Question

Does each individual in a prisoner's dilemma benefit more from cooperation or from pursuing selfinterest? Explain briefly.

Short answer

In the prisoner's dilemma, pursuing self-interest (betrayal) is the dominant strategy for both players, as it yields the best possible outcome for each individual, regardless of the other player's decision. Although cooperation (staying silent) would lead to a better overall outcome for both individuals, the inherent uncertainty and distrust in the scenario drive both players to pursue self-interest, resulting in a Nash Equilibrium and a socially sub-optimal outcome.

Step-by-step solution

Understanding the Prisoner's Dilemma

The prisoner's dilemma is a popular model in game theory that presents a scenario with two individuals who have been arrested for a crime and are being interrogated separately. Each prisoner has two choices: cooperate by staying silent or pursuing self-interest by betraying the other prisoner.

Payoff Matrix

The possible outcomes of the prisoner's dilemma can be represented by a payoff matrix, which can be used to analyze the decisions made by the players. The matrix displays the four combinations of decisions and their resulting payoffs: - Both prisoners cooperate (stay silent): Both serve a short sentence - Both prisoners pursue self-interest (betray each other): Both serve a longer sentence - Prisoner A betrays Prisoner B (pursues self-interest), while Prisoner B cooperates: Prisoner A goes free, Prisoner B serves the longest sentence (and vice versa)

Dominant Strategy

A dominant strategy is a decision that yields the best possible outcome for a player, regardless of the other player's decision. In the prisoner's dilemma, pursuing self-interest (betraying) is the dominant strategy for both players. This is because, regardless of the other person's decision, choosing to betray will result in either going free or serving a shorter sentence compared to staying silent and cooperating.

Nash Equilibrium

A Nash Equilibrium occurs when each player's strategy is the best response to the other player's strategy. In the prisoner's dilemma, both prisoners pursuing self-interest (betrayal) results in a Nash Equilibrium – neither player can improve their payoff by unilaterally changing their decision.

Individual Benefits and Socially Optimal Solution

Although both players have a dominant strategy to betray each other, this leads to a socially sub-optimal outcome. If both prisoners had cooperated (by staying silent), they would have served shorter sentences, which is a better outcome for both individuals. However, the fear of being betrayed results in both players choosing self-interest, even if cooperation would lead to a better outcome. In conclusion, each individual in a prisoner's dilemma benefits more from pursuing self-interest (betrayal), but this leads to a sub-optimal outcome for both players. Cooperation would lead to a better overall outcome, but due to the inherent uncertainty and distrust in the scenario, it is not the most beneficial strategy for each individual.