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A Characterization of Complexity in Public Goods Games

Author Matan Gilboa

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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

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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.

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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

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.

References

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  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.
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