On the Integration of Shapley-Scarf Housing Markets

23 Pages Posted: 6 May 2020

See all articles by Rajnish Kumar

Rajnish Kumar

Queen's University Management School

Kriti Manocha

Indian Statistical Institute

Josué Ortega

Queen’s Management School, Queen’s University Belfast

Date Written: May 5, 2020

Abstract

We study the welfare consequences of merging disjoint Shapley-Scarf housing markets. We obtain tight bounds on the number of agents harmed by integration and on the size of their losses. We show that, in the worst-case scenario, market integration may harm the vast majority of agents, and that the average rank of an agent's house can decrease (asymptotically) by 50% of the length of their preference list. We also obtain average-case results. We exactly compute the expected gains from integration in random markets, where each of the preference profiles is chosen uniformly at random. We show that, on average, market integration benefits all agents, particularly those in smaller markets. Using the expected number of cycles in the top trading cycles algorithm, we bound the expected number of agents harmed by integration. In particular, the expected fraction of agents harmed by integration is less than 50% if each market has the same size and this is below 26 (independent of the number of markets that merge). We conclude by providing a preference domain that ensures that those harmed by market integration are a minority.

Keywords: Shapley-Scarf markets, gains from integration, random markets

JEL Classification: C78

Suggested Citation

Kumar, Rajnish and Manocha, Kriti and Ortega, Josué, On the Integration of Shapley-Scarf Housing Markets (May 5, 2020). QMS Research Paper 2020/03, Available at SSRN: https://ssrn.com/abstract=3593239 or http://dx.doi.org/10.2139/ssrn.3593239

Rajnish Kumar

Queen's University Management School ( email )

25 University Square
Belfast, Northern Ireland BT7 1NN
Northern Ireland

Kriti Manocha

Indian Statistical Institute ( email )

7 S. J. S. Sansanwal Marg
New Delhi, 110016
India

Josué Ortega (Contact Author)

Queen’s Management School, Queen’s University Belfast ( email )

185 Stranmillis Road, Riddel Hall
Belfast, BT9 5EE
United Kingdom

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
16
Abstract Views
192
PlumX Metrics