A DUEL UNDER ARBITRARY MOVING OF THE DUELISTS

The purpose of the paper is to solve a mixed duel in which numbers of shots given to the players are independent random variables taking the values zero or one. The players know the distributions of these rando m variables as well as the accuracy function P the same for both playe rs. It is assumed that players can move as they like and that the maxi mum speed of the first player is greater than that of the second playe r. It is shown in the paper that the game has an optimum value and a p air of optimal strategies is found. The duel is solved under general a ssumptions on the payoff function and the accuracy function.