There is a famous folk tale that game theorists tell their kids before putting them to bed, the story of the Chain Store Paradox. The idea is simple, a large chain faces a finite and known sequence of challengers. It can either give in to them or fight. In each case, fighting is more costly than giving in, but if the chain gives in everywhere, they stand to lose a ton of money.
The reason it is called a paradox is that, on the basis of pure logic (and backward induction), the chain should optimally concede in every case. When told to MBA students, they reject this immediately and vehemently. And they're right--a chain store would be foolish to engage in such a strategy.
Enter clever game theorists to come to the rescue. They amend the story as follows: Suppose there is a small chance of a "tough" chain--one that actually enjoys fighting and prefers it to giving in, even on an individual store basis. Or, at least, suppose that would-be entrants are willing to contemplate such a possibility. Then, if there are enough entrants, the chain store should fight several so as to deter entry from the rest. (Or at least all but the final few.) Moreover, this is credible since a would-be challenger, after seeing several fights, is forced to increase the chance that the chain is tough, which deters entry and profits the chain.
All of the detailed logic aside, this latter conclusion seems sensible and much closer to the mark than the original case. The business lesson: cultivate a reputation for toughness, especially with early challengers.
So what does this have to do with politics?
Trump is like the chain store and the GOP legislators the entrants. Trump knows that he will face would be challengers over each of his policies. He also knows that there is a finite endpoint--4 or 8 years most likely---and so, by the end of his term of office, there is little point in fighting, i.e. he will, eventually, be a lame duck. But early on in the game, reputation is critically important--so fighting is called for.
What is key for the chain store in our little parable is that it never show weakness for, once it does, the entrants will conclude that it is not the tough type. They will know it dislikes fighting, and will enter 100% of the time thereafter. In lay terms, once reputation is lost, it is not easily, or perhaps ever, recovered.
But Trump seems to have just flunked game theory 101 with his handling of the AHCA vote.
In supporting the AHCA with all his power, he knew he would face challengers, and he did in the form of the Freedom Caucus. Chain store/game theory logic suggests that, since this is the first big issue on his watch, he has every reason to pretend to be the tough type of President and give little or no ground, even if he would rather concede and compromise. But, as Trump will tell you, he's an instinctive decision maker, and certainly not one to read the cockamamie theories of pointy-headed game theorists or other intellectual types. So he apparently never got the memo about how important it is to create a reputation for toughness.
Instead, he met with the Freedom Caucus guys in secret, and behind the Speaker's back. In this meeting, he offered them many concessions, hoping to get a deal. Smelling blood, the Caucus came back for more...and more...and more.
And so, remarkably, Trump already seems to have squandered a "tough" reputation among favor-seekers in Congress. He'll face a lot more "entrants" in future.