I wonder what would happen if one were to remove b and play the game iteratively. The game stops after 50 iterations or the first time S fails the test or defects.
b is then essentially replaced by S’s expected payoff over the remaining iterations if he remains loyal. However M would know this value so the game might need further modification.
I think we should still keep b even with the iterations, since I made the assumption that “degrees of loyalty” is a property of S, not entirely the outcome of a rational-game-playing.
(I still assume S rational outside of having b in his payoffs)
Otherwise those kind of tests probably makes little sense.
I also wonder what happens if M doesn’t know the repulsiveness of the test for certain, only a distribution of it (ie: CIA only knows that on average killing your spouse is pretty repulsive, except this lady here really hates her husband, oops), could that make a large impact.
I guess I was only trying to figure out whether this “repulsive loyalty test” story that seems to exist in history/mythology/real life in a few different cultures has any basis in logic.
Thanks, the final result is somewhat surprising, perhaps it’s a quirk of my construction.
Setting r to be higher than v does remove the “undercover agents” that have practically 0 obedience, but I didn’t know it’s the optimal choice for M.
I wonder what would happen if one were to remove b and play the game iteratively. The game stops after 50 iterations or the first time S fails the test or defects.
b is then essentially replaced by S’s expected payoff over the remaining iterations if he remains loyal. However M would know this value so the game might need further modification.
I think we should still keep b even with the iterations, since I made the assumption that “degrees of loyalty” is a property of S, not entirely the outcome of a rational-game-playing.
(I still assume S rational outside of having b in his payoffs)
Otherwise those kind of tests probably makes little sense.
I also wonder what happens if M doesn’t know the repulsiveness of the test for certain, only a distribution of it (ie: CIA only knows that on average killing your spouse is pretty repulsive, except this lady here really hates her husband, oops), could that make a large impact.
I guess I was only trying to figure out whether this “repulsive loyalty test” story that seems to exist in history/mythology/real life in a few different cultures has any basis in logic.