C,C − 10k, 10k (after trade) C,D − 0k, 15k (assuming I give him what I consider useless) D,C − 15k, 0k (and vice versa) D,D − 5k, 5k
I am not tracking how this is any different than the standard model except you can communicate beforehand. Does it have to do with the >99% certainty of value?
(Note) Thinking and typing here, so no guarantee of value. If someone sees a misstep though, please point it out. I am still learning this.
So… that would >99% certainty of 15k, 15k on cooperation, <1% certainty of 15k, 15k. Actually, no, that would be 15k, 0k if I was right and 0k, 15k if he was right. So ignore that, here is a new matrix.
I suppose, since we are assuming trading it would make it simpler to just consider the rewards as pooled afterwards. It really makes no difference which doctor ends up with the medicine.
C,C − 100% 10k; 99% 0k; 99% 15k; 99% 5k; <1% 5k
Taking out the failed diagnoses:
C,C − 100% 10k C,D − 99% 15k D,D − 100% 5k
Yeah, that is not a prisoner’s dilemma. Especially if you can convince the other doctor to cooperate. Assuming probability P for the other doctor cooperating (this is the part where I may need help):
C: P 10k + (1 - P) 99% 15k + (1 - P) 5k
And that is as far as I can go. I assume that there is some way to map which choice is better for which values of P.
Building the typical payoff matrix:
C,C − 10k, 10k (after trade)
C,D − 0k, 15k (assuming I give him what I consider useless)
D,C − 15k, 0k (and vice versa)
D,D − 5k, 5k
I am not tracking how this is any different than the standard model except you can communicate beforehand. Does it have to do with the >99% certainty of value?
(Note) Thinking and typing here, so no guarantee of value. If someone sees a misstep though, please point it out. I am still learning this.
So… that would >99% certainty of 15k, 15k on cooperation, <1% certainty of 15k, 15k. Actually, no, that would be 15k, 0k if I was right and 0k, 15k if he was right. So ignore that, here is a new matrix.
C,C - >99% 10k, 0k; 99% 0k, 0k; 99% 15k, 0k; 99% 5k, 0k; <1% 0k, 5k
I suppose, since we are assuming trading it would make it simpler to just consider the rewards as pooled afterwards. It really makes no difference which doctor ends up with the medicine.
C,C − 100% 10k; 99% 0k; 99% 15k; 99% 5k; <1% 5k
Taking out the failed diagnoses:
C,C − 100% 10k
C,D − 99% 15k
D,D − 100% 5k
Yeah, that is not a prisoner’s dilemma. Especially if you can convince the other doctor to cooperate. Assuming probability P for the other doctor cooperating (this is the part where I may need help):
C: P 10k + (1 - P) 99% 15k + (1 - P) 5k
And that is as far as I can go. I assume that there is some way to map which choice is better for which values of P.