🤖 AI Summary
This paper addresses the Shapley–Scarf housing market model by introducing the “local unanimity” axiom—a generalization of social choice-theoretic unanimity to arbitrary subsets of agents who mutually agree on endowment exchanges. Using axiomatic analysis and game-theoretic reasoning, it provides a formal characterization of the Top Trading Cycles (TTC) mechanism under both strict and weak preference domains. The key contribution is the first incorporation of local unanimity into housing market theory, yielding a concise and complete characterization of TTC: it is the unique mechanism satisfying individual rationality, Pareto efficiency, strategy-proofness, and local unanimity—regardless of the underlying preference structure. This result substantially strengthens the theoretical foundations of TTC and enhances its applicability in mechanism design across diverse preference environments.
📝 Abstract
In the housing market model introduced by Shapley and Scarf (1974), we propose a new axiom, local unanimity, that extends the unanimity condition widely used in social choice theory. It applies the unanimity condition to any subset of agents in the model who unanimously agree on the best exchange of their endowments. Building on this axiom, we provide several concise characterizations of the Top Trading Cycles (TTC) mechanism under both strict and weak preference domains.