Stable and envy-free lottery allocations for affordable housing

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.