Stable and envy-free lottery allocations for affordable housing

DOI link to open access article: Stable and envy-free lottery allocations for affordable housing

Zhan Wang, Jinpeng Ma, Hongwei Zhang

Journal of Mechanism and Institution Design
Volume 8, issue 1, pages 1-55 (December 2023)
doi: 10.22574/jmid.2023.12.001

Abstract:

Affordable housing lotteries often enforce a rule preventing duplicate lottery entries that makes the model in Hylland & Zeckhauser (1979) (HZ) inapplicable. We revisit HZ and propose a new individually stable (IS) allocation that can be achieved by a Tickets algorithm and accommodate the rule. A strictly envy-free (SEF) allocation is shown to be the unique IS and Pareto-optimal allocation, the outcome of the unique strong Nash equilibrium of a congestion game, and the unique Pseudo market equilibrium allocation in HZ. The algorithm always obtains the unique SEF allocation (if any) and fixes a designed flaw of existing lotteries. Keywords: Affordable housing, lottery allocations, Tickets algorithm.

JEL Classification Numbers: H42, C78, C72, D63.