Public Goods Games in Directed Networks with Constraints on Sharing

2025-11-14

AI Summary

This paper studies public goods games on directed networks with shared capacity constraints: each player decides whether to purchase an indivisible good and may share it with at most $k$ out-neighbors. The core questions concern existence, computability, and efficiency (e.g., price of anarchy) of pure- and mixed-strategy Nash equilibria. Leveraging tools from game theory, graph theory, and computational complexity, the authors establish the first sharp complexity dichotomy—precisely characterizing equilibrium existence and P vs. NP-hardness boundaries across values of $k$ and classes of directed graphs (e.g., DAGs, strongly connected graphs). Their theoretical contributions cover both pure and mixed strategies, systematically identifying capacity bottlenecks and topological asymmetry as fundamental sources of inefficiency. The results yield tight tractability criteria and design insights for networked public good allocation.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Multiagent Systems: Mechanism Design
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Social Networks and Social Media: Computational social science

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.

Problem

• Studying public goods games with indivisible goods in directed networks
• Analyzing equilibria existence and computation under capacity constraints
• Establishing complexity dichotomies for different network structures and capacities

Innovation

• Directed networks model public goods sharing
• Capacity constraints limit neighbor benefit selection
• Analyze Nash equilibria existence computation efficiency