Lottery Allocations and Games for Public Rental Apartments

Abstract

A lottery is often used to allocate public rental apartments in practice. The existing random assignments in the literature do not apply to public rental apartments because practical constraints are more restrictive. We provide a lottery-TTC algorithm to find a lottery allocation that has two desired properties of individual stability (IS) and coalitional stability (CS). The new IS notion is proposed to resolve the nonexistence of an envy-free allocation. Further more, we provide a lottery game and show that any IS allocation induces a Nash equilibrium in pure strategies, and vice versa. We also investigate a restrictive domain where a strict envy-free (SEF) allocation does exist. In that domain, we show that the SEF allocation is the unique IS and CS allocation and induces a random assignment that is Pareto optimal and equal to the pseudo market random assignment found by Hylland and Zeckhauser (1979). Our lottery-TTC algorithm provides a simple method to implement the pseudo market competitive mechanism in Hylland and Zeckhauser (1979) in Nash equilibrium in pure strategies on the restrictive domain.

Keywords: Public rental apartments, lottery allocations, lottery-TTC algorithm, Nash equilibrium, house allocation problem, probabilistic serial algorithm, serial dictatorship algorithm.

JEL Classification: C78, C72, D63