Top-trading-cycles for multiple-type housing markets by Di Feng , Bettina Klaus , and Flip Klijn

 On it's 50th anniversary, top trading cycles (TTC) is still well worth studying. Here's the latest:

Characterizing the typewise top-trading-cycles mechanism for multiple-type housing markets by Di Feng a, Bettina Klaus b, Flip Klijn , Games and Economic Behavior, Volume 146, July 2024, Pages 234-254

Abstract

"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) strategy-proofness. 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."