Here's the basic premise of any kind of "deal," in the true sense. A deal can be cut when two negotiators can each improve their utilities over what happens without a deal. Thus, their interactions cannot be zero-sum. It cannot be a circumstance in which one person gaining must come at the loss of the other actor. Here, of course, you see the problem for Donald Trump's world view, and any true deal. He fancies himself a dealmaker, but he views the world in zero-sum terms, which has important implications that I have been addressing for a while. There's no deal to be had in a zero-sum world. Just cons. That's why he is a con artist.
Most of the world, though, is not zero-sum. Thank you, Adam Smith.
What about prosecutors and defendants? How do they cut deals? Their interactions aren't quite zero-sum. Prosecutors care more about their conviction rates, whereas defendants might presume a conviction, and care more about reducing the penalty. If you know you are likely to be convicted of something, you plea down the charges and accept a lesser penalty. The prosecutor gets a sure thing conviction, reducing uncertainty from the possibility of some jackass juror doing something stupid, and the defendant eliminates the possibility of the tail-end extreme sentence. Deal. Yes, their preferences are different, but they aren't quite zero-sum because there are multiple elements to evaluate.
Note, though, that any kind of deal in a prosecutorial sense relies on the premise that a conviction of someone is likely. You plea to something and reduce the prosecutor's uncertainty over the conviction in order to reduce the likelihood of an extreme sentence. That's how a deal works.
Enter Rudy Giuliani. He's a former prosecutor. He, ostensibly, knows how this works. I'm just covering this from a game theory perspective because my training is in economics and political science rather than law, but this actually is a basic problem in game theory, and if you want to see a more elaborate, qualitative write-up, try Bruce Bueno de Mesquita's The Predictioneer's Game.
So, um... what would Giuliani, or Trump give to Mueller to make this go away? Plea to something? No, there's no way Trump does that. Hand over Kushner? I could see Trump wanting him out of the way to get to, um...
No, that's not gonna happen either.
You start to see the problem. And even if Trump hands someone over as part of any deal, he then undercuts that with a pardon. (Hi, Scooter! Enjoying that pardon yet?)
An actual deal requires compromise. Trump won't do that. There's nothing for Giuliani to negotiate. However, imagine the job interview.
Rudy walks into the Oval Office and tells Donny, "
As I have said repeatedly, Trump won't get impeached, tried or convicted. Embarrassed? Sure, but that's about it. Can he or Giuliani cut a deal to shut down the investigation, though? No. All they can do is fire Mueller. He isn't actually as badass as John McClane, or rather, Trump has comparatively more political firepower than Hans Gruber.
* I formally apologize to Alan Rickman for this comparison.