A Characterization of the Coordinate-Wise Top-Trading-Cycles Mechanism for Multiple-Type Housing Markets

Abstract

We consider the generalization of the classical Shapley and Scarf housing market model of trading indivisible objects (houses) (Shapley and Scarf, 1974) to so-called multiple-type housing markets (Moulin, 1995). When preferences are separable, the prominent solution for these markets is the coordinate-wise top-trading-cycles (cTTC) mechanism. We first show that on the subdomain of lexicographic preferences, a mechanism is unanimous (or onto), individually rational, strategy-proof, and non-bossy if and only if it is the cTTC mechanism (Theorem 1). Second, using Theorem 1, we obtain a corresponding characterization on the domain of separable preferences (Theorem 2). Finally, we show that on the domain of strict preferences, there is no mechanism satisfying unanimity (or ontoness), individual rationality, strategy-proofness, and non-bossiness (Theorem 3). Our characterization of the cTTC mechanism constitutes the first characterization of an extension of the prominent top-trading-cycles (TTC) mechanism to multiple-type housing markets.