  We consider a game in which each player must find a compromise between more
daring strategies that carry a high risk for him to be eliminated, and more
cautious ones that, however, reduce his final score. For two symmetric players
this game was originally formulated in 1961 by Dresher, who modeled a duel
between two opponents. The game has also been of interest in the description of
athletic competitions. We extend here the two-player game to an arbitrary
number $N$ of symmetric players. We show that there is a mixed-strategy Nash
equilibrium and find its exact analytic expression, which we analyze in
particular in the limit of large $N$, where mean-field behavior occurs. The
original game with $N=2$ arises as a singular limit of the general case.
