Silent mixed duels

The paper considers a class of a zero-sum two-person games of timing on [0,1], in which Player 1 possesses m actions and behaves as in a silent discrete duel, and Player 2 with some amount M of resources behaves as in a silent non-discrete duel (m natural, M real). The accuracy functions of the players are increasing and absolutely continuous functions from [0,1] onto [0,1]. It is shown that this game has a value and optimal strategies for the players.