To be even more technical, “Prisoner’s Dilemma” is actually used as a generic term in game theory. It refers to the set of two-player games with this kind of payoff matrix (see here). The classic prisoners dilemma also adds in the inability to communicate (as well as a bunch of backstory which isn’t relevant to the math), but not all prisoners dilemmas need to follow that pattern.
To be even more technical, “Prisoner’s Dilemma” is actually used as a generic term in game theory. It refers to the set of two-player games with this kind of payoff matrix (see here). The classic prisoners dilemma also adds in the inability to communicate (as well as a bunch of backstory which isn’t relevant to the math), but not all prisoners dilemmas need to follow that pattern.
In game theory terms, I’m not sure communication would do much for a one-off prisoner’s dilemma.