There isn’t a good justification for the prohibition on constant strategies, and the alternatives are too vague for it to be clear what the effects of prohibiting constant strategies actually is. You assumed the agents had the ability to “predispose themselves” to a particular action, but if they do that, then they still ultimately end up just making decisions based on what they think the other player is thinking, and not based on what they predisposed themselves to do, so it shouldn’t be called a predisposition. You’re trying to get something (mutual cooperation) out of nothing (a so-called predisposition that never gets acted on).
I edited the article to explain what I meant by predisposition, so please reread it.
As for constant strategies, adopting a constant strategy (if predicted by the opponent) leads to outcomes ranked 3rd or 4th in their preferences). If at least one of them adopts a constant strategy, then if the other predicts that, the other would adopt the defect invariant strategy regardless of the constant strategy adopted by the opponent. Thus, they would not adopt the constant strategy, because it is suboptimal.
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.
Please explain how it runs on wishful thinking?
There isn’t a good justification for the prohibition on constant strategies, and the alternatives are too vague for it to be clear what the effects of prohibiting constant strategies actually is. You assumed the agents had the ability to “predispose themselves” to a particular action, but if they do that, then they still ultimately end up just making decisions based on what they think the other player is thinking, and not based on what they predisposed themselves to do, so it shouldn’t be called a predisposition. You’re trying to get something (mutual cooperation) out of nothing (a so-called predisposition that never gets acted on).
I edited the article to explain what I meant by predisposition, so please reread it.
As for constant strategies, adopting a constant strategy (if predicted by the opponent) leads to outcomes ranked 3rd or 4th in their preferences). If at least one of them adopts a constant strategy, then if the other predicts that, the other would adopt the defect invariant strategy regardless of the constant strategy adopted by the opponent. Thus, they would not adopt the constant strategy, because it is suboptimal.
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.