[UTMD-095] Endowment manipulations involving population variations in object exchange problems (by Yuji Fujinaka, Takuma Wakayama)

Yuji Fujinaka, Takuma Wakayama

This study examines the object exchange problem introduced by Shapley and Scarf (1974). We focus on two properties of allocation rules that require robustness to endowment manipulations involving population variations: withdrawal-proofness and pre-delivery-proofness (Thomson, 2014). We first show that no rule satisfies individual rationality and withdrawal-proofness. This impossibility result holds not only on the strict preference domain but also on well-studied restricted domains. However, this negative finding can be avoided by weakening withdrawal-proofness. We characterize the Top Trading Cycles rule (TTC) using individual rationality, strategy-proofness, and weak withdrawal-proofness under a richness condition on the domain. In contrast to withdrawal-proofness, several individually rational rules satisfy pre-delivery-proofness. Furthermore, a stronger version of pre-delivery-proofness, combined with individual rationality, uniquely characterizes TTC. Notably, this characterization holds on many natural restricted domains.