Is a communication restriction necessary in a Prisoner's dilemma verbal formulation?

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To my understanding, a prisoner's dilemma is any symmetrical game with 2 players where the payoff matrix holds the following relations: A/B> B/B > A/A > B/A and (B/B)*2 > A/B + B/A thereby making A the optimal choice for the individual, but B/B the optimal choice for the group.

The dilemma is typically expressed where the two players cannot communicate:

"Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other."

However, to my understanding, this is not a necessary requirement for the interesting features of the dilemma to arise. Even if players could communicate, they would not be able to trust each other.

This is important because in reality, the vast majorities of cases where the prisoner's dilemma applies are cases where there are communication channels available. So why limit its applicability in its problem statement?

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Communication is a complex subject that involves attempts to transmit and receive information despite the presence of fake signals, strategies to deal with deceiving communication include establishing costly signals or building trust through accountabile relationships between agents.

In real life, the prisoner's dilemma emerges in situations where communication is available but not trustworthy, then it's not really communication. If we are about to play the prisoner's dilemma, and our life is on the line would you trust anything I say? We might as well be in different rooms.

The assumption that there is no communication is equivalent to the assumption that there is no trust between the players, which could have been implied in the formulation, but it is often explicit, so that preconceptions about cooperation, trust and altruism don't pollute the analysis.