ON A DUEL WITH TIME-LAG AND ARBITRARY ACCURACY FUNCTIONS

This paper deals with a two-person zero-sum game called duel with the following structure: Each of two players I and II has a gun with one bullet and he can fire his bullet at any time in [0, 1], aiming at his opponent. If I or II fires at time x, he hits his opponent with probability p (x) or q(x), respectively. The gun of I is silent, and hence, II does not know whether his opponent has fired or not, and the gun of II is noisy with time lag t, where t is a positive constant, i.e., if II fires at time x then I knows it at time x + t. Further, if I hits II without being hit himself before, the payoff is 1; if I is hit by II without hitting II before, the payoff is -1; if they hit each other at the same time or both survive, the payoff is 0. This paper gives optimal strategy for each player and the value of the game.