Phi relates this concept to Sigma during the Cyan door routes to pass the time after Sigma unwittingly locks himself and Phi in the AB Room forty minutes before the polling deadline, much to her annoyance (this is the matchup pitting them against Alice). She explains the Prisoner's Dilemma in order to explain to him the similarities between it and the AB Game. Her ultimate goal with the explanation is to reveal the paradox of everyone allying being the best decision for the group, but betraying being the most "rational" decision for the individual.
The in-depth explanation Phi gives in the Cyan door route is not given in the other routes; this is because the body of an old woman is found, and the reaction to discovering it fills in this time gap instead.
The Prisoner's Dilemma is one of the most heavily studied scenarios in history. It is named for the situation in which the thought experiment takes place: Two criminals commit a crime together and get caught by the police. The police only have enough evidence to prosecute them on a minor charge, but not enough for the crime unless they can get either of the accomplices to confess. They separate the two criminals and offer each of them a deal: Pin the crime on the other criminal and walk out on the lesser charge. There are three possible outcomes.
- If they both reject the deal, they'll both serve time in jail on the lesser charge. In Phi's example, this time is two years for each criminal, leading to a total duration of four years.
- If one betrays the other, the betrayer will go free and the betrayed criminal will serve jail time according to the severity of the crime. In Phi's example, the confessor still serves time for the lesser charge (a meager one year) but the one who stayed quiet must serve the maximum sentence of the crime; a rather sizable 15 years. The criminals will end up serving a total of 16 years.
- If they both betray each other, they will both get prosecuted and serve jail time according to the severity of the crime. In Phi's example, the police can reprieve the criminals of a few years from the maximum sentence, but both criminals will still end up serving ten years each. This is the worst cumulative outcome for the pair, leading to a total jail time duration of 20 years.
After the explanation, Sigma correctly states that for him, the best decision would be to betray since at best he would serve a single year and at worst he would serve ten years. Phi then notes that his accomplice would be thinking the same thing, leading to both picking to confess and throwing both into a ten-year sentence. If they both had stayed quiet, they would've only had to serve two years each. Thus, by looking out for themselves, the criminals needlessly extend each of their sentences by eight years. This is why the thought experiment is called the Prisoner's Dilemma, not the Prisoner's Solution. Sigma muses that if everyone could just think of the good of the team and agree to pick ally, they could all escape simultaneously. Phi ends the explanation by saying, "The AB game is the same: You want to pick [ally], but you can't."
The biggest difference between the AB Game and the Prisoner's Dilemma is in the positivity of the outcomes. In the Prisoner's Dilemma, the criminals will serve time regardless of what they do. Confession could lead to a halving of the initial sentence. If it backfires though, the sentence is extended five-fold. In the AB game, cooperation leads to a win/win because both parties gain BP. Betrayal of one party leads to a slight advantage for the betrayer at the expense of the one who was betrayed. Both parties betraying causes a stalemate with no change in BP. Additionally, the two sides of the AB game are asymmetrical; there is a pair and a solo playing against each other. Thus, there are four distinct outcomes instead of three:
- Pair ally + solo ally = +2 points for both parties. This is a 6-point gain for the total of all players, clearly the most desirable outcome.
- Pair ally + solo betray = -2 points for each member of the pair and +3 points for the solo. This is actually a one-point loss for the total of all players.
- Pair betray + solo ally = +3 points for each member of the pair and -2 points for the solo. The total number of points will increase by 4, making it the second-"best" outcome.
- Pair betray + solo betray = No gain for anyone. Intriguing to note, this is actually a better outcome for the point total than the outcome where just the solo betrays. There is no gain, but there is also no loss.
- During the story, the voice actor for the detective who arrests Apple and Banana is Jamieson Price; Zero Sr.'s voice actor.