A classmate put forth this conundrum in my Public Choice class this morning:
Let's say you are in a three-way duel, and all three of you have a gun with an unlimited amount of bullets. Your two opponents hit with an accuracy of 90% and 80%, and you shoot with a success rate of 50%. Sequential shooting rules apply, and it's your turn. What do you do? He was convinced of a set course of action that would emerge in the short-run; I'm not entirely sold on the idea. I'm curious what everyone else thinks. I also think the far more interesting scenario is if everyone has to choose at once, instead of sequentially.
I then got to thinking about a more general scenario-- a three-way duel, and everyone in the group has one bullet. Accuracy rates would matter at the limit, but anything away from that and I think risk preference plays a bigger role. Even more so in a four-person duel with one bullet apiece-- accuracy matters at the limit, but now you've got risk preferences mixed in with group sanction effects, though group sanction exists only insofar as there is more than one period to make decisions (all-at-once decision making with the option of inaction).