Final answer:
The fourth prisoner is going to jail as part of a strategy by the guards that plays on the prisoner's dilemma, where the prisoners are led to believe their partner is confessing to reduce their jail time, despite mutual silence being more advantageous.
Step-by-step explanation:
The fourth prisoner is going to jail under the pretense, as told by the guard, that their partner is confessing to the crime and hence getting a lighter sentence. The guard's strategy is rooted in the classic prisoner's dilemma, which is a fundamental example used in game theory to illustrate how two individuals might not cooperate, even if it appears that it is in their best interests to do so. The dilemma presents a situation where each prisoner is given the choice to confess or remain silent. If one confesses and the other does not, the one who confesses will get a lighter sentence while the other receives a harsher sentence. If both confess, they receive moderate sentences. However, if both remain silent, they receive the lightest sentences. This scenario emphasizes that mutual cooperation would be their best collective strategy, but without the ability to communicate and the mistrust between prisoners, they often end up confessing.