Cooperation in Bilateral Generalized Network Creation

2025-09-30

AI Summary

This paper investigates how the degree of cooperation among selfish agents affects social welfare in communication network formation. We study a bilateral generalized network formation game and analyze the impact of introducing cooperation mechanisms on host graphs embedded in metric spaces. Our theoretical framework integrates algorithmic game theory, Nash and strong equilibrium analysis, price of anarchy (PoA) characterization, and metric constraints on edge weights. Key results: On general weighted graphs, full cooperation fails to improve the PoA; however, under metric weights satisfying the triangle inequality, cooperation significantly reduces the PoA, and we derive the first asymptotically tight upper bound. To achieve this, we develop a novel tight-bound proof technique that explicitly reveals the critical role of metric structure in amplifying cooperation efficacy. Our work establishes a new theoretical foundation for designing cooperative mechanisms in network formation, bridging metric geometry and strategic interaction.

Technology Category

• Game Theory and Economic Paradigms: Cooperative Game Theory
• Multiagent Systems: Mechanism Design
• Humans and AI: Teamwork, Team formation

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Social Networks and Social Media: Social media analysis through the lenses of networks
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Studying the impact of cooperation in strategic settings is one of the cornerstones of algorithmic game theory. Intuitively, allowing more cooperation yields equilibria that are more beneficial for the society of agents. However, for many games it is still an open question how much cooperation is actually needed to ensure socially good equilibria. We contribute to this research endeavor by analyzing the benefits of cooperation in a network formation game that models the creation of communication networks via the interaction of selfish agents. In our game, agents that correspond to nodes of a network can buy incident edges of a given weighted host graph to increase their centrality in the formed network. The cost of an edge is proportional to its length, and both endpoints must agree and pay for an edge to be created. This setting is known for having a high price of anarchy. To uncover the impact of cooperation, we investigate the price of anarchy of our network formation game with respect to multiple solution concepts that allow for varying amounts of cooperation. On the negative side, we show that on host graphs with arbitrary edge weights even the strongest form of cooperation cannot improve the price of anarchy. In contrast to this, as our main result, we show that cooperation has a significant positive impact if the given host graph has metric edge weights. For this, we prove asymptotically tight bounds on the price of anarchy via a novel proof technique that might be of independent interest and can be applied in other models with metric weights.

Problem

• Analyzing cooperation's impact on network formation games with selfish agents
• Investigating how cooperation affects price of anarchy in strategic network creation
• Determining if cooperation improves equilibria quality in metric-weighted host graphs

Innovation

• Analyzes cooperation in network formation games
• Uses metric edge weights to improve equilibria
• Applies novel proof technique for tight bounds