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False-Name-Proof Facility Location on Wheel Graphs

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PRIMA 2022: Principles and Practice of Multi-Agent Systems (PRIMA 2022)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13753))

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Abstract

In this paper, we consider the study of two classes of mechanism design problems for locating a facility on a wheel graph with \(k \ge 4\) vertices, where a vertex is located at the center, which is surrounded by a cycle graph with \({k-1}\) vertices and connected to each vertex in the cycle. Two domains of agents’ preferences are considered; the single-peaked domain and the single-dipped domain. We are interested in the existence of anonymous social choice functions that are false-name-proof and Pareto efficient. For both domains of preferences, we provide the necessary and sufficient condition on the graph parameter k to guarantee the existence of such social choice functions. Namely, for the single-peaked preference domain, such social choice functions exist if and only if \(k \le 5\). On the other hand, for the single-dipped preference domain, such social choice functions exist if and only if \(k \le 7\).

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Notes

  1. 1.

    In the field of urban planning, such a city structure is usually called a “radial city” or “radial concentric city.”.

  2. 2.

    In their paper the subscript indicates the number of vertices in the cycle surrounding the hub, i.e., \(W_{4}\) in this paper is referred to as \(W_{3}\) in their paper, and \(W_{5}\) is referred to as \(W_{4}\).

  3. 3.

    This is true for any wheel graph, i.e., for any \(k \ge 4\).

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Acknowledgements

This work is partially supported by JSPS KAKENHI Grant Numbers JP20H00587, JP20H00609, and JP21H04979.

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Authors and Affiliations

  1. Graduate School of Information Science and Electrical Engineering (ISEE), Kyushu University, Fukuoka, 819-0395, Japan

    Koji Osoegawa, Taiki Todo & Makoto Yokoo

Authors
  1. Koji Osoegawa
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  2. Taiki Todo
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  3. Makoto Yokoo
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Corresponding author

Correspondence to Taiki Todo .

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Editors and Affiliations

  1. Özyeğin University, Istanbul, Turkey

    Reyhan Aydoğan

  2. Universitat Politècnica de València, Valencia, Spain

    Natalia Criado

  3. Université Paris-Dauphine, Paris, France

    Jérôme Lang

  4. Universitat Politècnica de València, Valencia, Spain

    Victor Sanchez-Anguix

  5. King's College London, London, UK

    Marc Serramia

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Osoegawa, K., Todo, T., Yokoo, M. (2023). False-Name-Proof Facility Location on Wheel Graphs. In: Aydoğan, R., Criado, N., Lang, J., Sanchez-Anguix, V., Serramia, M. (eds) PRIMA 2022: Principles and Practice of Multi-Agent Systems. PRIMA 2022. Lecture Notes in Computer Science(), vol 13753. Springer, Cham. https://doi.org/10.1007/978-3-031-21203-1_9

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  • DOI: https://doi.org/10.1007/978-3-031-21203-1_9

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