Strategy-proof house allocation with price restrictions

Abstract

This paper considers a house allocation problem with no initial ownership and where prices are bounded from below and above by exogenously given price restrictions. This type of housing market contains, e.g., the "assignment market" and the "student placement problem" as special cases. A mechanism called the minimal RPE mechanism is defined, and two main results are obtained. First, it is demonstrated that the mechanism is manipulable at some profile in the full preference domain R. Second, it is proved that there is a subsetR ⊂ R of the full domain, containing almost all profiles in R, such that the minimal RPE mechanism is strategy-proof in that subset. JEL Classification: C78; D71.

Sequential rules for house allocation with price restrictions

“…Note that the domainR, in a mathematical meaning, contains almost all profiles in R (see the Appendix in Andersson and Svensson, 2016). The next three results contain some fundamental properties of an EPS.…”

“…The paper also provides sufficient conditions for reported demand sets to be consistent with rational preferences. These conditions are important because if agents are required to report in accordance with these conditions, then Theorem 1 in Andersson and Svensson (2016) implies that truthful bidding is an ex post Nash equilibrium in the Iterative English Auction Rule.…”

“…Even if the main results of this paper only are valid on a restricted preference domain, the considered domain contains, in a mathematical meaning, almost all preference profiles that are rational and satisfy a monotonicity and a continuity assumption (see the Appendix in Andersson and Svensson, 2016). This is in contrast to previous auction rules that almost exclusively are defined on the domain where preferences are represented by quasi-linear utility functions (see, e.g., Ausubel, 2004Ausubel, , 2006Demange et al, 1986;Gul and Staccetti, 2000;Kelso and Crawford, 1982;Parkes, 2007, 2009).…”

“…More specifically,Andersson and Svensson (2016) provide a measure on subsets of preference profiles in the general preference domain, and prove that the subset of profiles that are excluded from the general domain has measure zero.2 Note that there exists dynamic rules for housing markets with price restrictions(Herings, 2015;Talman and Yang, 2008;Zhu and Zhang, 2011) but none of them generally converge to an RPE and none of them have been demonstrated to be satisfy any good incentive properties (not even in their direct versions, in contrast to the direct mechanism of Svensson, 2014, 2016).…”