Abstract
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 language | English |
|---|---|
| Pages (from-to) | 273-277 |
| Number of pages | 5 |
| Journal | Operations Research Letters |
| Volume | 46 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2018 May 1 |
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Keywords
- 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
Cite this
Directed graphical structure, Nash equilibrium, and potential games. / Liu, Shuige.
In: Operations Research Letters, Vol. 46, No. 3, 01.05.2018, p. 273-277.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Directed graphical structure, Nash equilibrium, and potential games
AU - Liu, Shuige
PY - 2018/5/1
Y1 - 2018/5/1
N2 - 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.
AB - 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.
KW - Directed graphical games
KW - Potential games
KW - Pure-strategy Nash equilibrium
UR - http://www.scopus.com/inward/record.url?scp=85042722041&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85042722041&partnerID=8YFLogxK
U2 - 10.1016/j.orl.2018.02.002
DO - 10.1016/j.orl.2018.02.002
M3 - Article
VL - 46
SP - 273
EP - 277
JO - Operations Research Letters
JF - Operations Research Letters
SN - 0167-6377
IS - 3
ER -