TY - JOUR
T1 - Directed graphical structure, Nash equilibrium, and potential games
AU - Liu, Shuige
N1 - Funding Information:
The author thanks Yukihiko Funaki, Mamoru Kaneko, Chih Chang, Yongsub Chun, János Flesch, Ayumi Igarashi, Ryoichiro Ishikawa, Biung-Ghi Ju, Dmitriy Kvasov, Zsombor Z. Méder, Satoshi Nakada, William S. Neilson, Martin J. Osborne, Carolyn Pitchik, Chengzhong Qin, Dan Qin, Tim Roughgarden, Agnieszka Rusinoska, Marco Scarsini, Nano Shion, Nobuyuki Suzuki, Robert Veszteg, Jun Wako, Makoto Yokoo, three anonymous reviewers, and the editor of this journal for their invaluable comments and suggestions. She is grateful for the support of Grant-in-Aids for Young Scientists (B) of JSPS No. 17K13707 and Grant for Special Research Project No. 2017K-016 of Waseda University.
Publisher Copyright:
© 2018 Elsevier B.V.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2018/5
Y1 - 2018/5
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
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U2 - 10.1016/j.orl.2018.02.002
DO - 10.1016/j.orl.2018.02.002
M3 - Article
AN - SCOPUS:85042722041
VL - 46
SP - 273
EP - 277
JO - Operations Research Letters
JF - Operations Research Letters
SN - 0167-6377
IS - 3
ER -