I am wondering what a PD tournament would look like if the goal was to maximize the score of the group rather than the individual player. For some payoff matrices, always cooperate trivially wins, but what if C/D provides a greater net payoff than C/C, which in turn is higher than D/D? Does that just devolve to the individual game? It feels like it should, but it also feels like giving both players the same goal ought to fundamentally change the game.
I haven’t worked out the math; the thought just struck me while reading other posts.
The game you are talking about should not be called PD.
The solution will be for everyone to pick randomly, (weighted based on the difference in C/C and D/D payoff) until they get a C/D outcome, and then just picking the same thing over and over. (This isn’t a unique solution, but it seems like a Schelling point to me.)
what if C/D provides a greater net payoff than C/C
The Prisoner’s Dilemma is technically defined as requiring that this not be the case, precisely so that one doesn’t ahve to consider the case (in iterated games) where the players agree to take turns cooperating and defecting. You are considering a related but not identical game. Which is of course totally fine, just saying.
If you allow C/D to have a higher total than CC, then it seems there is a meta-game in coordinating the taking-turns—“cooperating” in the meta-game takes the form of defecting only when it’s your turn. Then, the players maximise both their individual scores and the group score by meta-cooperating.
I am wondering what a PD tournament would look like if the goal was to maximize the score of the group rather than the individual player. For some payoff matrices, always cooperate trivially wins, but what if C/D provides a greater net payoff than C/C, which in turn is higher than D/D? Does that just devolve to the individual game? It feels like it should, but it also feels like giving both players the same goal ought to fundamentally change the game.
I haven’t worked out the math; the thought just struck me while reading other posts.
The game you are talking about should not be called PD.
The solution will be for everyone to pick randomly, (weighted based on the difference in C/C and D/D payoff) until they get a C/D outcome, and then just picking the same thing over and over. (This isn’t a unique solution, but it seems like a Schelling point to me.)
The Prisoner’s Dilemma is technically defined as requiring that this not be the case, precisely so that one doesn’t ahve to consider the case (in iterated games) where the players agree to take turns cooperating and defecting. You are considering a related but not identical game. Which is of course totally fine, just saying.
If you allow C/D to have a higher total than CC, then it seems there is a meta-game in coordinating the taking-turns—“cooperating” in the meta-game takes the form of defecting only when it’s your turn. Then, the players maximise both their individual scores and the group score by meta-cooperating.