Corrigendum to ‘Resource‐monotonicity for house allocation problems’

Ehlers and Klaus (Int J Game Theory 32:545–560, 2003) study so‐called allocation problems and claim to characterize all rules satisfying efficiency, independence of irrelevant objects, and resource‐monotonicity on two preference domains (Ehlers and Klaus 2003, Theorem 1). They explicitly prove Theorem 1 for preference domain ${ℛ}_0$ which requires that the null object is always the worst object and mention that the corresponding proofs for the larger domain $ℛ$ of unrestricted preferences ‘are completely analogous.’ In Example 1 and Lemma 1, this corrigendum provides a counterexample to Ehlers and Klaus (2003, Theorem 1) on the general domain $ℛ$ . We also propose a way of correcting the result on the general domain $ℛ$ by strengthening independence of irrelevant objects: in addition to requiring that the chosen allocation should depend only on preferences over the set of available objects (which always includes the null object), we add a situation in which the allocation should also be invariant when preferences over the null object change. Finally, we offer a short proof of the corrected result that uses the established result of Theorem 1 for the restricted domain ${ℛ}_0$ .