We consider the problem of maximizing the minimum (weighted) value of all components of a vector over a polymatroid. This is a special case of the lexicographically optimal base problem introduced and solved by Fujishige. We give an alternative formulation of the problem as a zero-sum game between a maximizing player whose mixed strategy set is the base of the polymatroid and a minimizing player whose mixed strategy set is a simplex. We show that this game and three variations of it unify several problems in search, sequential testing and queuing. We give a new, short derivation of optimal strategies for both players and an expression for the value of the game. Furthermore, we give a characterization of the set of optimal strategies for the minimizing player and we consider special cases for which optimal strategies can be found particularly easily.

翻译：我们考虑的是将矢量所有组成部分的最小值(加权)值最大化于多甲虫体的问题。这是藤石提出和解决的字典上最佳基础问题的一个特殊例子。我们给出了这个问题的替代提法,作为最大参与者之间的零和游戏,后者的混合战略是多甲虫的基数,而后者的混合战略是简单的。我们展示了这个游戏及其三种变式在搜索、顺序测试和排队方面统一了几个问题。我们给玩家两个最佳战略提供了新的简短的提法,并表达了游戏的价值。此外,我们给一套最佳战略的定性,以尽量减少玩家,我们考虑了特别容易找到最佳战略的特例。