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arXiv · 2402.14198

Tight Inapproximability of Nash Equilibria in Public Goods Games

Jérémi Do Dinh·Alexandros Hollender
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Abstract

We study public goods games, a type of game where every player has to decide whether or not to produce a good which is public, i.e., neighboring players can also benefit from it. Specifically, we consider a setting where the good is indivisible and where the neighborhood structure is represented by a directed graph, with the players being the nodes. Papadimitriou and Peng (2023) recently showed that in this setting computing mixed Nash equilibria is PPAD-hard, and that this remains the case even for $\varepsilon$-well-supported approximate equilibria for some sufficiently small constant $\varepsilon$. In this work, we strengthen this inapproximability result by showing that the problem remains PPAD-hard for any non-trivial approximation parameter $\varepsilon$.

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BibTeXRIS

Jérémi Do Dinh, Alexandros Hollender. 2024-02-22. Tight Inapproximability of Nash Equilibria in Public Goods Games. https://doi.org/10.1016/j.ipl.2024.106486

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