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.
- Directed graphical games
- Potential games
- Pure-strategy Nash equilibrium
ASJC Scopus subject areas
- Management Science and Operations Research
- Industrial and Manufacturing Engineering
- Applied Mathematics