One problem is that you seem to be assuming that the agents can predict each other. That is impossible, for the reason you explained yourself. If the agent predicts the other and then acts on that, then if they each predict the other, there is circular causality, which is impossible. So they cannot predict each other.
You cannot resolve the circular causality. What you are saying is that each agent realizes, “Oh, I can’t base my decision on predicting the other one. So I just have to decide what to do, without predicting.” Correct. But then they still cannot base their decision on predicting the other, since they just decided not to do that.
The question is where you stop in that method of procedure, and if each agent can perfectly predict where the other will stop thinking about it and act, the original circular causality will return.
One problem is that you seem to be assuming that the agents can predict each other. That is impossible, for the reason you explained yourself. If the agent predicts the other and then acts on that, then if they each predict the other, there is circular causality, which is impossible. So they cannot predict each other.
I explained how to resolve the circular causality with predisposition.
You cannot resolve the circular causality. What you are saying is that each agent realizes, “Oh, I can’t base my decision on predicting the other one. So I just have to decide what to do, without predicting.” Correct. But then they still cannot base their decision on predicting the other, since they just decided not to do that.
Yes, but they update that decision based on how they predict the other agent reacts to their predisposition? I added a diagram explaining it.
They temporarily decide on a choice (predisposition) say q. They then update q based on how they predict the other agent would react to q.
The question is where you stop in that method of procedure, and if each agent can perfectly predict where the other will stop thinking about it and act, the original circular causality will return.
Explain please?
At (D,D) no agent would change their strategy, because it is a Nash equilibrum.
(D,C) collapses into (D,D). (C,D) collapses into (D,D).
At (C,C) any attempt to change strategy leads to either (D,C) or (C,D) which both collapse into (D,D).
So (C,C) forms (for lack of a better name) a reflective equilibrium. I don’t understand how you reached circular causality.