Directed graphical structure, Nash equilibrium, and potential games

Shuige Liu

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


This paper considers the directed graphical structure of a game, called influence structure, where a directed edge from player i to player j indicates that player i may be able to affect j's payoff via his unilateral change of strategies. We give a necessary and sufficient condition for the existence of pure-strategy Nash equilibrium of games having a directed graph in terms of the structure of that graph. We also discuss the relationship between the structure of graphs and potential games.

Original languageEnglish
Pages (from-to)273-277
Number of pages5
JournalOperations Research Letters
Issue number3
Publication statusPublished - 2018 May


  • Directed graphical games
  • Potential games
  • Pure-strategy Nash equilibrium

ASJC Scopus subject areas

  • Software
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering
  • Applied Mathematics


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