The Prisoner's Dilemma which supposes that two criminal partners (Lets call them Mr. Whitman and Mr. Pink) arrested for a criminal offense of possesion of some blue narcotic with the intent to sell (which carries a sentence of 1 year for first time offense). The DEA agent working the case (Detective Shredder) suspects one of the two men is manufacturing blue narcotic (carries 2 years for first time offense, and an additional year if manufactured with the intention of selling (3 years total) ), but the evidence can't point to a single suspect.
Det. Shredder has realized this strategy:
If both Whitman and Pink remain silent, they will both be sentanced to 1 year in jail.
If Whitman remains silent, but Pink rolls on Whitman, Whitman will serve 3 years and Pink will go free and vice versa.
If Whitman and Pink roll on each other, he'll charge them with both with manufacture, but will get the prosecution to seek two years.
So the stakes for Mr. Shredder are different for his two criminals. In all situations, Mr. Shredder wants to put bad people behind bars, and the longer the better. He wins no matter which way this goes down. For the two criminals, going to jail is undesirable and only one way will get them the most benefitial outcome: Confess and name the other as the real mastermind.
So let's play with two scenarios:
Shredder talks to Pink first. After letting both men worry in separate holding cells, Shredder barges into Mr. Pink's room and declares Whitman ratted him out. Pink doesn't know about the prisoner's dilemma and calls bullshit. Shredder leaves for Whitman's cell.
Shredder starts with Whitman first. Whitman is aware of the dilema and immediately confesses and explains that Pink was the real mastermind. He had all the connections and preyed upon Whitman's low finances and chemistry knowledge to put him in this situation. Shredder leaves for Pink's cell.
In either scenario, Shredder wins because someone is going to jail for at least one year, possibly 3. What happens in the next cell determines the number of people going to jail. In scenario 1, whatever Whitman says, Pink is going to jail, because the only way out is to roll, which Pink didn't do. Depending on Whitman's reaction, Pink could be in for one year (Whitman doesn't talk) or 3 (Whitman sings). This doesn't matter to Shredder, who wants to put people in jail... the most time for the most people.
In scenario 2, Shredder also wins. Pink is still going to go to jail, no matter what he says. Whitman may or may not go to jail, but again, it doesn't matter if Shredder gets 2 criminals for two years or one criminal for 3.
Which just goes to show you the benefit to cops lying would be. The only possible real world way around this is for Mr. Whitman and Mr. Pink better call a lawyer (Oh come on, no one Saul that coming?)