The Price of Universal Temporal Reachability

TL;DR

This paper investigates the strategic behavior of players in dynamic networks where edges appear at specific times, revealing that the inefficiency of equilibrium states can grow proportionally with the network size, unlike static networks.

Contribution

It introduces a game-theoretic model for dynamic networks and demonstrates that the price of anarchy can be linear in the number of vertices for shortest-distance strategies.

Findings

Price of anarchy can be proportional to the number of vertices

Contrasts with the constant price conjectured for static networks

Highlights the impact of temporal dynamics on network efficiency

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 $\alpha$, 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.