Not necessarily. Various decision theories can come into play here. It depends precisely on what you mean by the prisoner's paradox. If you are playing a true one shot where you have no information about the entity in question then that might be true. But if you are playing a true one shot where you each before making the decision have each player have access to the other player's source code then defecting may not be the best solution. Some of the decision theory posts have discussed this. (Note that knowing each others' source code is not nearly as strong an assumption as it might seem since one common idea in game theory is to look at what game theory occurs when people know when the other players know your strategy. (I'm oversimplifying some technical details here. I don't fully understand all the issues. I'm not a game theorist. Add any other relevant disclaimers.))
No one on this thread has mentioned a "prisoner's paradox". We have been discussing the Prisoner's Dilemma, a well known and standard problem in game theory which involves two players who must decide without prior knowledge of the other player's decision.
A different problem in which neither player is actually making a decision, but instead is controlled by a deterministic algorithm, and in which both players, by looking at source, are able to know the other's decision in advance, is certainly an interesting puzzle to consider, but it has next to nothing in common with the Prisoner's Dilemma besides a payoff matrix.
A monthly thread for posting rationality-related quotes you've seen recently (or had stored in your quotesfile for ages).