A necessary conceit of the prisoner's dilemma is that they can't communicate, and therefore can't strategize together so that doesn't exactly apply here. It's just self preservation.
Consider the payoff matrix in this example, somewhat analogous to the case we're describing:
- Both defect -> both go to prison for life
- One defects, one cooperates -> the cooperating one goes to prison for life; the defector gets some minor punishment and otherwise goes free.
- Both cooperate -> both go free for a moment, spend some months or maybe even a few years living in fear, then with 95% chance go to prison for life. That's because the whole deal is about saving work for the Feds, but they will put in that work if needed, and come back with bullet-proof case.
There's hardly anything they can do to meaningfully increase their chances of surviving the "both cooperate" option, so the two prisoners will both try to defect.
This isn't necessarily the case. The Feds convict on 95% of the cases they decide to prosecute. Which means that they decide not to prosecute marginal cases.
It could be the case that there just isn't enough evidence to bury them.
But even if not, then have the prisoners multiply that 95% by whatever they believe is the chance Feds will eventually prosecute. Is it 50/50? That just gives them 52% chance of avoiding spending rest of their lives in prison, which is still not a good bet.
(Note that prisoners won't be unbiased here - the Feds will be trying to make them believe this chance is much higher than it really is.)
There is a third factor here, whether the prisoners can disappear before Feds go after them - I assumed they effectively can't, and/or it comes with sacrifices so big that it's not much different than prison.
Crucially, these particular prisoners have a very good idea of whether the Feds have enough evidence to go to trial (assuming the Feds get everything, which is probably prudent to assume). Especially with the advice of good council, which they apparently can afford.
> Note that prisoners won't be unbiased here - the Feds will be trying to make them believe this chance is much higher than it really is.
Which is mitigated by the advice of council. Of course, there is a chance that they are influenced too far in the opposite direction - their layers may be banking on raking in fees from going to trial.
That's the kicker though, and it's the lever the dilemma orchestrators (here, the Feds) have to force a result: smooth out any real-life considerations by making the payoff matrix more extreme. If the cost of failure is life in prison, "slightly increase" and "won't always work" isn't gonna cut it - they can practically guarantee the prisoners will make a specific choice.
SBF’s situation is different in that the game ends as soon as someone defects.
That's why underlings have strong incentives to defect, and defect quickly. (Defection is also rarely an option for the person at the top of the pyramid.)
Caroline's option to save Caroline regardless of what Sam does by testifying looks a lot better.