TY - JOUR

T1 - The existence of a pure Nash equilibrium in the two-player competitive diffusion game on graphs having chordality

AU - Fukuzono, Naoka

AU - Hanaka, Tesshu

AU - Kiya, Hironori

AU - Ono, Hirotaka

N1 - Funding Information:
This work was partially supported by JSPS KAKENHI Grant Number JP17H01698 , JP17K19960 , JP19K21537 , JP20H00081 , JP20H05967 , JP21H05852 , JP21K17707 , JP21K21283 .
Publisher Copyright:
© 2022 Elsevier B.V.

PY - 2022/11/15

Y1 - 2022/11/15

N2 - The competitive diffusion game is a game-theoretic model of information spreading on a graph proposed by Alon et al. (2010). It models the diffusion process of information in social networks where several competitive companies want to spread their information, for example. The nature of this game strongly depends on the graph topology, and the relationship is studied from several aspects. In this paper, we investigate the existence of a pure Nash equilibrium of the two-player competitive diffusion game on chordal and its related graphs. We show that a pure Nash equilibrium always exists on split graphs, block graphs, and interval graphs, all of which are well-known subclasses of chordal graphs. On the other hand, we show that a pure Nash equilibrium does not always exist on (strongly) chordal graphs; the boundary of the existence of a pure Nash equilibrium is found.

AB - The competitive diffusion game is a game-theoretic model of information spreading on a graph proposed by Alon et al. (2010). It models the diffusion process of information in social networks where several competitive companies want to spread their information, for example. The nature of this game strongly depends on the graph topology, and the relationship is studied from several aspects. In this paper, we investigate the existence of a pure Nash equilibrium of the two-player competitive diffusion game on chordal and its related graphs. We show that a pure Nash equilibrium always exists on split graphs, block graphs, and interval graphs, all of which are well-known subclasses of chordal graphs. On the other hand, we show that a pure Nash equilibrium does not always exist on (strongly) chordal graphs; the boundary of the existence of a pure Nash equilibrium is found.

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U2 - 10.1016/j.dam.2022.04.025

DO - 10.1016/j.dam.2022.04.025

M3 - Article

AN - SCOPUS:85134273214

VL - 321

SP - 281

EP - 294

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -