Alternative characterizations of the top trading cycles rule in housing markets☆
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 be the set of agents with . Let be the set of objects. Each agent owns an object and it is called endowment. Each agent has a strict preference over . Let be the weak preference induced from , such that if and only if either or . Let be the set of all strict preferences. Let be the preference profile of all agents. Given , and , let be , and be the preference profile
Results
Theorem 1 A rule satisfies individual rationality, Pareto efficiency, and rank monotonicity if and only if .
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)
A short proof for the characterization of the core in housing markets
Econom. Lett.
(2015)Matching with single-peaked preferences
J. Econom. Theory
(2019)Group incentive compatibility in a market with indivisible goods
Econom. Lett.
(1984)- et al.
Endowments-swapping-proof house allocation
Games Econom. Behav.
(2018) An alternative proof of a characterization of the TTC mechanism
Oper. Res. Lett.
(2016)- et al.
On cores and indivisibility
J. Math. Econ.
(1974)
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).