Axioms for Top Trading Cycles in Multi-Object Reallocation

Abstract

This paper studies multi-object reallocation without monetary transfers, where agents initially own multiple indivisible objects and have strict preferences over bundles (e.g., shift exchange among workers at a firm). Focusing on marginal rules that elicit only rankings over individual objects, we provide axiomatic characterizations of the generalized Top Trading Cycles rule (TTC) on the lexicographic and responsive domains. On the lexicographic domain, TTC is characterized by balancedness, individual-good efficiency, the worst-endowment lower bound, and either truncation-proofness or drop strategy-proofness. On the responsive domain, TTC is the unique marginal rule satisfying individual-good efficiency, truncation-proofness, and either the worst-endowment lower bound or individual rationality. In the Shapley--Scarf housing market, TTC is characterized by Pareto efficiency, individual rationality, and truncation-proofness. Finally, on the conditionally lexicographic domain, the augmented Top Trading Cycles rule is characterized by balancedness, Pareto efficiency, the worst-endowment lower bound, and drop strategy-proofness. The conditionally lexicographic domain is a maximal domain on which Pareto efficiency coincides with individual-good efficiency.