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An Introduction to the Prisoner's Dilemma

The Prisoner's Dilemma is a game used to illustrate how cooperative, altruistic behavior could arise from agents (people, animals, organizations ...) whose motivations are purely selfish.  It is a simple game, designed to illustrate the most striking features of this dilemma.

Much of the terminology in this field is idiosyncratic, and the label Prisoner's Dilemma is no exception.  Though there are many situations that could illustrate selfish vs. altruistic choices, it is the plight of two prisoners that is always cited.

Two men (I mean no sexism, but the example always uses men) have jointly committed a grave crime.  They have been apprehended by the police, and are being held in separate cells, unable to communicate with each other.  The police have very little physical evidence indicating that these two men have committed the crime, and so they need to rely on confessions to make convictions.  The police offer each prisoner a simple choice - confess to the crime, or remain silent.  But they qualify the offer.  If both prisoners confess, then their punishment will be moderate.  If one prisoner confesses, while the other remains silent, the confessor will be given special treatment, a reward, for providing the necessary evidence, while the prisoner who remains silent will receive a heavier punishment.  If neither prisoner confesses, then the police have no evidence, and both men will go free.

So each prisoner has two choices - confess or remain silent.  In the odd terminology of this field, the confession is called Defection or Betrayal (the prisoner betrays his partner).  Remaining silent is called Cooperation or Trust (the prisoner maintains loyalty to his partner).  In the classical Prisoner's Dilemma, the rewards and punishments are the same for each prisoner (symmetrical).  The prisoners' dilemmas are expressed in the form of payoff matrices, where rows and columns indicate their choices, and the cells contain the payoff consequences.




OTHER'S CHOICES



SELF PAYOFF

OTHER PAYOFF


Coop
Defe

Coop
Defe
SELF'S
Coop
1
-2

1
2
CHOICES
Defe
2
-1

-2
-1

Different descriptions of the Prisoner's Dilemma use slightly different values for the rewards and punishments.  I present a matrix where mutual Cooperation yields positive reward, whereas mutual Defection yields negative punishment.

The essence of the dilemma (should you be a prisoner) is:

1) Your defection will always be the more rewarding choice, regardless of the choice your partner makes.

2) Your defection will always punish your partner, regardless of the choice he makes.

3) Yet, if, against all selfish rationality, you and your partner both Cooperate (with themselves, not with the police), then your mutual gain will be its greatest.

In this situation, how is it possible for the two prisoners to both rationally choose Cooperation, facing these consequences?  The answer to this question would (probably) provide the explanation of how cooperative or altruistic behavior arises from inherently selfish individuals.

As befits scientific or philosophical analysis, it is best to start with the most simple examples, and the Prisoner's Dilemma is as simple as it gets.  In a symmetrical Prisoner's Dilemma, statistically, there are only three degrees of freedom.

For this one-time decision, the most rational response is to Defect.  But what if the two Agents (I now use a more neutral term to label the participants in this dilemma) are to meet again, in a similar situation?  Unconditional Defection may no longer be the best strategy.

Analysis of the Prisoner's Dilemma, in its current incarnation, began with the publication of "The Evolution of Cooperation" by Robert Axelrod, approximately 20 years ago.  Game theory, as a discipline, had been established decades earlier.  In the 1950's the RAND Corporation used a modified form of the Prisoner's Dilemma to examine how the USA and the USSR might interact during the Cold War.  And before that, John von Newmann discussed game theory in 1920's.

Many computer tournaments and simulations have been conducted where decision-making strategies were pitted against each other in repeated rounds of the 2-choice Prisoner's Dilemma.  I present some of those results here.  But before you view these results, you might want to acquaint yourself with some of the eccentric terminology used in this field.  For the sake of conciseness, I also present some common abbreviations for these terms.  After reviewing the current wisdom regarding the Prisoner's Dilemma, I encourage you to read about my research and how it might describe the rise of ethical decision making.