Prisoner's Dilemma — Find the Nash Equilibrium

The Scenario

Two suspects are arrested. The prosecutor offers each the same deal: testify against the other (defect), or remain silent (cooperate). If both stay silent, each gets 1 year. If one testifies while the other stays silent, the testifier goes free and the silent one gets 5 years. If both testify, each gets 3 years.

The payoffs below are written as years avoided (higher is better): getting 0 years = payoff of 5, getting 1 year = 4, getting 3 years = 2, and getting 5 years = 0.

Payoff Matrix

	Suspect 2: Silent	Suspect 2: Testify
Suspect 1: Silent	4 , 4 ★ Nash Equilibrium ★	0 , 5 ★ Nash Equilibrium ★
Suspect 1: Testify	5 , 0 ★ Nash Equilibrium ★	2 , 2 ★ Nash Equilibrium ★

Suspect 1's payoff (row player)

Suspect 2's payoff (column player)

Instructions

Suspect 1's best responses

Consider each of Suspect 2's choices (columns) separately. Click the blue number that gives Suspect 1 the highest payoff in that situation.

Suspect 2's best responses

Consider each of Suspect 1's choices (rows) separately. Click the red number that gives Suspect 2 the highest payoff in that situation.

Find the Nash Equilibrium

The logic of best responses leads to the solution. The cell with two stars is the Nash Equilibrium.

Explanation

A best response is the action that gives a player the highest payoff, taking the other player's choice as given. To find Suspect 1's best responses, you fix each column (Suspect 2's action) and ask: which row gives Suspect 1 the higher blue payoff? You mark that with a ★. You do the same for Suspect 2 across rows.

A Nash Equilibrium is an outcome where every player is simultaneously playing a best response — no one can do better by unilaterally changing their strategy. In the Prisoner's Dilemma, the only Nash Equilibrium is (Testify, Testify), even though (Silent, Silent) gives both players a higher payoff. This is the "dilemma": individual rationality leads to a collectively worse outcome.