Robust Exchange under Single-Peaked Preferences

Abstract

Kamada and Yasuda (2025) consider the standard housing exchange problem of Shapley and Scarf (1974) with a constraint on the cycle size. This paper shows that their impossibility results-there is no mechanism with certain desirable properties-continue to hold under the restricted domain of single-peaked preferences except for some special cases. One important case is where the cycle size is restricted to be at most 2, where we construct a strategy-proof mechanism that always induces a constrained efficient exchange that respects the cycle size constraint.

Keywords: cycle size, efficiency, single-peaked preferences