In many real-life scenarios, a group of agents needs to agree on a common action, e.g., on a location for a public facility, while there is some consistency between their preferences, e.g., all preferences are derived from a common metric space. The facility location problem models such scenarios and it is a well-studied problem in social choice. We study mechanisms for facility location on unweighted undirected graphs that are resistant to manipulations (strategy-proof, abstention-proof, and false-name-proof) by both individuals and coalitions on one hand and anonymous and efficient (Pareto-optimal) on the other. We define a new family of graphs, ZV-line graphs, and show a general facility location mechanism for these graphs that satisfies all these desired properties. This mechanism can also be computed in polynomial time and it can equivalently be defined as the first Pareto-optimal location according to some predefined order. Our main result, the ZV-line graphs family and the mechanism we present for it, unifies all works in the literature of false-name-proof facility location on discrete graphs including the preliminary (unpublished) works we are aware of. In particular, we show mechanisms for all graphs of at most five vertices, discrete trees, bicliques, and clique tree graphs. Finally, we discuss some generalizations and limitations of our result for facility location problems on other structures: Weighted graphs, large discrete cycles, infinite graphs; and for facility location problems concerning infinite societies.
Bibliographical noteFunding Information:
This work was partially supported by Israel Science Foundation Grant #1626/18, JSPS KAKENHI Grants #JP17H00761, #JP17H04695, #JP20H00587, #JP20H00609, and JST SICORP JPMJSC1607.
We would like to thank Kentaro Yahiro, Nathanaël Barrot, Tomer Siedner, and Edith Elkind for their comments, and the anonymous reviewers of AAMAS and Autonomous Agents and Multi-Agent Systems for their detailed reviews, which helped us to improve the presentation of this work. Preliminary versions of this work were presented by Ilan Nehama in The 14th Meeting of the Society for Social Choice and Welfare (2016), COMSOC 2018, The 7th International Workshop on Computational Social Choice, WINE 2018, the 14th Conference on Web and Internet Economics, AAMAS 2019, the 18th International Conference on Autonomous Agents and Multiagent Systems, and Haifa 1st Social Choice Workshop. We would like to thank the participants of these meetings for their comments.
© 2022, The Author(s).
- Facility location
- ZV-line graphs
ASJC Scopus subject areas
- Artificial Intelligence