TY - GEN
T1 - Complexity of Public Goods Games on Graphs
AU - Gilboa, Matan
AU - Nisan, Noam
N1 - 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.
AB - 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.
KW - Computational Complexity
KW - Nash Equilibrium
KW - Public Goods
UR - http://www.scopus.com/inward/record.url?scp=85138816766&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-15714-1_9
DO - 10.1007/978-3-031-15714-1_9
M3 - منشور من مؤتمر
SN - 9783031157134
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 151
EP - 168
BT - Algorithmic Game Theory - 15th International Symposium, SAGT 2022, Proceedings
A2 - Kanellopoulos, Panagiotis
A2 - Kyropoulou, Maria
A2 - Voudouris, Alexandros
PB - Springer Science and Business Media Deutschland GmbH
T2 - 15th International Symposium on Algorithmic Game Theory, SAGT 2022
Y2 - 12 September 2022 through 15 September 2022
ER -