Shapley-Scarf Markets with Objective Indifferences

Will Sandholtz and Andrew Tai

Papers from arXiv.org

Abstract: In many object allocation problems, some of the objects may be indistinguishable from each other. For example, in a college dormitory, rooms in the same building with the same floor plan are effectively identical. In such cases, it is reasonable to assume that agents are indifferent between identical objects, and matching mechanisms in these settings should account for the agents' indifferences. Top trading cycles (TTC) with fixed tie-breaking has been suggested and used in practice to deal with indifferences in object allocation problems. Under general indifferences, TTC with fixed tie-breaking is neither Pareto efficient nor group strategy-proof. Furthermore, it may not select an allocation in the core of the market, even when the core is non-empty. We introduce a new setting, objective indifferences, in which any indifferences are shared by all agents. In this setting, which includes strict preferences as a special case, TTC with fixed tie-breaking maintains Pareto efficiency, group strategy-proofness, and core selection. Further, we characterize objective indifferences as the most general setting where TTC with fixed tie-breaking maintains these important properties.

Date: 2025-03, Revised 2025-07
New Economics Papers: this item is included in nep-des
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