Re: Reducing risk for a client. Is this the right solution?
Hi,
The response from adviser 1, he quoted me. I didn't quote myself. Here is another response from adviser 2.
Adviser 2 solution:
I might as well throw my hat in here (even though the example is pretty macabre).
Fishy, as I was reading your last message, I thought the same thing as Tony did: that you are making an implicit assumption that the bullet was in the sixth chamber of the gun. This is clearly incorrect. If we knew that with certainty, then this would be a moot point because we would shoot first and take the 1, 3, 5 package instead of the 2, 4, 6 package and live with certainty (assuming the game is always played to completion).
The EV of this game is:
EV= .5(-infinity-->assuming we die) + .5(0-->assuming we get zero utility from living) = .5(-infinity)= -infinity
An interesting aside is to think about though (completely unrelated) is what we should do if we must play this game but then get the option of switching positions with our opponent. For example, shoot first then elect to take the 2, 4, 6 package or continue with the 1, 3, 5 package. Then this becomes similar to a Monte Hall problem and it is always better to shoot first and then switch to the 2, 4, 6 package since if we fire the first shot and then do not die, then given the fact that there is no bullet in chamber one the conditional probability of it being in chamber 3 or 5 is greater than the conditional probability of it being in chamber 2, 4, or 6.
This kind of gets back to what adviser 1 was saying in that as the game goes on, it becomes more and more likely that somebody will "default" and not play since the sample size of barrels is getting smaller and smaller and the conditional probability of the bullet being in the next chamber increases after each time somebody pulls the trigger and doesn't die.
Adviser 1, don't mean to be a nit (yes I do hehe), but if we assume people are risk averse then we must multiply all your probabilities by the natural log of the value of one's life.
If we absolutely must play this game (i.e. somebody is LITERALLY holding a gun to our head) then perhaps the best option would be to elect to shoot first, then grab the gun and continually fire at the other guy until we kill him.
(A better use of this guy's money would have been to go to a good psychiatrist).
|