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Pfft comments on Prisoner's Dilemma on game show Golden Balls - Less Wrong
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The usual definition of Nash equilibrium requires only ≤, not <, so Defect-Defect, Cooperate-Defect and Defect-Cooperate are Nash equilibria (and pure) but not "strong" Nash equilibria. You want this definition, because games need not have strong Nash equilibria, even if you allow mixed strategies.
(Apparently the game is called "weak prisoner's dilemma" in the literature).
Oops, didn't realize that.