Discussion @ 1565. The Duel for Three @ Timus Online Judge

Vedernikoff Sergey Pay attention (+) [9] // Problem 1565. The Duel for Three 9 Oct 2007 22:14

Pay attention: players can shot in the air!

{AESC USU} Dembel Re: Pay attention (+) [5] // Problem 1565. The Duel for Three 9 Oct 2007 22:17

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

svr Re: Pay attention (+) [4] // Problem 1565. The Duel for Three 10 Oct 2007 09:21

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.

Vedernikoff Sergey Re: Pay attention (+) // Problem 1565. The Duel for Three 10 Oct 2007 17:05

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

Chmel_Tolstiy Re: Pay attention (+) [2] // Problem 1565. The Duel for Three 11 Oct 2007 12:35

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

svr Re: Pay attention (+) [1] // Problem 1565. The Duel for Three 11 Oct 2007 13:45

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

Vedernikoff Sergey Re: Pay attention (+) // Problem 1565. The Duel for Three 20 Nov 2007 21:56

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.

Snetch Re: Pay attention (+) [1] // Problem 1565. The Duel for Three 22 Dec 2007 07:37

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!

Vedernikoff Sergey Re: Pay attention (+) // Problem 1565. The Duel for Three 23 Dec 2007 04:31

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...

Fyodor Menshikov Re: Pay attention (+) // Problem 1565. The Duel for Three 22 Mar 2009 13:29

Vedernikoff Sergey wrote 9 October 2007 22:14

Pay attention: players can shot in the air!

Thanks!

Discussion of Problem 1565. The Duel for Three