منابع مشابه
Rental harmony with roommates
We prove existence of envy-free allocations in markets with heterogenous indivisible goods and money, when a given quantity is supplied from each of the goods and agents have unit demands. We depart from most of the previous literature by allowing agents’ preferences over the goods to depend on the entire vector of prices. Our proof uses Shapley’s K-K-M-S theorem and Hall’s marriage lemma. We t...
متن کاملRental Harmony: Sperner's Lemma in Fair Division
My friend’s dilemma was a practical question that mathematics could answer, both elegantly and constructively. He and his housemates were moving to a house with rooms of various sizes and features, and were having trouble deciding who should get which room and for what part of the total rent. He asked, “Do you think there’s always a way to partition the rent so that each person will prefer a di...
متن کاملThe Stable Roommates Problem with Ties
We study the variant of the well-known Stable Roommates problem in which participants are permitted to express ties in their preference lists. In this setting, more than one definition of stability is possible. Here we consider two of these stability criteria, so-called super-stability and weak stability. We present a linear-time algorithm for finding a super-stable matching if one exists, give...
متن کاملRepresenting roommates' preferences with symmetric utilities
In the context of the stable roommates problem, it is shown that acyclicity of preferences is equivalent to the existence of symmetric utility functions, i.e. the utility of agent i when matched with j is the same as j’s utility when matched with i. © 2007 Published by Elsevier Inc. JEL classification: C78
متن کاملStable Roommates Problem with Random Preferences
Matching under preferences is a topic of great practical importance, deep mathematical structure, and elegant algorithmics [Manlove 2013; Gusfield and Irving 1989]. The most famous example is the stable marriage problem, where n men and n women compete with each other in the “marriage market.” Each man ranks all the women according to his individual preferences, and each woman does the same wit...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Economic Theory
سال: 2014
ISSN: 0022-0531
DOI: 10.1016/j.jet.2014.06.006