An impossibility result for housing markets with fractional endowments

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.

Organizing Time Exchanges: Lessons from Matching Markets

“…Even if a similar impossibility is present in our model, the fractional setting is analyzed using different axioms and mechanisms. In addition, Athanassoglou and Sethuraman (2011) and Aziz (2016) are unable to find any positive results related to non-manipulability in their considered reduced preference domains. Biró et al (2017a) consider, as does this paper, a model where agents are endowed with multiple units of an indivisible and agent-specific good, searching for balanced allocations.…”

“…The papers closest to the model investigated in this study are Athanassoglou andSethuraman (2011), Aziz (2016), Biró et al (2017a,b) and Manjunath and Westkamp (2019), which we describe next. Athanassoglou and Sethuraman (2011) and Aziz (2016) consider a housing market where initial endowments as well as allocations are described by a vector of fractions of the houses in the economy.…”