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

Naoka Fukuzono, Tesshu Hanaka, Hironori Kiya, Hirotaka Ono

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)281-294
Number of pages14
JournalDiscrete Applied Mathematics
Volume321
DOIs
Publication statusPublished - Nov 15 2022

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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