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A game theoretic approach to a problem in polymatroid maximization

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  • Hellerstein, Lisa
  • Lidbetter, Thomas

Abstract

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.

Suggested Citation

  • Hellerstein, Lisa & Lidbetter, Thomas, 2023. "A game theoretic approach to a problem in polymatroid maximization," European Journal of Operational Research, Elsevier, vol. 305(2), pages 979-988.
    • Handle: RePEc:eee:ejores:v:305:y:2023:i:2:p:979-988
    DOI: 10.1016/j.ejor.2022.06.018
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    References listed on IDEAS

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