Characterizing the Coordinatewise Top-Trading-Cycles Mechanism for Multiple-Type Housing Markets


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 coordinatewise top-trading-cycles (cTTC) mechanism. We first show that for 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 for separable preferences (Theorem 2). We obtain corresponding results when replacing [strategy-proofness and non-bossiness] with effective group (or pairwise) strategy-proofness (Corollaries 1 and 2). Finally, we show that for strict preferences, there is no mechanism satisfying unanimity, individual rationality, and strategy-proofness (Theorem 3). We obtain three further impossibility results for strict preferences based on weakening unanimity to ontoness (Corollary 3) and on extending the cTTC solution (Corollary 4, Theorem 4). Our characterizations of the cTTC mechanism constitute the first characterizations of an extension of the prominent top-trading-cycles (TTC) mechanism to multiple-type housing markets.