A silent duel under arbitrary movements

The paper considers the dual game in which each player has one missile, maximum velocities of players are v1 and v2, respectively, with v1>v2>0. Each player knows that the other one has one bullet. The duel is silent, that is, neither player hears the shot of his adversary. The duel is a zero-sum, of course. The paper refers primarily to literature on the games of timing. The paper gives the strategies of both players for arbitrary accuracy and payoff functions and for arbitrary (velocity of) motion of each player.