A Characterization of Complexity in Public Goods Games

Author Matan Gilboa



PDF
Thumbnail PDF

File

LIPIcs.ICALP.2024.73.pdf
  • Filesize: 0.83 MB
  • 19 pages

Document Identifiers

Author Details

Matan Gilboa
  • University of Oxford, UK

Acknowledgements

I would like to thank Noam Nisan for many useful conversations, and for suggesting the Copy Gadget in the proof of Theorem 3.2. I would like to thank Roy Gilboa for many useful conversations, and for adjusting the Copy Gadget in the proof of Theorem 3.2. I would like to thank Noam Nisan for communicating to me the alternative solution to the monotone case (see footnote 2), which was suggested by Sigal Oren. I would like to thank the anonymous ICALP reviewers for their helpful feedback.

Cite AsGet BibTex

Matan Gilboa. A Characterization of Complexity in Public Goods Games. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 73:1-73:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ICALP.2024.73

Abstract

We complete the characterization of the computational complexity of equilibrium in public goods games on graphs. In this model, each vertex represents an agent deciding whether to produce a public good, with utility defined by a "best-response pattern" determining the best response to any number of productive neighbors. We prove that the equilibrium problem is NP-complete for every finite non-monotone best-response pattern. This answers the open problem of [Gilboa and Nisan, 2022], and completes the answer to a question raised by [Papadimitriou and Peng, 2021], for all finite best-response patterns.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic game theory
  • Theory of computation → Exact and approximate computation of equilibria
  • Theory of computation → Problems, reductions and completeness
Keywords
  • Nash Equilibrium
  • Public Goods
  • Computational Complexity

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads

References

  1. Yann Bramoullé and Rachel Kranton. Public goods in networks. Journal of Economic Theory, 135(1):478-494, 2007. URL: https://doi.org/10.1016/j.jet.2006.06.006.
  2. Mustapha Chellali, Odile Favaron, Adriana Hansberg, and Lutz Volkmann. k-domination and k-independence in graphs: A survey. Graphs and Combinatorics, 28(1):1-55, 2012. URL: https://doi.org/10.1007/s00373-011-1040-3.
  3. Matan Gilboa and Noam Nisan. Complexity of public goods games on graphs. In Panagiotis Kanellopoulos, Maria Kyropoulou, and Alexandros A. Voudouris, editors, Algorithmic Game Theory - 15th International Symposium, SAGT 2022, Colchester, UK, September 12-15, 2022, Proceedings, volume 13584 of Lecture Notes in Computer Science, pages 151-168. Springer, 2022. URL: https://doi.org/10.1007/978-3-031-15714-1_9.
  4. David Kempe, Sixie Yu, and Yevgeniy Vorobeychik. Inducing equilibria in networked public goods games through network structure modification. In Amal El Fallah Seghrouchni, Gita Sukthankar, Bo An, and Neil Yorke-Smith, editors, Proceedings of the 19th International Conference on Autonomous Agents and Multiagent Systems, AAMAS '20, Auckland, New Zealand, May 9-13, 2020, pages 611-619. International Foundation for Autonomous Agents and Multiagent Systems, 2020. URL: https://doi.org/10.5555/3398761.3398835.
  5. Max Klimm and Maximilian J. Stahlberg. Complexity of equilibria in binary public goods games on undirected graphs. In Kevin Leyton-Brown, Jason D. Hartline, and Larry Samuelson, editors, Proceedings of the 24th ACM Conference on Economics and Computation, EC 2023, London, United Kingdom, July 9-12, 2023, pages 938-955. ACM, 2023. URL: https://doi.org/10.1145/3580507.3597780.
  6. Arnab Maiti and Palash Dey. On parameterized complexity of binary networked public goods game. In Piotr Faliszewski, Viviana Mascardi, Catherine Pelachaud, and Matthew E. Taylor, editors, proceedings of the 20th International Conference on Autonomous Agents and Multiagent Systems (AAMAS-2022), pages 871-879, Auckland New Zealand, 2022. International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS). URL: https://doi.org/10.5555/3535850.3535948.
  7. Christos H. Papadimitriou and Binghui Peng. Public goods games in directed networks. In Péter Biró, Shuchi Chawla, and Federico Echenique, editors, EC '21: The 22nd ACM Conference on Economics and Computation, Budapest, Hungary, July 18-23, 2021, pages 745-762, Budapest Hungary, 2021. ACM. URL: https://doi.org/10.1145/3465456.3467616.
  8. Thomas J. Schaefer. The complexity of satisfiability problems. In Richard J. Lipton, Walter A. Burkhard, Walter J. Savitch, Emily P. Friedman, and Alfred V. Aho, editors, Proceedings of the 10th Annual ACM Symposium on Theory of Computing, May 1-3, 1978, San Diego, California, USA, pages 216-226, San Diego California USA, 1978. ACM. URL: https://doi.org/10.1145/800133.804350.
  9. Yongjie Yang and Jianxin Wang. A refined study of the complexity of binary networked public goods games. CoRR, abs/2012.02916, 2020. URL: https://doi.org/10.48550/arXiv.2012.02916.
  10. Sixie Yu, Kai Zhou, P. Jeffrey Brantingham, and Yevgeniy Vorobeychik. Computing equilibria in binary networked public goods games. CoRR, abs/1911.05788, 2019. URL: https://doi.org/10.48550/arXiv.1911.05788.
  11. Sixie Yu, Kai Zhou, P. Jeffrey Brantingham, and Yevgeniy Vorobeychik. Computing equilibria in binary networked public goods games. In The 34th AAAI Conference on Artificial Intelligence, AAAI 2020, The 32nd Innovative Applications of Artificial Intelligence Conference, IAAI 2020, The 10th AAAI Symposium on Educational Advances in Artificial Intelligence, EAAI 2020, New York, NY, USA, February 7-12, 2020, volume 34(2), pages 2310-2317. AAAI Press, 2020. URL: https://doi.org/10.1609/aaai.v34i02.5609.