Institute of Semantic Restructuring

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The Prisoners' Dilemma

What matters more...

...what you do, or how you label what you do? Are you sure? I don't mean, "Which one should be more important?" I mean, "Which one truly has the biggest impact on your behavior?" Perceptions and labels control our actions to a much larger extent than you might think. As an example, here is a little story, followed by a game. Play the game, read your results, and then ask yourself how much labels control your life.

Frankie and Johnny were robbers...

Once upon a time there were two criminals, Frankie and Johnny. The local police arrested them on charges of armed robbery. Frankie and Johnny were guilty as sin. However, the District Attorney's office didn't have the hard evidence for a conviction. The circumstantial evidence would get a grand jury indictment (1), but there was little chance of the DA's winning the case. To make the most of the situation, the DA had Frankie and Johnny brought into her office for a little talk.

"We all know," said the DA, "that you're guilty, so I won't ask. I'll even tell you a little secret. As sure as we all know you're guilty, I also know that we don't have the evidence to put you two away like you deserve. If this goes to trial, all I can do is pop you for illegal possession of firearms. That's just a six month trip for you both. All you have to do is keep your lips sealed, and you can resume you criminal careers in six short months. Or you could both confess, nice and easy, like good little criminals. Do that and I'll promise you, nice and legal, the minimum for armed robbery...a short two years instead of the maximum twenty you'd get if I could win this case."

Frankie looked at Johnny. Johnny looked at Frankie. Neither said a word. Silence would get them each six months, squealing would get them four times that. Easy choice; but the DA continued.

"There is one other possibility. If only one of you confesses, turns State's Witness, I'll get them off Scot free, and the other will get burned for the full twenty years. If you sing and your buddy doesn't, you're on your way home. Not even the short six months. Free."

"You might want to think about it, and I'm going to give you the chance." Whereupon the DA instructed the guards, "Have these prisoners taken to separate cells. They are not to talk to each other until they have each decided: confess, or don't confess."


What to do?

The story you just read is a dramatized version of a classic called "The Prisoner's Dilemma." According to Dr. Paul Watzlawick, in his book "How Real is Real,"

The concept of interdependence is perhaps best introduced by the game-theoretical model of the Prisoner's Dilemma, formulated and named by Albert W. Tucker, a professor of mathematics at Princeton. In it's original version, a district attorney is holding two men suspected of armed robbery. There is not enough evidence to take the case to court, so he has the two men brought to his office. He tells them that in order to have them convicted he needs a confession; without one he can charge them only with illegal possession of firearms, which carries a penalty of six months in jail. If they both confess, he promises them the minimum sentence for armed robbery, which is two years. If, however, only one confesses, he will be considered a state witness and go free, while the other will get twenty years, the maximum sentence. Then, without giving them a chance to arrive at a joint decision, he has them locked up in separate cells from which they cannot communicate with each other.

Every discussion of game theory I have seen includes a reference to this story. Texts offer it as the basic unit of game theory. Geometry has the point and the line; Game Theory has the Prisoner's Dilemma.

In early 1996 I found a program for playing the Prisoner's Dilemma against a computer, on line, as a way of exploring basic ideas of game theory. I thought this was great. I played the game, choosing to confess. Next thing I knew, the computer told me my strategy of confessing was cheating! To be accused of cheating by a computer program didn't sit well with me, but it made me think.

Many presentations of the Prisoner's Dilemma lead to a conclusion or a moral. The moral usually claims it is best to trust and to cooperate with others. Trusting is the option dictated by the "science" of game theory, or so some game theorists claim. This portion of my site is dedicated to exploring and exposing the fallacies(2) used to support this moral.

Below you can see a 2 by 2 grid that represents the situation in the Prisoner's Dilemma story. You might notice that the stakes in this game are all negative, there is nothing to win. The options are between various amounts to lose, with a loss of zero as the best possible "score." This game is not about how much a player can win; it is about how much each can keep from losing(3).

After the initial grid, there are seven pairs of "radio buttons," each describing a different complementary set of strategies. Play against the computer by checking the strategy you prefer in each pair, then click the submit button. You will next see seven sets of results, one for each strategy you choose.

Note: The payoff grid for all seven sets of strategies(4) is indicated by the one grid below.


Your name:

Confessing, or Not Confessing?
Competing, or Cooperating?
Cheating, or Fidelity?
Defecting, or Patriotism?
Investing, or Gambling?
Conserving, or Risking?
A, or B?

In the classic form of the dilemma, strategy doesn't really exist. The game plays for only one round, and there is no way one player's choice can affect the other player's choice. The seven results you receive from playing are each calculated independently of the others. There is a vital difference between playing a game once and only once, as in the story above, and playing repeatedly. Later pages on this site will explore such differences in game structure.

Just above the pay off grid there is a note saying the same grid controls all seven sets of choices. This means Confessing, Competing, Cheating, Defecting, Investing, Conserving, and A were identical, based on the possible pay-offs. All of these options carried the possible results of zero months served to 24 months served. Going strictly by the pay off grid, Not Confessing, Cooperating, Fidelity, Patriotism, Gambling, Risking, and B were also all the same. Each of these options carried the possible results of six months served or two-hundred-forty months served.

People often fail to base their choices in life on potential results of those choices. Instead, they act on their feelings about the labels of their choices. Many people have trouble equating Cheating with Conserving, or Patriotism with Gambling, but your feelings about those words make no difference in scoring this game. We need to pay attention to how we---and others---apply labels to our actions, and how labels lead us to make choices we might regret.


Footnotes

A link in the text brought you here, and the links here will return you.

(1) "Given today's Grand Jury system, I could indict a ham sandwich."
--Anonymous attorney.

(2) Please recognize the difference between challenging a fallacy and disagreeing with a conclusion. I am all in favor of cooperation and trust, when circumstances don't prohibit them. What I oppose is the venerating of cooperation and trust at all costs. I oppose cooperating with and trusting con artists, yet this is exactly what happens to people who put trust before consequences. (By definition, a con artist is one who gains and then abuses trust, "confidence." Most cases of kidnapping and child abuse share one trait; the perpetrator gains and then abuses the trust of the victim's guardians .)

(3) Later pages on this site will explore differences among winning, gaining, and not losing. Some game theorists seem to think the difference between losing one dollar and losing zero dollars is the same as the difference between winning zero dollars and winning one dollar. This is the fallacy of false quantification. False quantification is like having one orange and one apple and then saying they are the same because there is one of each. True, the difference between losing a dollar and not losing a dollar is one dollar, and the difference between winning a dollar and not winning a dollar is one dollar. Quantitatively these payoffs are the same, but; qualitatively, the difference between being short a dollar and having a dollar extra is profound. .

(4) Later pages will also discuss strategies in the Prisoner's Dilemma and other game theory topics, including:

  1. The difference between fluctuating labels in a stable pay-off grid (as played on this page) and stable labels for a fluctuating grid.
  2. Important differences between turns and rounds. As a brief example, the classic children's game of "rock-scissors-paper" is a single turn game. It can be played for one round or many, but each game takes only one turn to play. In contrast, chess is a multiple turn game (two turns minimum). Like "rock-scissors-paper", chess can be played for one round or many. The Prisoner's Dilemma is a single-turn, single-round game.
  3. Differences between different types of multi-round games, such as playing a known number of rounds or an unknown number of rounds. Each of these distinctions shed light on problems with standard presentations of game theory. At the same time each of the above distinctions offers insight into the ways labels control behavior for better or for worse .