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 r0{\mathcal{r}_0} which requires that the null object is always the worst object and mention that the corresponding proofs for the larger domain r r{\mathcal{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 r{\mathcal{r}} . We also propose a way of correcting the result on the general domain r r{\mathcal{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 r0{\mathcal{r}_0}.