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.
Like others said, it's not about communication, but trust. If you stack the payoff matrix severely enough, there's nothing the prisoners can strategize, and you can literally keep the prisoners in the same room, and it will still work.
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.
> 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.
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.
That's a generic case. Parent is describing a specific case in which prisoners determine they have a 95% chance they will be convicted. Given such a case, parent's argument follows logically. How many cases the Fed prosecutes or convicts is irrelevant to the scenario.
Yes, in this scenario the prisoners assume the Feds are going to bring a case in eventually. This, I believe, tracks the real-world situation, because this case is already notable enough that the government is determined to see it through, however long it takes to prepare.
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.
> 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?
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.
This is almost accurate. You can slightly increase your chances if you say "I will defect, but will take care of your family and give you half my income forever. If you also defect, we will both go to prison and you will be worse off", then don't actually defect - which means you both cooperate!
It won't always work, but it did work flawlessly in a show called "Split or Steal", which basically made the prisoner's dilemma a TV show: https://www.youtube.com/watch?v=S0qjK3TWZE8
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.
Prisoner's dilemma has a Nash equilibrium where defection is the best move regardless of anything else that happens. If you change the game to be a repetitive 'prisoner's dilemma' with the same actors the best strategy would be tit for tat.
Yes, and this kind of prisoner's dillema isn't an accurate description of the hypothetical one. When it comes to the DOJ making a case against two people, both of them co-operating will likely get both of them harsher sentencing than what the defector will get.
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.)
Yep. Lack of realistic prospect of cooperation working and the asymmetry are key here. I don't think any option either or both of them can take will save Sam, but Sam could possibly save Caroline from the most serious charges by taking full responsibility for the decision to transfer FTX customer funds to Alameda (except I suspect there are other issues with Alameda's compliance they could still nail her for)
Caroline's option to save Caroline regardless of what Sam does by testifying looks a lot better.
'with communication' does a lot of work here. tit for tat is a strategy where you start with the positive-for-both-parties strategy and then just copy whatever the other party did last time.
Yes but the only way repeated cooperation can be maintained is if players can “punish” defectors by also defecting for a certain # of turns (thus making the PV of breaking ranks and defecting < keeping cooperating for every player).
SBF’s situation is different in that the game ends as soon as someone defects.
The prisoner's dilemma isn't predicated on the inability to communicate. It's predicated on (the lack of) trust. Put it this way: if you could lock in your decisions in an atomic fashion there would be no dilemma.
