n person prison dilemma
The "n person prison dilemma" refers to a hypothetical situation in game theory that explores the dynamics of cooperation and betrayal among multiple individuals. It is an extension of the classic prisoner's dilemma, which involves only two individuals.
In the n person prison dilemma, a group of n individuals is faced with a decision to cooperate or betray each other. Each person has the option to either collaborate with all others, known as cooperation, or betray the others, known as defection. The outcomes of these decisions are determined by the collective choices of the group.
If all individuals choose to cooperate, they all receive a moderate reward or reduced prison sentence. However, if one or more individuals decide to betray the rest, those who cooperate receive severe punishment or a longer prison sentence, while those who betray receive a smaller punishment or shorter sentence.
The dilemma arises from the uncertainty and lack of trust among participants. Each individual has to weigh the potential benefits of betraying others against the risks of being betrayed themselves. The optimal decision depends on the expected actions of others and the overall dynamics of the group.
In a smaller group, such as a two-person prisoner's dilemma, it is generally more rational to defect rather than cooperate. However, in a larger group, the dynamics become more complex. Cooperation can be more beneficial if individuals can build trust and cooperation over time, whereas betrayal can lead to a breakdown of trust and long-term negative consequences for all involved.
The n person prison dilemma is often used as a theoretical framework to understand social dilemmas, collective action problems, and the emergence of cooperation in different contexts. It highlights the challenges and complexities of decision-making in situations where individual and collective interests are at stake.