Prisoner's Dilemma

You may be looking for the Big Finish audio drama of the same name.

The prisoner's dilemma was a theoretical problem used in game theory, which demonstrated how cooperation, or a lack of it, could affect the outcome of a situation. If two prisoners were separated and each was given the opportunity to betray his accomplice, there were several different outcomes depending on what each decided and what his accomplice did.

Dr Judson had a logic diagram of the prisoner's dilemma on the blackboard in his office at Maiden's Point. The Seventh Doctor recognised it immediately, which enabled him to break the ice with Judson. (TV: The Curse of Fenric)

Zara and Ace ended up in the dilemma unwittingly when imprisoned on Erratoon, which led to Ace losing her memory when Zara betrayed her. (AUDIO: The Prisoner's Dilemma) Bernice Summerfield also used it to escape being locked up after she and the Doctor were caught over a dead body. (AUDIO: The Library in the Body)