An Impossibility Result for Housing Markets with Fractional Endowments

TL;DR

This paper proves that in housing markets with fractional endowments, it is impossible to design an allocation mechanism that simultaneously satisfies individual rationality, weak strategyproofness, and efficiency.

Contribution

The paper establishes an impossibility theorem showing the incompatibility of key axioms in fractional housing market settings.

Findings

Individual rationality, weak strategyproofness, and efficiency cannot all be achieved simultaneously.

Extends the understanding of limitations in fractional endowment housing markets.

Addresses an open problem posed by previous research.

Abstract

The housing market setting constitutes a fundamental model of exchange economies of goods. Most of the work concerning housing markets does not cater for randomized assignments or allocation of time-shares. House allocation with fractional endowments of houses was considered by Athanassoglou and Sethuraman (2011) who posed the open problem whether individual rationality, weak strategyproofness, and efficiency are compatible for the setting. We show that the three axioms are incompatible.