Prisoner's Dilemma

• Content map: SMU H3 Game Theory Map

Setup

Definition:

Prisoner’s Dilemma

• Players: Player 1 and Player 2.
• Strategies: Each player chooses Red or Black.
• Rules: Players move simultaneously without observing the other player’s action.

Payoff Matrix

Derivation (Iterative Deletion of Dominant Strategies)

• For Player 1:
  • If Player 2 plays Red, then $2>0$
  • If Player 2 plays Black, then $5>3$.
• Hence Red strictly dominates Black.
• By symmetry, Red strictly dominates Black for Player 2 as well.

Nash Equilibrium

Result:

The unique Nash equilibrium (dominant-strategy equilibrium) is:

yielding payoffs $(2,2)$.

Insights

Insight:

However, the equilibrium is inefficient.

(Black,Black) yields $(3,3)$ and Pareto dominates $(2,2)$, but is not stable under unilateral deviation.