Temporal Network Creation Games: The Impact of Flexible Labels

2026-03-06

AI Summary

This work proposes a novel temporal network formation game that relaxes the common assumption of fixed edge timestamps by allowing agents to strategically choose both the purchase and activation time of their edges. This modeling choice better captures the dynamic nature of real-world network formation, where timing decisions are integral to connectivity. By incorporating a flexible timestamp mechanism into a game-theoretic framework, the study establishes the existence of Nash equilibria under various reachability objectives and cost functions. Furthermore, it derives tight upper and lower bounds on the Price of Anarchy (PoA) and Price of Stability (PoS), thereby quantifying the impact of strategic temporal decisions on overall system efficiency. The analysis reveals how endogenous timing choices influence equilibrium outcomes and social welfare in temporal networks.

Technology Category

• Planning, Routing, and Scheduling: Temporal Planning
• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Cooperative Game Theory

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: Efficient manipulation of static and dynamic Web-related graphs

Abstract

A crucial aspect of research is understanding how real-world networks, such as transportation and information networks, are formed. A prominent model for such networks was introduced by \cite{fabrikant_network_2003} and extended by \cite{bilo_temporal_2023}, incorporating temporal graphs to better represent real-world networks. In this model, there is a given host graph with $n$ agents (represented by nodes) and time labels on the edges. Each agent can establish connections by purchasing edges. This makes the edges present at the time steps given by the time labels of the host graph. The goal of each agent is to reach as many other agents as possible while minimizing the number of edges bought. However, this model makes the simplifying assumption that each edge comes with predetermined time steps. We address this deficiency by extending the model of Bilo et al. \cite{bilo_temporal_2023} to allow agents to purchase edges and to decide when they appear. To capture a variety of real-world applications, we study two reachability models and several cost functions based on the label an agent assigns to an edge. For these settings, we provide proofs of existence of Nash equilibria, as well as lower and upper bounds on the Price of Anarchy and Price of Stability.

Problem

• Temporal Network Creation Games
• Flexible Time Labels
• Network Formation
• Reachability
• Strategic Edge Purchase

Innovation

• Temporal Network Creation Games
• Flexible Time Labels
• Nash Equilibrium
• Price of Anarchy
• Reachability Models