معضلة السجين 2

The Nash Equilibrium occurs when both suspects choose to betray each other. Each suspect recognizes that betrayal is their best response regardless of what the other does. Neither suspect can improve their outcome by unilaterally changing their strategy, making this equilibrium stable. This mutual betrayal results in both serving two years in prison, even though cooperation would have yielded shorter sentences.

Each suspect betrays because it minimizes their worst-case outcome. If Suspect A remains silent while B betrays, A faces three years in prison. If A betrays, A serves at most two years. This risk aversion logic applies equally to both suspects, compelling mutual betrayal despite the suboptimal collective result.

The Prisoner's Dilemma is a dominant strategy equilibrium because betrayal is the best choice for each suspect regardless of the other's decision. For both players, betrayal dominates silence in every scenario. However, not all Nash Equilibria involve dominant strategies, making this distinction important in game theory analysis.

If both remain silent, each serves one year. If one betrays while the other stays silent, the betrayer goes free and the silent suspect serves three years. If both betray, each serves two years. These payoffs create the dilemma: mutual silence yields better outcomes than mutual betrayal, yet individual incentives drive both toward betrayal.

The Nash Equilibrium outcome is suboptimal because both suspects would receive shorter sentences if they cooperated and remained silent together. However, rational self-interest and fear of being exploited by the other suspect prevent this cooperative outcome. The equilibrium demonstrates how individual rationality can lead to worse collective results.

No. If one suspect remains silent while the other betrays, the silent suspect receives the harshest penalty of three years. This asymmetry ensures both suspects are locked into betrayal. Changing strategy unilaterally only worsens an individual's position, which is why the Nash Equilibrium remains stable.

Risk aversion compels both suspects to betray because it avoids the worst possible outcome of three years in prison. Each suspect prioritizes minimizing maximum loss over achieving mutual cooperation. This defensive strategy, while individually rational, produces the equilibrium where both serve two years instead of the one year they would serve through mutual silence.