部分成员没有毁伤能力的随机格斗的获胜概率

The Probability of Wining of Stochastic Duel of One Side with Some Members not Having Ability to Attack

建立了一方全部成员具有毁伤能力,另一方部分成员具有毁伤能力的随机格斗模型。在双方随机瞄准的条件下,分别就进攻方分组和不分组的情况建立了格斗双方的状态概率微分方程组。在不同的作战停止规则下,给出了进攻方分组和不分组情况下进攻方获胜、防御方防御成功以及出现和局的概率递推算法。在进攻方分组的条件下,证明了不同作战停止规则下获胜概率的性质,不同的作战停止规则导致获胜概率的性质有较大差异。在进攻方不分组与分组的情况下,通过具体数值例子比较进攻方的不同参数下的获胜概率,结果发现没有一种进攻方案绝对占优。

The stochastic duel models between two forces that on one side all members have ability to attack and on the other side some members do not have the ability to attack are established. Under the condition of stochastic aiming, the differential equations of state probability of the grouped and not grouped offensive side are established. Under the different combat termination decision rules, the algorithms for the proba- bility of wining of the grouped and not grouped offensive side, the probability of successful defense of de- fense side and the probability of the draw of two side based on recursive formulae are given. In the cases that offensive side grouped, the properties of the probability of winning are proved under the conditions o~ different combat termination decision rules. Different combat termination decision rules result in a very dif- ferent property of probability of winning of offensive side. Through the concrete numerical example proba- bilities of winning with different parameters of the grouped and not grouped offensive side are compared. The results show that there is not a attack scenario which is the absolute dominant.