Core and top trading cycles in a market with indivisible goods and externalities

In this paper, we incorporate externalities into Shapley–Scarf housing markets, expressing agents’ preferences as defined over allocations rather than houses. We introduce a class of preferences called hedonic preferences, extend the top trading cycles (TTC) algorithm to housing markets with hedonic preferences, and investigate the existence and core properties of TTC allocations. In order to further expand the applicability of the TTC algorithm, we consider a class of preferences called trading-cycle-lexicographic preferences, and we also construct worst-case hedonic preferences from arbitrary preferences. Lastly, we study the properties of the TTC algorithm as a mechanism on the domain of preferences called egocentric preferences. Our results show that many desirable properties of the TTC algorithm for housing markets without externalities can be extended to housing markets with certain kinds of externalities.