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A Characterization of Complexity in Public Goods Games
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Matan Gilboa 
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51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Colloquium on Automata, Languages, and Programming (ICALP) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2024-07-02
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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.
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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
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
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References
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