Prisoner's Dilemma II

The matrix provided represents the payoffs of a Prisoner's Dilemma.

To find the Nash Equilibrium, first consider Suspect A's options.

If B remains silent, A benefits more by betraying, as it results in no prison time compared to one year.

If B betrays, A again finds betraying better, serving two years instead of three.

Next, examine Suspect B's options.

If A remains silent, B will choose to betray since this results in zero years instead of one. Similarly, if A betrays, B will betray as well, preferring two years in prison over three.

The Nash Equilibrium is reached when both suspects betray each other. They choose betrayal to avoid the worst outcome of trusting and being betrayed. This risk aversion makes the Nash Equilibrium stable.

Neither suspect gains by changing their strategy alone. If one remains silent and the other betrays, the silent one faces a harsher penalty. This ensures that both are compelled into betraying.

This equilibrium is also a dominant strategy equilibrium. It's important to note that while all dominant strategy equilibria are Nash Equilibria, not all Nash Equilibria involve dominant strategies.