A game theoretic approach to a problem in polymatroid maximization

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