Your Best Move? A Prisoner's Dilemma Teaser

Two suspects, two rooms, one choice. Work out the best move, then see why the logical answer leaves both players worse off.

Two people are arrested and put in separate rooms. Neither can talk to the other. Each gets the same offer, and each has to pick before the door opens. What would you do?

Here is the setup, with illustrative numbers. Alice and Bob are accomplices. Each can stay silent or confess.
If Alice confesses and Bob stays silent, Alice goes free and Bob serves 10 years. The reverse also holds.
If both confess, each serves 5 years.
If both stay silent, each serves 1 year.
You are Alice. Bob faces the same choice. What is your best move?

Two empty, separate interrogation rooms lit by single hanging lamps, with closed steel doors waiting to open, illustrating two suspects who must each make a choice alone.

Take a minute first

Before you read on, pick your move. Then ask one more question: what do you expect Bob to do? Write both answers down if you like.

The sentence counts above are made up for the teaser. The Stanford Encyclopedia of Philosophy describes the puzzle in general terms. Two suspects are questioned separately, and whatever the other does, each is better off confessing [1]. Yet both confessing leaves each worse off than both staying silent. Keep that tension in mind as you test your instinct against the logic below.

The answer

Confess. Walk through it from Alice's chair.

Suppose Bob stays silent. If you stay silent too, you serve 1 year. If you confess, you walk free. Confessing is better.

Now suppose Bob confesses. If you stay silent, you serve 10 years. If you confess, you serve 5. Confessing is better again.

So confessing wins in both cases. Game theorists call that a dominant strategy. Bob reasons the same way, so both of you confess and both serve 5 years. Mutual silence would have cost each of you only 1 year [1]. Each choice is sound on its own terms. Together they leave both players worse off.

A common reading is that the puzzle exposes a clash between individual and group rationality. Self-interested players can all end up worse off [1]. Some philosophers frame it instead as a choice between selfishness and altruism, since each move helps one side whatever the other does [1]. The sources do not settle how the one-shot puzzle should be resolved. The Stanford entry says later editions will survey attempts to solve it.

Where the puzzle came from

Merrill Flood and Melvin Dresher devised the puzzle in 1950 during game theory work at the RAND Corporation. Albert Tucker later gave it the prison-sentence story and the name it carries today [3][4]. The story is a costume. The same shape appears in other settings where cheating pays for one side and hurts both when each does it.

Econlib offers a business version. Two firms each choose a high or low price. If both charge high, each earns ten million dollars a month. If one undercuts, it earns twelve million while the rival falls to seven million. If both go low, each earns nine million [4]. Low pricing is the dominant move, just as confessing is. Both firms drift to nine million when ten was on offer. The same source applies the logic to arms races between nations [4].

The idea also drew a huge following. The Stanford entry reports over a thousand articles in the sixties and seventies, and a bibliography of 209 entries on Axelrod's research from 1988 to 1994 [3].

What changes when the game repeats

Play the game once and the answer above stands. Play it again and again with the same partner, and strategies matter. The Stanford entry on the iterated game lists several [2]:

Unconditional Cooperator: always cooperates.
Unconditional Defector: always defects.
Tit for Tat: cooperates first, then copies the opponent's previous move.
Pavlov: cooperates if both players moved alike last round, and defects if they moved differently.

Take Tit for Tat against itself. Round one, both cooperate. Round two, each copies the other's cooperation. The pattern holds.

Now let an Unconditional Defector face Tit for Tat. In round one, Tit for Tat cooperates and the defector gains. From round two on, Tit for Tat copies the defection, so both defect. The easy gain does not come back. This follows from the strategy definitions in the source.

The entry also describes gentler variants. Gradual Tit for Tat apologizes by cooperating in the following two rounds. Generous Tit for Tat sometimes cooperates even after a defection, with a probability set by the payoffs [2]. The source also notes that Omega Tit for Tat finished second in the 2005 reprise of Axelrod's tournament.

The sources I have do not say which strategy wins overall, and they give no method for picking one [2]. They do point to a question you can ask in any real situation: will we meet again?

Questions to carry away

Two checks help when you spot this pattern outside a puzzle. First, is the game played once or repeated? The strategies in the source are defined for the repeated version [2]. Second, do the payoffs really reflect what each player wants? The Stanford entry notes the dilemma can hold even when they do not reflect self-interest [1].

Two separate, empty rooms lit in contrasting cool and warm light, divided by glass and reflected on a polished floor, suggesting two people facing the same isolated choice.

So, did you confess? If you stayed silent, you were hoping Bob would too. That is the whole puzzle in one hunch.