A Rank-Based Assignment Lottery for an Assignment Problem
For a traditional assignment problem with the same number of objects and agents, we introduce a new assignment lottery based on the notion of rank and analyze some of its properties. In particular, we prove that, like the Random Serial Dictatorship, it is ex post efficient and guarantees positive pr...
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MDPI AG
2025-06-01
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| Series: | AppliedMath |
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| Online Access: | https://www.mdpi.com/2673-9909/5/2/67 |
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| author | Claudia Meo |
| author_facet | Claudia Meo |
| author_sort | Claudia Meo |
| collection | DOAJ |
| description | For a traditional assignment problem with the same number of objects and agents, we introduce a new assignment lottery based on the notion of rank and analyze some of its properties. In particular, we prove that, like the Random Serial Dictatorship, it is ex post efficient and guarantees positive probability to each Pareto optimal deterministic assignment; moreover, the expected rank of this new assignment lottery, which is a measure of the social welfare, cannot be greater than the Random Serial Dictatorship’s one and there exist assignment problems where it is strictly lower. |
| format | Article |
| id | doaj-art-75b7d26cd17d48f8a6eebea18768927d |
| institution | Kabale University |
| issn | 2673-9909 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | AppliedMath |
| spelling | doaj-art-75b7d26cd17d48f8a6eebea18768927d2025-08-20T03:26:57ZengMDPI AGAppliedMath2673-99092025-06-01526710.3390/appliedmath5020067A Rank-Based Assignment Lottery for an Assignment ProblemClaudia Meo0Dipartimento di Scienze Economiche e Statistiche, Università di Napoli Federico II, 80126 Naples, ItalyFor a traditional assignment problem with the same number of objects and agents, we introduce a new assignment lottery based on the notion of rank and analyze some of its properties. In particular, we prove that, like the Random Serial Dictatorship, it is ex post efficient and guarantees positive probability to each Pareto optimal deterministic assignment; moreover, the expected rank of this new assignment lottery, which is a measure of the social welfare, cannot be greater than the Random Serial Dictatorship’s one and there exist assignment problems where it is strictly lower.https://www.mdpi.com/2673-9909/5/2/67assignment problemsassignment lotteriesrank |
| spellingShingle | Claudia Meo A Rank-Based Assignment Lottery for an Assignment Problem AppliedMath assignment problems assignment lotteries rank |
| title | A Rank-Based Assignment Lottery for an Assignment Problem |
| title_full | A Rank-Based Assignment Lottery for an Assignment Problem |
| title_fullStr | A Rank-Based Assignment Lottery for an Assignment Problem |
| title_full_unstemmed | A Rank-Based Assignment Lottery for an Assignment Problem |
| title_short | A Rank-Based Assignment Lottery for an Assignment Problem |
| title_sort | rank based assignment lottery for an assignment problem |
| topic | assignment problems assignment lotteries rank |
| url | https://www.mdpi.com/2673-9909/5/2/67 |
| work_keys_str_mv | AT claudiameo arankbasedassignmentlotteryforanassignmentproblem AT claudiameo rankbasedassignmentlotteryforanassignmentproblem |