Use of Linear Programming to Find an Envy-Free Solution Closest to the Brams–Kilgour Gap Solution for the Housemates Problem
- Richard F. Potthoff
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Although the Gap Procedure that Brams and Kilgour (2001) proposed for determining the price of each room in the housemates problem has many favorable properties, it also has one drawback: Its solution is not always envy-free. Described herein is an approach that uses linear programming to find an envy-free solution closest (in a certain sense) to the Gap solution when the latter is not envy-free. If negative prices are allowed, such a solution always exists. If not, it sometimes exists, in which case linear programming can find it by disallowing negative prices. Several examples are presented.
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- Use of Linear Programming to Find an Envy-Free Solution Closest to the Brams–Kilgour Gap Solution for the Housemates Problem
Group Decision and Negotiation
Volume 11, Issue 5 , pp 405-414
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
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- fair division
- housemates problem
- linear programming
- Industry Sectors
- Author Affiliations
- 1. Department of Political Science, Duke University, Durham, North Carolina, 27708-0204, USA