Complexity of Public Goods Games on Graphs

Matan Gilboa*, Noam Nisan

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations


We study the computational complexity of “public goods games on networks”. In this model, each vertex in a graph is an agent that needs to take a binary decision of whether to “produce a good” or not. Each agent’s utility depends on the number of its neighbors in the graph that produce the good, as well as on its own action. This dependence can be captured by a “pattern” T:IN→{0,1} that describes an agent’s best response to every possible number of neighbors that produce the good. Answering a question of [Papadimitriou and Peng, 2021], we prove that for some simple pattern T the problem of determining whether a non-trivial pure Nash equilibrium exists is NP-complete. We extend our result to a wide class of such T, but also find a new polynomial time algorithm for some specific simple pattern T. We leave open the goal of characterizing the complexity for all patterns.

Original languageAmerican English
Title of host publicationAlgorithmic Game Theory - 15th International Symposium, SAGT 2022, Proceedings
EditorsPanagiotis Kanellopoulos, Maria Kyropoulou, Alexandros Voudouris
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages18
ISBN (Print)9783031157134
StatePublished - 2022
Event15th International Symposium on Algorithmic Game Theory, SAGT 2022 - Colchester, United Kingdom
Duration: 12 Sep 202215 Sep 2022

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13584 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference15th International Symposium on Algorithmic Game Theory, SAGT 2022
Country/TerritoryUnited Kingdom

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.


  • Computational Complexity
  • Nash Equilibrium
  • Public Goods


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