A Characterization of Complexity in Public Goods Games

TL;DR

This paper fully characterizes the computational complexity of finding equilibria in public goods games on graphs, showing NP-completeness for all finite non-monotone best-response patterns, thus resolving open problems in the field.

Contribution

It proves NP-completeness of equilibrium computation for all finite non-monotone best-response patterns in public goods games on graphs, completing prior open questions.

Findings

NP-complete for all finite non-monotone patterns

Answers open problems from Gilboa and Nisan (2022)

Completes characterization for all finite best-response patterns

Abstract

We complete the characterization of the computational complexity of equilibrium in public goods games on graphs. In this model, each vertex represents an agent deciding whether to produce a public good, with utility defined by a "best-response pattern" determining the best response to any number of productive neighbors. We prove that the equilibrium problem is NP-complete for every finite non-monotone best-response pattern. This answers the open problem of [Gilboa and Nisan, 2022], and completes the answer to a question raised by [Papadimitriou and Peng, 2021], for all finite best-response patterns.