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Prisoner's Dilemma

This page introduces the concept of a Prisoner's Dilemma. Additional information can be found in Douglas R. Hofstadter's book Metamagical Themas: Questing for the Essence of Mind and Pattern, and my article Offshoring: Individual Short-Term Gain versus Collective Long-Term Loss? published in IEEE IT Professional, July-August 2005.

Prisoner's Dilemma is a topic within Game Theory, and Game Theory is a topic within Applied Mathmatics.

Prisoner's Dilemma describes in Game Theory terms a transaction between two participants, and the resulting payoff, provided two prerequisites are satisfied (see below). The transaction can be either one time or multiple iterations. The payoff is represented by a payoff matrix.

Participant A is used to indicate the first participant, Participant B is used to indicate the second participant.

The letters T, R, P, S are used to represent the payoff exchanged between Participant A and Participant B.

Payoff Matrix
Prisoner's Dilemma Payoff Matrix

R is the reward, the total payoff for mutual cooperation between Participant A and Participant B.

T is the temptation payoff for defecting with its resulting higher payoff for the defector. Defection occurs when an individual, group, or organization acting in his/her/its own best interest, regardless of the consequences to others.  Or as Noam Chomsky put it, "Greed and the desire to maximize personal gain at the expense of the other".

S is the sucker's payoff that the cooperating participant receives when the other participant defects.

P is the punishment for mutual defection.


The two prerequisites mentioned above are:

  • T > R > P > S
  • (T + S) / 2 < R
The first simply states it is more profitable for a participant to defect than cooperate for a single transaction.  As an example, a business might garner greater profits by defecting rather than by cooperating (at least in the short term).  It would do so without any moral concern, as long as the transaction did not involve deception or fraud.

The second states that the average of the temptation for defecting and the sucker's payoff is less than the reward for mutual cooperation.  For example, by keeping key operations in house instead of offshoring, a business could retain its key corporate asset - knowledge (skills, intellect, creativity, and know-how of individuals) in the organization, creating value for the customer ("Tougher Than Ever: The Information Age Makes Management More Complex, Not Simpler," Intelligent Enterprise, 30 Oct. 2002, p. 14).   In other words, a growing economy producing the most wealth overall is based on cooperation, not defection.

The payoff matrix and the central issue are the characteristics identifying a case of Prisoner's Dilemma. Prisoner's Dilemma is a paradox with practical applications - its central issue is, Does logic prevent cooperation?


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