Okay. I think I get what you are saying now, but it wasn’t clear on my initial read through.
I did understand on the initial read-through (or, currently think I understand?) that when you say “most games turn out to be Battle of the Sexes in practice”, you mean that there is an emergent property of the iterated game that turns it into Battle of the Sexes.
My current summary of what you are intending to say (correct me if I got it wrong ) is:
1. Most prisoners dilemma games are actually iterated.
2. Iterated prisoners dilemma is actually a different game with a different payoff matrix that has a different set of nash equilibria. Choosing which strategy to play in iterated prisoner’s dilemma is similar to playing Stag Hunt.
3. Then there is a further step where the process of deciding on how to coordinate (meta-strategy?) that you are choosing in a stag hunt is more similar to battle of the sexes.
I think what I was missing the first time through was #2. I was intepreting you to mean “the thing about stag hunts is that they are iterated, and your PD is probably iterated”, where what you actually meant was “your PD is iterated, and iterated PD is actually isomorphic to stag hunt.”
Okay. I think I get what you are saying now, but it wasn’t clear on my initial read through.
I did understand on the initial read-through (or, currently think I understand?) that when you say “most games turn out to be Battle of the Sexes in practice”, you mean that there is an emergent property of the iterated game that turns it into Battle of the Sexes.
My current summary of what you are intending to say (correct me if I got it wrong ) is:
1. Most prisoners dilemma games are actually iterated.
2. Iterated prisoners dilemma is actually a different game with a different payoff matrix that has a different set of nash equilibria. Choosing which strategy to play in iterated prisoner’s dilemma is similar to playing Stag Hunt.
3. Then there is a further step where the process of deciding on how to coordinate (meta-strategy?) that you are choosing in a stag hunt is more similar to battle of the sexes.
I think what I was missing the first time through was #2. I was intepreting you to mean “the thing about stag hunts is that they are iterated, and your PD is probably iterated”, where what you actually meant was “your PD is iterated, and iterated PD is actually isomorphic to stag hunt.”