Generalized Form
The structure of the traditional Prisoners’ Dilemma can be analyzed by removing its original prisoner setting. Suppose that the two players are represented by colors, red and blue, and that each player chooses to either "Cooperate" or "Defect".
If both players play "Cooperate" they both get the payoff A. If Blue plays "Defect" while Red plays "Cooperate" then Blue gets B while Red gets C. Symmetrically, if Blue plays "Cooperate" while Red plays "Defect" then Blue gets payoff C while Red gets payoff B. If both players play "Defect" they both get the payoff D.
In terms of general point values:
| Cooperate | Defect | |
|---|---|---|
| Cooperate | A, A | C, B |
| Defect | B, C | D, D |
To be a prisoner's dilemma, the following must be true:
B > A > D > C
The fact that A>D implies that the "Both Cooperate" outcome is better than the "Both Defect" outcome, while B>A and D>C imply that "Defect" is the dominant strategy for both agents.
It is not necessary for a Prisoner's Dilemma to be strictly symmetric as in the above example, merely that the choices which are individually optimal result in an equilibrium which is socially inferior.
Read more about this topic: Prisoner's Dilemma
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