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.

我们考虑在多矩阵上最大化向量的所有分量的最小（加权）值的问题。这是由 Fujishige 引入并解决的词典优化基础问题的一个特例。我们将问题的另一种表述为一个零和博弈，一个最大化玩家的混合策略集是多拟矩阵的基础，一个最小化玩家的混合策略集是一个单纯形。我们展示了这个游戏和它的三个变体统一了搜索、顺序测试和排队中的几个问题。我们为双方玩家提供了一个新的、简短的最佳策略推导，并表达了游戏的价值。此外，