Lottery Allocations and Games for Public Rental Apartments

32 Pages Posted: 17 Mar 2015 Last revised: 12 Feb 2016

See all articles by Zhan Wang

Zhan Wang

Sichuan University - School of Economics

Jinpeng Ma

Rutgers University-Camden

Hongwei Zhang

Sichuan University - School of Economics

Date Written: March 1, 2015

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

Suggested Citation

Wang, Zhan and Ma, Jinpeng and Zhang, Hongwei, Lottery Allocations and Games for Public Rental Apartments (March 1, 2015). Available at SSRN: https://ssrn.com/abstract=2579233 or http://dx.doi.org/10.2139/ssrn.2579233

Zhan Wang

Sichuan University - School of Economics ( email )

Chengdu, Sichuan
China

Jinpeng Ma (Contact Author)

Rutgers University-Camden ( email )

Camden, NJ 08102
United States

Hongwei Zhang

Sichuan University - School of Economics ( email )

Chengdu, Sichuan
China

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