Pareto-undominated strategy-proof rules in economies with multidimensional single-peaked preferences

TL;DR

This paper characterizes strategy-proof rules that are not Pareto-dominated in multidimensional single-peaked preference settings, extending previous two-agent results and introducing new classes of rules.

Contribution

It provides a sufficient condition for Pareto-undominated strategy-proof rules, introduces a broad class of such rules, and characterizes the multidimensional uniform rule.

Findings

Established a sufficient condition for Pareto-undominated strategy-proof rules.

Extended sequential allotment rules to multidimensional preferences.

Provided a new characterization of the multidimensional uniform rule.

Abstract

In the problem of fully allocating a social endowment of perfectly divisible commodities among a group of agents with multidimensional single-peaked preferences, we study strategy-proof rules that are not Pareto-dominated by other strategy-proof rules. Specifically, we: (i) establish a sufficient condition for a rule to be Pareto-undominated strategy-proof; (ii) introduce a broad class of rules satisfying this property by extending the family of "sequential allotment rules" to the multidimensional setting; and (iii) provide a new characterization of the "multidimensional uniform rule" involving Pareto-undominated strategy-proofness. Results (i) and (iii) generalize previous findings that were only applicable to the two-agent case.