receives the temptation payoff , while Red receives the "sucker's" payoff, . Similarly, if Blue cooperates while Red defects, then Blue receives the sucker's payoff , while Red receives the temptation payoff .

This can be expressed in normal form:

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

The payoff relationship implies that mutual cooperation is superior to mutual defection, while the payoff relationships

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