The Price of Universal Temporal Reachability

2026-03-16

AI Summary

This study investigates the strategic behavior of selfish nodes in dynamic networks under temporal connectivity constraints and its impact on system efficiency. By formulating a network formation game where rational nodes add or remove time-labeled edges to minimize their individual costs—comprising both construction expenses and communication costs based on shortest temporal paths—the work integrates temporal graph theory with game-theoretic analysis. It establishes, for the first time, that under the definition of shortest temporal paths, the Price of Anarchy grows linearly with the number of nodes. This finding challenges the conventional understanding derived from static networks, where the Price of Anarchy remains constant, thereby revealing that network dynamics substantially exacerbate efficiency loss in decentralized settings.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• 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

Abstract

Dynamic networks are graphs in which edges are available only at specific time instants, modeling connections that change over time. The dynamic network creation game studies this setting as a strategic interaction where each vertex represents a player. Players can add or remove time-labeled edges in order to minimize their personal cost. This cost has two components: a construction cost, calculated as the number of time instants during which a player maintains edges multiplied by a constant $α$, and a communication cost, defined as the average distance to all other vertices in the network. Communication occurs through temporal paths, which are sequences of adjacent edges with strictly increasing time labels and no repeated vertices. We show for the shortest distance (minimizing the number of edges) that the price of anarchy can be proportional to the number of vertices, contrasting the constant price conjectured for static networks.

Problem

• dynamic networks
• temporal paths
• price of anarchy
• network creation game
• reachability

Innovation

• dynamic networks
• temporal paths
• price of anarchy
• network creation game
• time-labeled edges