Editing Prisoner's dilemma (section)

==Generalized form==
{{More citations needed section|date=January 2023}}

The structure of the traditional prisoner's dilemma can be generalized from its original prisoner setting. Suppose that the two players are represented by the colors red and blue and that each player chooses to either "cooperate" or "defect".

If both players cooperate, they both receive the reward <math>R</math> for cooperating. If both players defect, they both receive the punishment payoff <math>P</math>. If Blue defects while Red cooperates, then Blue receives the temptation payoff <math>T</math>, while Red receives the "sucker's" payoff, <math>S</math>. Similarly, if Blue cooperates while Red defects, then Blue receives the sucker's payoff <math>S</math>, while Red receives the temptation payoff <math>T</math>.

This can be expressed in [[Normal-form game|normal form]]:

{| class="wikitable" style="text-align:center"
|+ Canonical prisoner's dilemma payoff matrix
! {{diagonal split header|{{color|#009|Blue}}|{{color|#900|Red}}}}
! scope="col" style="width:60px;" | {{color|#900|Cooperate}}
! scope="col" style="width:60px;" | {{color|#900|Defect}}
|-
! scope="row" style="width:60px;" | {{color|#009|Cooperate}}
| {{diagonal split header|{{color|#009|''R''}}|{{color|#900|''R''}}|transparent}}
| {{diagonal split header|{{color|#009|''S''}}|{{color|#900|''T''}}|transparent}}
|-
! scope="row" | {{color|#009|Defect}}
| {{diagonal split header|{{color|#009|''T''}}|{{color|#900|''S''}}|transparent}}
| {{diagonal split header|{{color|#009|''P''}}|{{color|#900|''P''}}|transparent}}
|}

and to be a prisoner's dilemma game in the strong sense, the following condition must hold for the payoffs:

:{{tmath|T > R > P > S}}

The payoff relationship {{tmath|R > P}} implies that mutual cooperation is superior to mutual defection, while the payoff relationships {{tmath|T > R}} and {{tmath|P > S}} imply that defection is the dominant strategy for both agents.