On a duel with time lag and equal accuracy functions (Q1095049)

This paper deals with a duel with time lag which has 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. The gun of player I is silent and the gun of player II is noisy with time lag t (i.e., if player II fires at time x, then player I knows it at time \(x+t)\). They both have equal accuracy functions. Furthermore, if player I hits player II without being hit himself before, the payoff is \(+1\); if player I is hit by player II without hitting player 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 the optimal strategy for each player, the game value, and some examples.