Characterizing the typewise top-trading-cycles mechanism for multiple-type housing markets

We consider the generalization of the classical Shapley and Scarf housing market model (Shapley and Scarf, 1974) to so-called multiple -type housing markets (Moulin, 1995). Throughout the paper, we focus on strict preferences. When preferences are separable, the prominent solution for these markets is the typewise top -trading -cycles (tTTC) 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 tTTC mechanism. Second, we obtain a corresponding characterization for separable preferences. We obtain additional characterizations when replacing [strategy-proofness and non -bossiness] with self -enforcing group (or pairwise) strategyproofness. Finally, we show that for strict preferences, there is no mechanism satisfying unanimity, individual rationality, and strategy-proofness. Our characterizations of the tTTC mechanism constitute the first characterizations of an extension of the prominent top -trading -cycles (TTC) mechanism to multiple -type housing markets.