This paper is dealing with a multiple person game model under the antagonistic duel type setup. The unique multiple person duel game with the one-shooting-to-kill-all condition is analytically solved and the explicit formulas are obtained to determine the time dependent duel game model by using the first exceed theory. The model could be directly applied into real-world situations and an analogue of the theory in the paper is designed for solving the best shooting time for hitting all other players at once which optimizes the payoff function under random time conditions. It also mathematically explains to build the marketing strategies for the entry timing for both blue and red ocean markets.

中文翻译：

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对抗一对一随机对决游戏

本文研究的是对抗对决类型设置下的多人博弈模型。解析了具有“一枪多杀”条件的唯一多人对决游戏，并使用第一个超越理论，获得了明确的公式来确定时间相关的对决游戏模型。该模型可以直接应用于现实情况，该论文的理论类似物旨在解决最佳击球时间，以便一次击中所有其他球员，从而优化随机时间条件下的收益功能。它还从数学上解释了为蓝海和红海市场的进入时机建立营销策略。