Variable population manipulations of reallocation rules in economies with single-peaked preferences

In a one-commodity economy with single-peaked preferences and individual endowments, we study different ways in which reallocation rules can be strategically distorted by affecting the set of active agents. We introduce and characterize the family of monotonic reallocation rules and show that each rule in this class is withdrawal-proof and endowments-merging-proof, at least one is endowments-splitting-proof and that no such rule is pre-delivery-proof.