The Price of Universal Temporal Reachability
This addresses inefficiency in decentralized network design for dynamic systems, such as communication or transportation networks, but is incremental as it builds on known game-theoretic models.
The paper tackles the problem of strategic network formation in dynamic graphs where edges exist at specific times, showing that the price of anarchy—measuring inefficiency due to selfish behavior—can be proportional to the number of vertices, in contrast to constant bounds conjectured for static networks.
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.