Abstract
We consider the following "silent duel" of m players with a possible economic interpretation. Each player has one "bullet", which she can shoot at any time during the time interval (0,1). The probability that the i-th player hits the "target" at moment t is given by an increasing accuracy function fi(t) .T he winner is the player who hits the target first. Under natural assumptions on the functions fi(t) we prove the existence and uniqueness of a Nash equilibrium point in this game, and we provide an explicit construction of this equilibrium. Thisconstructionallowsustoobtainexactsolutionsformanyspecificexamples. Some of them are presented.
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