Complexity of Public Goods Games on Graphs

Matan Gilboa; Noam Nisan

doi:10.1007/978-3-031-15714-1_9

Complexity of Public Goods Games on Graphs

Matan Gilboa^*, Noam Nisan

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

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 language	American English
Title of host publication	Algorithmic Game Theory - 15th International Symposium, SAGT 2022, Proceedings
Editors	Panagiotis Kanellopoulos, Maria Kyropoulou, Alexandros Voudouris
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	151-168
Number of pages	18
ISBN (Print)	9783031157134
DOIs	https://doi.org/10.1007/978-3-031-15714-1_9
State	Published - 2022
Event	15th International Symposium on Algorithmic Game Theory, SAGT 2022 - Colchester, United Kingdom Duration: 12 Sep 2022 → 15 Sep 2022

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	13584 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	15th International Symposium on Algorithmic Game Theory, SAGT 2022
Country/Territory	United Kingdom
City	Colchester
Period	12/09/22 → 15/09/22

Bibliographical note

Funding Information:
This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation Programme (grant agreement no. 740282).

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

Keywords

Computational Complexity
Nash Equilibrium
Public Goods

Access to Document

10.1007/978-3-031-15714-1_9

Cite this

Gilboa, M., & Nisan, N. (2022). Complexity of Public Goods Games on Graphs. In P. Kanellopoulos, M. Kyropoulou, & A. Voudouris (Eds.), Algorithmic Game Theory - 15th International Symposium, SAGT 2022, Proceedings (pp. 151-168). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13584 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-15714-1_9

Gilboa, Matan ; Nisan, Noam. / Complexity of Public Goods Games on Graphs. Algorithmic Game Theory - 15th International Symposium, SAGT 2022, Proceedings. editor / Panagiotis Kanellopoulos ; Maria Kyropoulou ; Alexandros Voudouris. Springer Science and Business Media Deutschland GmbH, 2022. pp. 151-168 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Gilboa, M & Nisan, N 2022, Complexity of Public Goods Games on Graphs. in P Kanellopoulos, M Kyropoulou & A Voudouris (eds), Algorithmic Game Theory - 15th International Symposium, SAGT 2022, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 13584 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 151-168, 15th International Symposium on Algorithmic Game Theory, SAGT 2022, Colchester, United Kingdom, 12/09/22. https://doi.org/10.1007/978-3-031-15714-1_9

Complexity of Public Goods Games on Graphs. / Gilboa, Matan; Nisan, Noam.
Algorithmic Game Theory - 15th International Symposium, SAGT 2022, Proceedings. ed. / Panagiotis Kanellopoulos; Maria Kyropoulou; Alexandros Voudouris. Springer Science and Business Media Deutschland GmbH, 2022. p. 151-168 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13584 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N1 - Funding Information: This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation Programme (grant agreement no. 740282). Publisher Copyright: © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

PY - 2022

Y1 - 2022

N2 - 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.

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Gilboa M, Nisan N. Complexity of Public Goods Games on Graphs. In Kanellopoulos P, Kyropoulou M, Voudouris A, editors, Algorithmic Game Theory - 15th International Symposium, SAGT 2022, Proceedings. Springer Science and Business Media Deutschland GmbH. 2022. p. 151-168. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-031-15714-1_9

Complexity of Public Goods Games on Graphs

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