Two-Player Competitive Diffusion Game: Graph Classes and the Existence of a Nash Equilibrium

Fukuzono, Naoka; Hanaka, Tesshu; Kiya, Hironori; Ono, Hiroyuki; Yamaguchi, Ryogo

doi:10.1007/978-3-030-38919-2_52

Cited by 5 publications

(2 citation statements)

References 14 publications

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“…Recently, a new line of work established to capture the nature of real world social networks moving from static graphs to temporal graphs [6]. They study the complexity of competitive diffusion games [3,15] and Voronoi games [12,2].…”

Section: Related Workmentioning

confidence: 99%

Being an Influencer is Hard: The Complexity of Influence Maximization in Temporal Graphs with a Fixed Source

Deligkas¹,

Döring²,

Eiben³

et al. 2023

Preprint

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We consider the influence maximization problem over a temporal graph, where there is a single fixed source. We deviate from the standard model of influence maximization, where the goal is to choose the set of most influential vertices. Instead, in our model we are given a fixed vertex, or source, and the goal is to find the best time steps to transmit so that the influence of this vertex is maximized. We frame this problem as a spreading process that follows a variant of the susceptible-infected-susceptible (SIS) model and we focus on four objective functions. In the MaxSpread objective, the goal is to maximize the total number of vertices that get infected at least once. In the MaxViral objective, the goal is to maximize the number of vertices that are infected at the same time step. In the MaxViralTstep objective, the goal is to maximize the number of vertices that are infected at a given time step. Finally, in MinNonViralTime, the goal is to maximize the total number of vertices that get infected every d time steps. We perform a thorough complexity theoretic analysis for these four objectives over three different scenarios: (1) the unconstrained setting where the source can transmit whenever it wants; (2) the window-constrained setting where the source has to transmit at either a predetermined, or a shifting window; (3) the periodic setting where the temporal graph has a small period. We prove that all of these problems, with the exception of MaxSpread for periodic graphs, are intractable even for very simple underlying graphs.

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Section: Related Workmentioning

confidence: 99%

Being an Influencer is Hard: The Complexity of Influence Maximization in Temporal Graphs with a Fixed Source

Deligkas¹,

Döring²,

Eiben³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Competitive diffusion games were introduced by Alon et al [2]. Research on competitive diffusion games so far mainly focused on the existence of Nash equilibria on a variety of graph classes for different numbers of players [2,6,17,23,24,25,27]. Also, the (parameterized) computational complexity of deciding the existence of a Nash equilibrium has been studied [14,18].…”

Section: Introductionmentioning

confidence: 99%

Two Influence Maximization Games on Graphs Made Temporal

Boehmer¹,

Froese²,

Henkel³

et al. 2021

Preprint

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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.

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Existence of pure Nash equilibria in 2-player information diffusion games with strict public preferences

Fujii

2022

Cent Eur J Oper Res

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Two-Player Competitive Diffusion Game: Graph Classes and the Existence of a Nash Equilibrium

Cited by 5 publications

References 14 publications

Being an Influencer is Hard: The Complexity of Influence Maximization in Temporal Graphs with a Fixed Source

Being an Influencer is Hard: The Complexity of Influence Maximization in Temporal Graphs with a Fixed Source

Two Influence Maximization Games on Graphs Made Temporal

Existence of pure Nash equilibria in 2-player information diffusion games with strict public preferences

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