False-Name-Proof Facility Location on Discrete Structures
Computer Science and Game Theory
2019-11-20 v2
Abstract
We consider the problem of locating a single facility on a vertex in a given graph based on agents' preferences, where the domain of the preferences is either single-peaked or single-dipped. Our main interest is the existence of deterministic social choice functions (SCFs) that are Pareto efficient and false-name-proof, i.e., resistant to fake votes. We show that regardless of whether preferences are single-peaked or single-dipped, such an SCF exists (i) for any tree graph, and (ii) for a cycle graph if and only if its length is less than six. We also show that when the preferences are single-peaked, such an SCF exists for any ladder (i.e., 2-by-m grid) graph, and does not exist for any larger hypergrid.
Cite
@article{arxiv.1907.08914,
title = {False-Name-Proof Facility Location on Discrete Structures},
author = {Taiki Todo and Nodoka Okada and Makoto Yokoo},
journal= {arXiv preprint arXiv:1907.08914},
year = {2019}
}