Greedy Routing Reachability Games

2026-01-30

AI Summary

This study addresses the problem of achieving global reachability via greedy routing in networks of autonomous agents equipped only with local views, while minimizing the number of connections per agent. By formulating a strategic link-formation game in a metric space, agents simultaneously minimize their own degrees and ensure network-wide reachability. The work reveals, for the first time, the fundamental mechanisms underlying greedy-routing-compatible network formation without relying on distributional assumptions or predefined protocols, and provides a systematic analysis distinguishing directed and undirected settings. The main contributions include proving that in the directed case, an optimal equilibrium exists and is efficiently computable; in the undirected two-dimensional setting, the proposed approximate equilibrium outperforms Delaunay triangulation, achieves a price of anarchy between 1.75 and 1.8, and is computable in polynomial time.

Technology Category

• Multiagent Systems: Mechanism Design
• Planning, Routing, and Scheduling: Planning under Uncertainty
• Game Theory and Economic Paradigms: Mechanism Design

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: Social media analysis through the lenses of networks

Abstract

Today's networks consist of many autonomous entities that follow their own objectives, i.e., smart devices or parts of large AI systems, that are interconnected. Given the size and complexity of most communication networks, each entity typically only has a local view and thus must rely on a local routing protocol for sending and forwarding packets. A common solution for this is greedy routing, where packets are locally forwarded to a neighbor in the network that is closer to the packet's destination. In this paper we investigate a game-theoretic model with autonomous agents that aim at forming a network where greedy routing is enabled. The agents are positioned in a metric space and each agent tries to establish as few links as possible, while maintaining that it can reach every other agent via greedy routing. Thus, this model captures how greedy routing networks are formed without any assumption on the distribution of the agents or the specific employed greedy routing protocol. Hence, it distills the essence that makes greedy routing work. We study two variants of the model: with directed edges or with undirected edges. For the former, we show that equilibria exist, have optimal total cost, and that in Euclidean metrics they can be found efficiently. However, even for this simple setting computing optimal strategies is NP-hard. For the much more challenging setting with undirected edges, we show for the realistic setting with agents in 2D Euclidean space that the price of anarchy is between 1.75 and 1.8 and for higher dimensions it is less than 2. Also, we show that best response dynamics may cycle, but that in Euclidean space almost optimal approximate equilibria can be computed in polynomial time. Moreover, for 2D Euclidean space, these approximate equilibria outperform the well-known Delaunay triangulation.

Problem

• greedy routing
• network formation
• autonomous agents
• reachability
• game theory

Innovation

• Greedy Routing
• Network Formation Game
• Price of Anarchy
• Best Response Dynamics
• Delaunay Triangulation