Local Sufficiency for Partial Strategyproofness

TL;DR

This paper explores the relationship between local and global partial strategyproofness in assignment mechanisms, establishing tight polynomial bounds and unifying previous local sufficiency results for strategyproofness.

Contribution

It proves that r-local partial strategyproofness implies r^2-partial strategyproofness, providing the tightest polynomial bound and unifying prior local sufficiency results.

Findings

r-local partial strategyproofness implies r^2-partial strategyproofness

The polynomial bound r^2 is tight for this implication

Unifies previous local sufficiency results for strategyproofness

Abstract

In (Mennle and Seuken, 2017), we have introduced partial strategyproofness, a new, relaxed notion of strategyproofness, to study the incentive properties of non-strategyproof assignment mechanisms. In this paper, we present results pertaining to local sufficiency for partial strategyproofness: We show that, for any r in [0,1], r-local partial strategyproofness implies r^2-partial strategyproofness, and we show that this is the tightest polynomial bound for which a guarantee can be proven. Our results unify the two prior local sufficiency results for strategyproofness (Carroll, 2012) and lexicographic dominance-strategyproofness (Cho, 2012).