Oh, fun! This is sometimes called an envy free division. A nice book on this topic is
Fair Division: From Cake-Cutting to Dispute Resolution
www.amazon.com/Fair-Division-Cake-Cutting-Dispute-Resolution/dp/0521556449
Stable matchings are a related problem (sometimes called the stable marriage problem), where you want to match men and women to "marry", such that no two couples would want to swap partners. It is applied in real life to matching medical interns to hospital placements. One of my all time favorite technical books* is on this subject:
Comments
Oh, fun! This is sometimes called an envy free division. A nice book on this topic is
Fair Division: From Cake-Cutting to Dispute Resolution www.amazon.com/Fair-Division-Cake-Cutting-Dispute-Resolution/dp/0521556449
Stable matchings are a related problem (sometimes called the stable marriage problem), where you want to match men and women to "marry", such that no two couples would want to swap partners. It is applied in real life to matching medical interns to hospital placements. One of my all time favorite technical books* is on this subject:
Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis http://www.amazon.com/Two-Sided-Matching-Game-Theoretic-Econ...
(* yes, that may make me weird)