Elsevier

Economics Letters

Volume 201, April 2021, 109806
Economics Letters

Alternative characterizations of the top trading cycles rule in housing markets

https://doi.org/10.1016/j.econlet.2021.109806Get rights and content

Highlights

  • We study the housing market.

  • The top trading cycles rule is first characterized by individual rationality, Pareto efficiency, and rank monotonicity.

  • The top trading cycles rule is also characterized by individual rationality, endowments-swapping-proofness, and rank monotonicity.

Abstract

Building on Ma (1994) and Fujinaka and Wakayama (2018), this paper characterizes the top trading cycles rule in housing markets without the help of strategy-proofness, by the following two groups of axioms: individual rationality, Pareto efficiency, rank monotonicity; individual rationality, endowments-swapping-proofness, rank monotonicity.

Introduction

This paper considers the housing market introduced by Shapley and Scarf (1974). The top trading cycles (TTC) rule,which selects an allocation via the TTC algorithm, has been characterized by previous works such as Ma (1994) through Pareto efficiency, individual rationality, and strategy-proofness,1 and Fujinaka and Wakayama (2018) through individual rationality, strategy-proofness, and endowments-swapping-proofness. The purpose of this paper is to provide alternative characterizations of the TTC rule. In order to achieve this aim, we introduce a new axiom called rank monotonicity proposed by Chen (2017). Rank monotonicity is similar to, but weaker than, weak Maskin monotonicity due to Kojima and Manea (2010), which is weaker than Maskin monotonicity proposed by Maskin (1999). Our main theorems show that if we replace strategy-proofness with rank monotonicity in the above two characterizations, the TTC rule remains to be the unique candidate under such criteria.

Section snippets

Model

Let N{1,2,,n} be the set of agents with n2. Let H{h1,h2,,hn} be the set of objects. Each agent iN owns an object ωiH and it is called is endowment. Each agent iN has a strict preference Pi over H. Let Ri be the weak preference induced from Pi, such that hRih if and only if either hPih or h=h. Let P be the set of all strict preferences. Let P=(P1,P2,,Pn)Pn be the preference profile of all agents. Given iN, PiP and PPn, let i be N{i}, and (Pi,Pi) be the preference profile

Results

Theorem 1

A rule φ satisfies individual rationality, Pareto efficiency, and rank monotonicity if and only if φ=τ.

Proof

The “if” part of Theorem 1 follows immediately from the existing literature of Ma (1994), Takamiya (2001), and Bird (1984).3

Conclusion

This paper presents two new characterizations of the well-known TTC rules in housing market problems and hence provides further justifications for the use of this rule in relevant applications. This paper is also the first one characterizing the TTC rule without the help of strategy-proofness. Future works are needed to investigate whether it is possible to substitute rank monotonicity for strategy-proofness in characterizations of other allocation rules.

References (12)

There are more references available in the full text version of this article.

Cited by (0)

The author thanks Peng Liu for his valuable discussions and suggestions. This research is supported by The National Natural Science Foundation of China, China (No. 71703038), The Ministry of Education Project of Youth Fund of Humanities and Social Sciences, China (No. 17YJC790012), and Innovation Program of Shanghai Municipal Education Commission, China (No. 2017-01-07-00-02-E00008).

View full text