On Parameterized Complexity of Binary Networked Public Goods Game

TL;DR

This paper investigates the computational complexity of finding pure strategy Nash equilibria in binary networked public goods games, analyzing various graph parameters and identifying cases with guaranteed equilibria.

Contribution

It provides a detailed parameterized complexity analysis of the problem, including hardness results and fixed-parameter tractable algorithms for specific graph classes.

Findings

NP-complete in general

W[1]-hardness for certain parameters

Existence of PSNE in specific graph classes with homogeneous utilities

Abstract

In the Binary Networked Public Goods game, every player needs to decide if she participates in a public project whose utility is shared equally by the community. We study the problem of deciding if there exists a pure strategy Nash equilibrium (PSNE) in such games. The problem is already known to be NP-complete. We provide fine-grained analysis of this problem under the lens of parameterized complexity theory. We consider various natural graph parameters and show either W[1]-hardness or exhibit an FPT algorithm. We finally exhibit some special graph classes, for example path, cycle, bi-clique, complete graph, etc., which always have a PSNE if the utility function of the players are fully homogeneous.