The prisoners' dilemma story

abstraction of two people seperated by a wall

There are too many ways to tell the prisoner’s dillema story. The original is due to Tucker, a version memorialized in a handout dated May 1950, part of which I have transcribed below, as it is so hard to find. The story can be made real short by using a game where money is exchanged, or further frippery added to better motivate the payoffs.

Tucker’s version

Albert Tucker introduced what became known as the prisoner’s dilemma during a lecture he delivered at Stanford in 1950 while there on sabbatical. Tucker included results of his student John Nash on non-zero sum games and related experimental work by Merrill Flood and Melvin Dresher conducted at RAND. In some informal experiments they had asked colleagues well versed with von Neumann and Morgenstern’s book to play 100 rounds of a game having the prisoners’ dilemma structure, although they did not call it that (it went by the catchy name of A non-cooperative pair experiment). The expectation was that the two players would opt for the Nash equilibrium, even though they were not familiar with the concept, but they did not. Over repeated rounds of the game they chose collaborative moves without ever interacting. The numerical values of the matrix involved half-pennies (which would be 5ยข in 2016 dollars) and appeared random. Tucker simplified the matrix and created a fanciful story to go with it, as was his habit, to help convey its structure.

Tucker’s handout titled A two person dilemma starts out so:

Two men, charged with a joint violation of law, are held separ-
ately by the police. Each is told that
 (1) if one confesses and the other does not, the former
     will be given a reward of one unit in the latter
     will be fined two units,
 (2) if both confess, each will be fined one unit.
At the same time each has good reason to believe that
 (3) if neither confesses, both will go clear.

The handout was published as a part of short note written by Philip Straffin, Changing the way we think about the social world, for the UMAP Journal, volume 1, pp. 101-103 published in 1980 (another rare online item in 2016). He thanks William (not Robert) Lucas for giving him a copy of the handout. Most of the digging into this comes from Eric Rasmusen, the Dalton Professor at the Kelley School of Business, Indiana University. A scan can be found in his reading list on Games and Information.

The prisoners’ dilemma story

It is fun to add more details to the story. Here is my version:

The police apprehended two burglars at the back door of a jewelry store. At the police station they are placed in separate rooms. Having broken parole, each burglar faces at least one year in prison, but the prosecutor is hoping to get one or both for attempted robbery. The prosecutor explains separately to each that she is offering them the same deal: fink and get a year off your sentence. If found guilty they know they face up to three years in prison, but if one talks and the accomplice does not, the talkative one could go away without any jail time. The problem is that if they both fink, each will get three years minus the one year for cooperating. What should each burglar do?

Market exchange

The matrix of the prisoners’ dilemma is also the matrix for market transactions. If Alex and Bobbie want to exchange something, say Alex has a bag of potatoes and Bobbie a role of sausages, then at some point they need to meet for an exchange. If Alex shows up empty handed and takes Bobbie’s sausages, or if Bobbie shows up empty handed and takes the potatoes, then the cheater is better off than if they both had brought their goods to the exchange. If both come empty handed or do not show at all, then they are not better off, but neither are they worse off.

The story can be made fanciful by imagining it is two spies that exchange information without ever meeting. They arrange for drop offs located at different places, choosing either to cheat by taking the material without leaving something in exchange, or to cooperate, by also leaving something.

A direct interpretation

A simple interpretation of the prisoners’ dilemma is to assume it a game played by Alex and Bobbie. The two are placed in separate rooms and told that they are both getting the same offer: keep \$100 or give the other player \$300. Defecting means keeping the \$100, whereas collaborating means offering the \$300 in the hope that the other player will too.