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On Parameterized Complexity of Binary Networked Public Goods Game

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Abstract

In the binary networked public goods (BNPG for short) game, every player needs to decide if she participates in a public project whose utility is shared equally by the community. We study the problem of deciding if there exists a pure strategy Nash equilibrium (PSNE) in such games. The problem is already known to be \(\textsf{NP}\)-complete. This casts doubt on predictive power of PSNE in BNPG games. We provide fine-grained analysis of this problem under the lens of parameterized complexity theory. We consider various natural graph parameters and show \(\mathsf {W[1]}\)-hardness, XP, and \(\textsf{FPT}\) results. Hence, our work significantly improves our understanding of BNPG games where PSNE serves as a reliable solution concept. We finally prove that some graph classes, for example path, cycle, bi-clique, and complete graph, always have a PSNE if the utility function of the players are same.

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  1. IIT Kharagpur, Kharagpur, India

    Arnab Maiti & Palash Dey

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  1. Arnab Maiti
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  2. Palash Dey
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Correspondence to Palash Dey.

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Maiti, A., Dey, P. On Parameterized Complexity of Binary Networked Public Goods Game. Algorithmica 86, 307–333 (2024). https://doi.org/10.1007/s00453-023-01174-4

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