Rental harmony with roommates

Yaron Azrieli*, Eran Shmaya

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


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. We then show how our theorem may be applied in two related problems: Existence of envy-free allocations in a version of the cake-cutting problem, and existence of equilibrium in an exchange economy with indivisible goods and money. Our proof uses Shapley's K-K-M-S theorem and Hall's marriage lemma.

Original languageEnglish (US)
Pages (from-to)128-137
Number of pages10
JournalJournal of Economic Theory
Issue number1
StatePublished - Sep 2014


  • Assignment problem
  • Cake cutting
  • Envy-free
  • Rental harmony

ASJC Scopus subject areas

  • Economics and Econometrics


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