RIEB Discussion Paper Series No.2023-14

Title

Endowments-swapping-proofness and Efficiency in Multiple-Type Housing Markets

Abstract

For Shapley-Scarf housing markets (Shapley and Scarf, 1974), Fujinaka and Wakayama (2018) propose a new incentive property, endowments-swapping-proofness, that excludes manipulations that a pair of agents can conduct before the operation of the selected mechanism by swapping their endowments. We investigate endowments-swapping-proofness for Moulin (1995)'s multiple-type housing markets, which are an extension of Shapley-Scarf housing markets with multi-unit demands. Differing from Shapley-Scarf housing markets, for multiple-type housing markets, there are various ways to swap endowments. Motivated by this observation, we introduce three extensions of endowments-swapping-proofness: bundle endowments-swapping-proofness, one type endowments-swapping-proofness, and flexible endowments-swapping-proofness.

Based on the first two weaker endowments-swapping-proofness properties that we propose, and other well-studied properties (individual rationality, strategy-proofness, and non-bossiness), on several domains of preference profiles, we provide characterizations of two extensions of the top-trading-cycles (TTC) mechanism: the bundle top-trading cycles (bTTC) mechanism and the coordinatewise top-trading-cycles (cTTC) mechanism. Moreover, we also show that the strongest possible endowments-swapping-proofness property (flexible endowments-swapping-proofness) leads to an impossibility. Furthermore, our results explicitly show that our new properties correspond to efficiency notions.

Keywords

Multiple-type housing markets; Endowments-swapping-proofness; Strategy proofness; Constrained efficiency; Top-trading-cycles (TTC) mechanism; Market designy

JEL Classification

C78, D61, D47

Inquiries

Di FENG*
Faculty of Business and Economics, University of Laussane
Junior Research Fellow, RIEB, Kobe University

*This Discussion Paper won the Kanematsu Prize (FY 2022).