Efficiency in Multiple-Type Housing Markets

TL;DR

This paper extends the analysis of housing market mechanisms to multiple types, introducing coordinatewise and pairwise efficiency, and characterizes two mechanisms, cTTC and bTTC, as optimal under these properties.

Contribution

It introduces weaker efficiency concepts suitable for multi-type markets and characterizes two mechanisms, cTTC and bTTC, as the ones satisfying these properties along with strategy-proofness.

Findings

cTTC and bTTC mechanisms are characterized by the new efficiency properties.

Both properties are compatible with individual rationality and strategy-proofness.

The results extend the understanding of efficient mechanisms in multi-type housing markets.

Abstract

We consider multiple-type housing markets (Moulin, 1995), which extend Shapley-Scarf housing markets (Shapley and Scarf, 1974) from one dimension to higher dimensions. In this model, Pareto efficiency is incompatible with individual rationality and strategy-proofness (Konishi et al., 2001). Therefore, we consider two weaker efficiency properties: coordinatewise efficiency and pairwise efficiency. We show that these two properties both (i) are compatible with individual rationality and strategy-proofness, and (ii) help us to identify two specific mechanisms. To be more precise, on various domains of preference profiles, together with other well-studied properties (individual rationality, strategy-proofness, and non-bossiness), coordinatewise efficiency and pairwise efficiency respectively characterize two extensions of the top-trading-cycles mechanism (TTC): the coordinatewise top-trading-cycles mechanism (cTTC) and the bundle top-trading-cycles mechanism (bTTC). Moreover, we propose several variations of our efficiency properties, and we find that each of them is either satisfied by cTTC or bTTC, or leads to an impossibility result (together with individual rationality and strategy-proofness). Therefore, our characterizations can be primarily interpreted as a compatibility test: any reasonable efficiency property that is not satisfied by cTTC or bTTC could be considered incompatible with individual rationality and strategy-proofness. The external validity of our results in the context of general environments is also discussed. For multiple-type housing markets with strict preferences, our characterization of bTTC constitutes the first characterization of an extension of the prominent TTC mechanism