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Two prisoners are arrested.
Both are given a choice: Rat out your buddy, and we'll let you go with one year in prison. Keep your moth shut and we'll give you four years. If you keep your moth shut and your buddy rats you out, you'll get ten. If you both rat, you both get eight years.
The dominant strategy of both prisoners is to speak: In either case, ratting on their buddy will lower their punishment. However, if both prisoners choose this strategy, they end up losing collectively: Rather than both receiving four years as they would if they both kept their moth shut, they both yet eight years because they both talk.
That's the basics of the dilemma. The years don't matter, just the ranking of preferences.
If the prisoners can communicate, they will know that the other prisoner didn't talk, and if one prisoner opens his mouth, he will know that the other prisoner will immediately do the same.
I learned the prisoner's dilemma when I studied game theory. The fact that it depends on a lack of information flowing between the prisoners and that snitching is only the dominant strategy when it's a single-round game is just parts of the assumptions of the dilemma.
They do not, as lying exists
Well, sure, it's if they are in the same room or they can hear through the walls or whatever. An actual flow of information, not just them lying to each other. I assumed that was obvious.
That's like saying poker is a solved game if you can view eachothers cards :D
I assumed it was obvious that it would remain a game where full knowledge of the game state is never granted to a participant. And the variant you proposed just added a communication channel.
That's to say: it stays realistic.
Yeah, when I stated that it literally wouldn't be a dilemma any more it's because having the prisoners sitting in the same interrogation room would destroy it, the same way playing poker with your cards backwards would destroy the game to the point where it cannot really be considered poker any more.
Wasn't making a smarter point than that. :)