Public Goods Games in Directed Networks with Constraints on Sharing

TL;DR

This paper analyzes public goods games on directed networks with capacity constraints, exploring equilibrium existence, computation, and efficiency, and providing complexity results based on network structure and sharing capacity.

Contribution

It introduces a novel model of public goods games with directed sharing constraints and offers a comprehensive analysis of equilibrium properties and computational complexity.

Findings

Existence and computation of Nash equilibria depend on network structure and capacity.

Complexity dichotomies are established for equilibrium analysis.

The study provides insights into efficiency and strategic behavior in constrained sharing networks.

Abstract

In a public goods game, every player chooses whether or not to buy a good that all neighboring players will have access to. We consider a setting in which the good is indivisible, neighboring players are out-neighbors in a directed graph, and there is a capacity constraint on their number, k, that can benefit from the good. This means that each player makes a two-pronged decision: decide whether or not to buy and, conditional on buying, choose which k out-neighbors to share access. We examine both pure and mixed Nash equilibria in the model from the perspective of existence, computation, and efficiency. We perform a comprehensive study for these three dimensions with respect to both sharing capacity (k) and the network structure (the underlying directed graph), and establish sharp complexity dichotomies for each.