Maybe I have the solution for everyone having it though -
In the case of perfect knowledge on the part of the participants - for instance mathematicians picking a number between 1 and 10 and the one who gets the perfect number is killed - then obviously its best to go within the first nine.
In the other limiting case of no knowledge (as above) it doesn't matter where you go.
I'd guess that with knowledge between these two limits its still better to be early in the choosing - ideally first, but the advantage is not as good as the perfect knowledge limit.
In the case of only one person having any knowledge I suspect the same will apply - if his knowledge is perfect then he'll want a choice - i.e. to be anywhere in the first n-1 people - if his knowledge is not perfect then he'll still want to be early to have as great a choice as possible.
Re: Complications
Maybe I have the solution for everyone having it though -
In the case of perfect knowledge on the part of the participants - for instance mathematicians picking a number between 1 and 10 and the one who gets the perfect number is killed - then obviously its best to go within the first nine.
In the other limiting case of no knowledge (as above) it doesn't matter where you go.
I'd guess that with knowledge between these two limits its still better to be early in the choosing - ideally first, but the advantage is not as good as the perfect knowledge limit.
In the case of only one person having any knowledge I suspect the same will apply - if his knowledge is perfect then he'll want a choice - i.e. to be anywhere in the first n-1 people - if his knowledge is not perfect then he'll still want to be early to have as great a choice as possible.