Make it an iterated prisoner’s dilemma, or add some other way for players to punish each other after seeing their choice, and that does change the game.
Make it an iterated prisoner’s dilemma, or add some other way for players to punish each other after seeing their choice, and that does change the game.
All models are wrong, some models are useful, and in this case it seems more wrong than useful.
Edit: thought you were OP, whoops
Saying that communication doesn't change the prisoner's dilemma so long as each player can't communicate is a contradiction. The only difference is you used the word "see" instead of the word "communicate", but "see"ing is a form of communication.
But OP is saying there is no distinction.
In that context, not being able to objectively see the choice made by other players making their own choice is functionally equivalent to making simultaneous choices. You can re-order when the players make choices and communicate at will without changing the payoff matrix and mathematical model.