We consider a game in which each player must find a compromise between moredaring strategies that carry a high risk for him to be eliminated, and morecautious ones that, however, reduce his final score. For two symmetric playersthis game was originally formulated in 1961 by Dresher, who modeled a duelbetween two opponents. The game has also been of interest in the description ofathletic competitions. We extend here the two-player game to an arbitrarynumber $N$ of symmetric players. We show that there is a mixed-strategy Nashequilibrium and find its exact analytic expression, which we analyze inparticular in the limit of large $N$, where mean-field behavior occurs. Theoriginal game with $N=2$ arises as a singular limit of the general case.
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机译：我们考虑一种游戏，其中每个玩家都必须在较冒险的策略与较谨慎的策略之间做出折衷，这些策略会给他带来很高的风险，而后者会降低其最终得分。对于两名对称玩家，此游戏最初由德雷舍（Dresher）于1961年提出，他模拟了两个对手之间的决斗。该游戏也引起了竞技比赛的描述。在这里，我们将两人游戏扩展到任意数量的$ N $对称玩家。我们表明存在一种混合策略的纳什均衡，并找到其精确的解析表达式，尤其是在发生平均场行为的大$ N $范围内进行分析。 $ N = 2 $的原始游戏是一般情况的单数极限。
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