If 2W<X+Y, then defecting while your playmate cooperates creates value (relative to cooperating). From a social perspective, Krump/Flitz or Flitz/Krump is preferable to Krump/Krump; and in an iterated game of this sort, you’d prefer to alternate X with Y, than to get a constant W. Wikipedia still classes this as a Prisoner’s Dilemma, but I think that’s dubious terminology, and I don’t think it’s standard. I might offhand suggest calling it the Too Many Cooks game.
But the only Nash is still Z,Z, and so there is an incentive to defect from Krump/Flitz. Furthermore, that defection reduces total social welfare, so I think it makes sense to call this variant “PD” still.
I absolutely think it makes sense, I just don’t know if I endorse it. Maybe it’s context dependent; someone who just wants to write about the Nash equilibria of games won’t have any reason to distinguish these cases, and lumping them all under “Prisoner’s Dilemma” seems absolutely fine. But Iterated Prisoner’s Dilemma (in my sense) is probably a very different game from Iterated Too Many Cooks, but I’m not sure I’ve ever heard anyone talk about ITMC. And from a social perspective, “punish anyone who defects in a PD” makes sense but “punish anyone who doesn’t cook in TMC” risks leaving value on the table.
Maybe it would make sense to call them a “(something) Prisoner’s Dilemma” and a “(something else) Prisoner’s Dilemma” but I’m not sure what the somethings would be.
Maybe it would make sense to call them a “(something) Prisoner’s Dilemma” and a “(something else) Prisoner’s Dilemma” but I’m not sure what the somethings would be.
Later I used synergistic/discordant as these somethings.
But the only Nash is still Z,Z, and so there is an incentive to defect from Krump/Flitz. Furthermore, that defection reduces total social welfare, so I think it makes sense to call this variant “PD” still.
I absolutely think it makes sense, I just don’t know if I endorse it. Maybe it’s context dependent; someone who just wants to write about the Nash equilibria of games won’t have any reason to distinguish these cases, and lumping them all under “Prisoner’s Dilemma” seems absolutely fine. But Iterated Prisoner’s Dilemma (in my sense) is probably a very different game from Iterated Too Many Cooks, but I’m not sure I’ve ever heard anyone talk about ITMC. And from a social perspective, “punish anyone who defects in a PD” makes sense but “punish anyone who doesn’t cook in TMC” risks leaving value on the table.
Maybe it would make sense to call them a “(something) Prisoner’s Dilemma” and a “(something else) Prisoner’s Dilemma” but I’m not sure what the somethings would be.
Later I used synergistic/discordant as these somethings.