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 competitive diffusion and Voronoi games on different temporal graph classes. Even when restricting our studies to temporal paths 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 paths and cycles. Our two main technical results are (algorithmic) proofs for the existence of Nash equilibria in temporal competitive diffusion and temporal Voronoi games when the edges are restricted not to disappear over time.

翻译：为了应对现实世界网络的动态性质,我们推广了从静态到时间图的竞争性传播游戏和Voronoi游戏,其中边缘可能出现或随着时间的推移消失。这为图表游戏领域的研究提供了新的方向,其动机是影响力扩散等应用。作为第一步,我们调查了Nash在竞争性传播中的平衡和Voronoi游戏在不同时间图类中的平衡。即使我们的研究限于时间路径和周期,这证明是一项具有挑战性的工作,揭示了两个游戏在时间环境中的巨大差异。值得注意的是,这两种游戏都相当于静态路径和周期。我们的两个主要技术成果是(定量)证明Nash均衡存在于时间竞争性传播和时间性Voronoi游戏中,当边缘局限于不随着时间的推移消失时。