Tight Inapproximability of Nash Equilibria in Public Goods Games (2402.14198v1)
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 $\varepsilon$.
- Nizar Allouch. On the private provision of public goods on networks. Journal of Economic Theory, 157:527–552, 2015. doi:10.1016/j.jet.2015.01.007.
- Public goods in networks. Journal of Economic Theory, 135(1):478–494, 2007. doi:10.1016/j.jet.2006.06.006.
- Games played on networks. In The Oxford Handbook of the Economics of Networks, pages 83–112. Oxford University Press, 2016. doi:10.1093/oxfordhb/9780199948277.013.8.
- Strategic interaction and networks. American Economic Review, 104(3):898–930, 2014. doi:10.1257/aer.104.3.898.
- Best-response dynamics in directed network games. Journal of Economic Theory, 213:105720, 2023. doi:10.1016/j.jet.2023.105720.
- Settling the complexity of computing two-player Nash equilibria. Journal of the ACM, 56(3):14:1–14:57, 2009. doi:10.1145/1516512.1516516.
- Pure-circuit: Strong inapproximability for PPAD. In Proceedings of the 63rd IEEE Symposium on Foundations of Computer Science (FOCS), pages 159–170, 2022. doi:10.1109/focs54457.2022.00022.
- Optimal equilibria of the best shot game. Journal of Public Economic Theory, 13(6):885–901, 2011. doi:10.1111/j.1467-9779.2011.01523.x.
- On the complexity of Nash equilibria and other fixed points. SIAM Journal on Computing, 39(6):2531–2597, 2010. doi:10.1137/080720826.
- Network games. Review of Economic Studies, 77(1):218–244, 2009. doi:10.1111/j.1467-937x.2009.00570.x.
- Matan Gilboa. A characterization of complexity in public goods games. ArXiv, 2023. doi:10.48550/arxiv.2301.11580.
- Complexity of public goods games on graphs. In Proceedings of the 15th International Symposium on Algorithmic Game Theory (SAGT), pages 151–168, 2022. doi:10.1007/978-3-031-15714-1_9.
- Complexity of equilibria in binary public goods games on undirected graphs. In Proceedings of the 24th ACM Conference on Economics and Computation (EC), pages 938–955, 2023. doi:10.1145/3580507.3597780.
- Dunia López-Pintado. Public goods in directed networks. Economics Letters, 121(2):160–162, 2013. doi:10.1016/j.econlet.2013.08.003.
- Public goods games in directed networks. Games and Economic Behavior, 139:161–179, 2023. doi:10.1016/j.geb.2023.02.002.
- Aviad Rubinstein. Inapproximability of Nash equilibrium. SIAM Journal on Computing, 47(3):917–959, 2018. doi:10.1137/15M1039274.
- Computing equilibria in binary networked public goods games. Proceedings of the 34th AAAI Conference on Artificial Intelligence (AAAI), pages 2310–2317, 2020. doi:10.1609/aaai.v34i02.5609.