned this on the phone – how we would approach this in conference to say, for my last 60th vote, it has to have Nelson/Hatch/Casey.

LSN: Why didn’t you stop it right then and there and say, “No Nelson/Hatch – nothing.”

NELSON: Because, at that point and time, the leverage wasn’t as strong – you have to play it

LSN: You were the 60th vote, though.

NELSON: Yes, but there were some on the other side who probably wouldn’t have gone along with it at that point – they would have had no choice.  A whole bunch of people didn’t the Nelson/Hatch/Casey – you saw that.  There were a whole bunch of people who didn’t like the Nelson language – they only went along with because I could be the 60th vote.  Leverage increases, exponentially, like the difference between a number 2 earthquake, 3 earthquake, 4 earthquake – goes up exponentially like that – your leverage goes like that at the very end…..if you are going to match Stupak, you match him at the end when you have the most leverage.

If the plan failed, he was willing to accept his own (!) language:

NELSON: If everything failed, Nelson is better than the language that is in the bill…..I could live with Nelson, but it is not my preference.

The Nelson strategy contradicts simple backward induction in complete information games in two ways.  First, if a player has significant leverage at the end of the game, he should have the same leverage right now.  There is no sense in which leverage increases at the end.  Second, if it is common knowledge that Nelson will accept Nelson language in the end, then he has no leverage at the end in conference anyway.

Perhaps both issues can be rationalized with incomplete information?  I do not know of models that do this but perhaps others are.  There is an Abreu-Gul paper where players concede slowly over time in a war of attrition but there is a deadline effect here that is not in their paper.