Pay attention: players can shot in the air!

YES
"Each time a duelist may aim at any other alive duelist or purposely shoot in the air."

Conditions are not defined fully.
Let A killed and B,C presense.
Optimal strategy for each: to  shoot in air with pb=1 and pc=1.

In such a situation every will have an incentive to shoot at other player. Pure prisoners' dilemma!

The accuracy of A is equal to 1, and the accuracies of B and C are different

With pB=pC=1 I meant objective functions for optimal strategy of B and C as probability to be alive. This maximal income achived when both shoot in air. This correspond to real life:if main aim to be alive peace is best solution.
P.S. Having AC understood that such situation is absent in real tests for 1565.
More exactly: the strategy have a next nature:
when B and C are without A they shout to each other
to kill one and geometric progressive appears.

Edited by author 26.10.2007 18:54

Edited by author 26.10.2007 19:03

This is not correct. Take any book on game theory and read there the concept of Nash Equilibria. Then apply it to the solution of the problem and you'll find that if there are 2 players left, they will always shoot at each other.

Why should anybody want to shoot in the air at any moment?????? That makes no sense: if you shoot in the air, your opponent will have more chance to kill you, since you skipped your turn!

Let player B shoots first, and he is the weakest among all players (for simplicity, let we assume PC also = 1). If he shoots and kills any pleyer, then after shot of the player who alived he will definitely die. The best strategy for him is to shoot in the air and wait, while in the next turn player C kills player A, and then player B has a chance to win by killing C...

Thanks!