Mechanism Design for Multi-Type Housing Markets with Acceptable Bundles

Abstract

We extend the Top-Trading-Cycles (TTC) mechanism to select strict core allocations for housing markets with multiple types of items, where each agent may be endowed and allocated with multiple items of each type. In doing so, we advance the state of the art in mechanism design for housing markets along two dimensions: First, our setting is more general than multi-type housing markets (Moulin 1995; Sikdar, Adali, and Xia 2017) and the setting of Fujita et al. (2015). Further, we introduce housing markets with acceptable bundles (HMABs) as a more general setting where each agent may have arbitrary sets of acceptable bundles. Second, our extension of TTC is strict core selecting under the weaker restriction on preferences of CMI-trees, which we introduce as a new domain restriction on preferences that generalizes commonly-studied languages in previous works.

A Complexity Approach for Core-Selecting Exchange under Conditionally Lexicographic Preferences

“…Similar exchange rules as ATTC procedure have been studied in recent papers (Sikdar, Adalı, & Xia, 2017, 2018. Sikdar et al (2017) consider an exchange problem where goods are partitioned into types (car, house, and so on).…”

“…Similar exchange rules as ATTC procedure have been studied in recent papers (Sikdar, Adalı, & Xia, 2017, 2018. Sikdar et al (2017) consider an exchange problem where goods are partitioned into types (car, house, and so on). Each agent has initially a single good of each type and receives at the end of the procedure a single good of each type.…”

Multi-Type Resource Allocation with Partial Preferences

“…Mackin and Xia (2016) characterize serial dictatorships for MTRAs by strategyproofness, neutrality, and non-bossiness. The exchange economy of multi-type housing markets (Moulin 1995) is considered in (Sikdar, Adali, and Xia 2017;2018) under lexicographic preferences, while Fujita et al (2015) consider the exchange economy where agents may consume multiple units of a single type of items under lexicographic preferences.…”

“…CPnets are an important restriction on the domain of partial preferences, and induce a partial ordering on the set of all bundles. Sikdar, Adali, and Xia (2017) design mechanisms for multi-type housing markets under lexicographic extensions of CP-nets. Several works in the combinatorial voting literature assume CP-net preferences (Rossi, Venable, and Walsh 2004;Lang 2007), and that agents' CP-nets have a common dependence structure (see (Lang and Xia 2016) for a recent survey).…”

Strategyproof multi-item exchange under single-minded dichotomous preferences

“…Some positive results depend on the fact that agents have lexicographic preferences over items or items types. Under these assumptions, it is possible to construct extensions of TTC that achieve strategyproofness, individual rationality, and Pareto optimality (see e.g., (Fujita et al, 2015;Sikdar et al, 2017)). The preferences we consider do not assume any of these structural restrictions that are based on lexicographic or conditional lexicographic comparisons.…”