N-person prison dilemma
The N-person prison dilemma is a variation of the classic prisoner's dilemma game theory, where rather than just two individuals being involved, there are N number of people facing the dilemma.
In the N-person prison dilemma, N individuals are arrested for a crime but the authorities do not have enough evidence to convict them. Each person is placed in a separate cell, and the authorities offer each individual a deal: if they confess and implicate the others, they will receive a reduced sentence. However, if all or a majority of them confess, they will all receive a harsher punishment than if none of them confess.
This dilemma arises because each person has to make a decision without knowing what the others will choose. They have to weigh the risks and benefits of confessing or remaining silent based on the assumptions about what the others might do.
Suppose there are three individuals, A, B, and C, facing the N-person prison dilemma. If they all remain silent, they will each receive a minimal sentence. But if one of them confesses while the others remain silent, the confessor will receive an even shorter sentence while the others will receive a longer one. If all confess, they will all receive a harsher punishment than if none had confessed.
The dilemma lies in the fact that if each individual acts selfishly, they will opt to confess, assuming the others will do the same. This results in a suboptimal outcome for everyone involved. However, if they all trust each other and decide to remain silent, they can collectively achieve the best possible outcome. But the lack of trust and uncertainty about others' decisions often leads to a situation where everyone chooses to confess, resulting in a worse outcome for all.
The N-person prison dilemma highlights the complexities of decision-making in a group setting where individual self-interest clashes with the collective interest. It demonstrates how cooperation and trust are essential for achieving the best outcome, but also how the lack of trust and uncertainty can lead to a breakdown in cooperation and suboptimal outcomes.