In this paper we examine a two-person zero-sum timing game
with the following structure: Player I
has a gun with two bullets and player II has
a gun with one bullet and they fight a duel.
Both guns are silent so that neither player can determine
whether his opponent has fired the bullets or not.
Player I is at the place 0 at the moment when the duel begins
and he can move as he likes and player II is always at
the place 1. Accuracy functions,
which denote the probability of hitting the
opponent when each player fires his bullet, are identical
for both players.
If player I hits player II without being hit himself first,
then the payoff is +1; if player I is hit by player II without
hitting player II first, the payoff is -1;
if they hit each other at the same time or both survive,
the payoff is 0.
The objective of this paper is to obtain the game value
and the optimal strategies for the timing game.