Two Influence Maximization Games on Graphs Made Temporal

TL;DR

This paper extends influence spreading games to temporal graphs where edges change over time, exploring Nash equilibria existence and differences from static cases, with implications for dynamic network influence modeling.

Contribution

It introduces a new framework for competitive diffusion and Voronoi games on temporal graphs, analyzing Nash equilibria existence and differences from static graphs.

Findings

Nash equilibria exist in certain temporal graph classes when edges do not disappear.

Temporal diffusion and Voronoi games differ significantly from static cases.

Equivalence of the two games on static trees and cycles does not hold in the temporal setting.

Abstract

To address the dynamic nature of real-world networks, we generalize competitive diffusion games and Voronoi games from static to temporal graphs, where edges may appear or disappear over time. This establishes a new direction of studies in the area of graph games, motivated by applications such as influence spreading. As a first step, we investigate the existence of Nash equilibria in 2-player competitive diffusion and Voronoi games on different temporal graph classes. Even when restricting our studies to temporal trees and cycles, this turns out to be a challenging undertaking, revealing significant differences between the two games in the temporal setting. Notably, both games are equivalent on static trees and cycles. Our two main technical results are (algorithmic) proofs for the existence of Nash equilibria in 2-player competitive diffusion and temporal Voronoi games when the edges are restricted not to disappear over time.