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

TL;DR

This paper explores how different reallocation rules in economies with single-peaked preferences can be strategically manipulated by altering active agents, introducing a class of monotonic rules with specific strategic-proofness properties.

Contribution

It introduces and characterizes a family of monotonic reallocation rules, analyzing their strategic robustness in economies with single-peaked preferences.

Findings

Monotonic reallocation rules are withdrawal-proof.

Some rules are endowments-merging-proof.

No rules are pre-delivery-proof.

Abstract

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.