Endowments-swapping-proofness in house allocation problems with private and social endowments

Abstract

This study addresses the house allocation problem where each agent initially owns an object and some objects are social endowments. By using the concept of structure of ownership rights, David Gale's Top Trading Cycles (TTC) rule is extended to this problem (Pycia and Ünver, 2017). However, some TTC rules associated with a given structure of ownership rights violate endowments-swapping-proofness, which requires that no pair of agents can benefit from swapping their endowments before operating a given rule. Therefore, we identify a necessary and sufficient condition for a structure of ownership rights under which the associated TTC rule is endowments-swapping-proof. Based on this result, we characterize a subclass of TTC rules and provide new insights into the kidney exchange problem.

Keywords: top trading cycles rule, endowments-swapping-proofness, house allocation, kidney exchange