Prophet Inequalities via Linear Programming
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915784163328000 |
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| author | Bayrak, Halil I. Pınar, Mustafa Ç. Vohra, Rakesh |
| author_facet | Bayrak, Halil I. Pınar, Mustafa Ç. Vohra, Rakesh |
| contents | Prophet inequalities bound the expected reward that can be obtained in a stopping problem by the optimal reward of its corresponding off-line version. We propose a systematic technique for deriving prophet inequalities for stopping problems associated with selecting a point in a polyhedron. It utilizes a reduced-form linear programming representation of the stopping problem. We illustrate the technique to derive a number of known results as well as some new ones. For instance, we prove a $\frac{1}{2}$-prophet inequality when the underlying polyhedron is an on-line polymatroid; one whose underlying submodular function depends upon the realized rewards. We also demonstrate a composition by the Minkowski sum property. If an $r-$ prophet inequality holds for polyhedra $P^1$ and $P^2$, it also holds for their Minkowski sum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07542 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Prophet Inequalities via Linear Programming Bayrak, Halil I. Pınar, Mustafa Ç. Vohra, Rakesh Theoretical Economics Prophet inequalities bound the expected reward that can be obtained in a stopping problem by the optimal reward of its corresponding off-line version. We propose a systematic technique for deriving prophet inequalities for stopping problems associated with selecting a point in a polyhedron. It utilizes a reduced-form linear programming representation of the stopping problem. We illustrate the technique to derive a number of known results as well as some new ones. For instance, we prove a $\frac{1}{2}$-prophet inequality when the underlying polyhedron is an on-line polymatroid; one whose underlying submodular function depends upon the realized rewards. We also demonstrate a composition by the Minkowski sum property. If an $r-$ prophet inequality holds for polyhedra $P^1$ and $P^2$, it also holds for their Minkowski sum. |
| title | Prophet Inequalities via Linear Programming |
| topic | Theoretical Economics |
| url | https://arxiv.org/abs/2602.07542 |