Strategic Network Creation for Enabling Greedy Routing

2024-03-22

arXiv.org

AI Summary

This paper addresses the challenge of achieving low-latency, high-stability, and cost-efficient routing in dynamic complex networks. We propose the first game-theoretic network formation framework that unifies greedy routing feasibility with strategic edge creation by autonomous agents. Agents self-organize edges in a metric space to jointly optimize global routability and local path stretch. Our theoretical contributions are threefold: (1) We prove the existence of Nash equilibria for tree topologies and 1–2 metric spaces; (2) In Euclidean space, we construct low-stretch Θ-graphs and establish their approximate Nash stability; (3) For general metrics, we provide existence guarantees for approximate equilibria parameterized by link cost functions. Collectively, these results yield a novel design paradigm and rigorous theoretical foundation for self-organizing, greedily routable networks.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

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: Applications and emergent phenomena

Abstract

Today we rely on networks that are created and maintained by smart devices. For such networks, there is no governing central authority but instead the network structure is shaped by the decisions of selfish intelligent agents. A key property of such communication networks is that they should be easy to navigate for routing data. For this, a common approach is greedy routing, where every device simply routes data to a neighbor that is closer to the respective destination. Networks of intelligent agents can be analyzed via a game-theoretic approach and in the last decades many variants of network creation games have been proposed and analyzed. In this paper we present the first game-theoretic network creation model that incorporates greedy routing, i.e., the strategic agents in our model are embedded in some metric space and strive for creating a network among themselves where all-pairs greedy routing is enabled. Besides this, the agents optimize their connection quality within the created network by aiming for greedy routing paths with low stretch. For our model, we analyze the existence of (approximate)-equilibria and the computational hardness in different underlying metric spaces. E.g., we characterize the set of equilibria in 1-2-metrics and tree metrics and show that Nash equilibria always exist. For Euclidean space, the setting which is most relevant in practice, we prove that equilibria are not guaranteed to exist but that the well-known $Theta$-graph construction yields networks having a low stretch that are game-theoretically almost stable. For general metric spaces, we show that approximate equilibria exist where the approximation factor depends on the cost of maintaining any link.

Problem

• Network Routing Strategy
• Fast Data Transmission
• Complex Dynamic Environment

Innovation

• Greedy Routing Strategy
• Game-Theoretic Network Construction
• Stable State Approximation