Game theory question: after mutual silence, who is supposed to cooperate first?
I've been thinking about Tit-for-Tat and I feel like I'm missing something.
The basic rule is simple: start by cooperating, then copy whatever the other person did last.
But doesn't that assume there will always be another round?
Imagine this:
A does something unreasonable to B.
B confronts A.
A doesn't apologize or really respond.
So B stops talking to A.
Now they're both silent.
A's last meaningful move was arguably a defection. B already responded to that by defecting/withdrawing.
But now suppose weeks pass.
There isn't automatically another turn. Someone has to create the next interaction.
So what is B supposed to do under Tit-for-Tat?
If B contacts A, is B supposed to defect because A's previous move was defection?
Or does initiating contact itself count as cooperation?
Or should B simply wait indefinitely because technically it's A's turn to cooperate?
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That made me wonder whether the real-world game isn't just:
Cooperate / Defect
but actually:
Initiate / Don't Initiate → then Cooperate / Defect
I found some research on optional/repeated games where players can leave and later rejoin, so apparently this isn't completely unexplored.
But I'm curious how someone who actually understands game theory would model this.
Is there a standard solution to this, or does Tit-for-Tat genuinely become underspecified once the players control whether another round happens at all?