  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.
