TY - JOUR
T1 - On the Structure of Weakly Acyclic Games
AU - Fabrikant, Alex
AU - Jaggard, Aaron D.
AU - Schapira, Michael
N1 - Funding Information: The first author was supported by a Cisco URP grant and a Princeton University postdoctoral fellowship. The second author was partially supported by NSF grants 0751674, 0753492, and 1101690. The third author was supported by a grant from the Israel Science Foundation (ISF) and by the Marie Curie Career Integration Grant (CIG). This is a revised and expanded version of a paper that appeared in the Proceedings of SAGT 2010.
PY - 2013/7
Y1 - 2013/7
N2 - The class of weakly acyclic games, which includes potential games and dominance-solvable games, captures many practical application domains. In a weakly acyclic game, from any starting state, there is a sequence of better-response moves that leads to a pure Nash equilibrium; informally, these are games in which natural distributed dynamics, such as better-response dynamics, cannot enter inescapable oscillations. We establish a novel link between such games and the existence of pure Nash equilibria in subgames. Specifically, we show that the existence of a unique pure Nash equilibrium in every subgame implies the weak acyclicity of a game. In contrast, the possible existence of multiple pure Nash equilibria in every subgame is insufficient for weak acyclicity in general; here, we also systematically identify the special cases (in terms of the number of players and strategies) for which this is sufficient to guarantee weak acyclicity.
AB - The class of weakly acyclic games, which includes potential games and dominance-solvable games, captures many practical application domains. In a weakly acyclic game, from any starting state, there is a sequence of better-response moves that leads to a pure Nash equilibrium; informally, these are games in which natural distributed dynamics, such as better-response dynamics, cannot enter inescapable oscillations. We establish a novel link between such games and the existence of pure Nash equilibria in subgames. Specifically, we show that the existence of a unique pure Nash equilibrium in every subgame implies the weak acyclicity of a game. In contrast, the possible existence of multiple pure Nash equilibria in every subgame is insufficient for weak acyclicity in general; here, we also systematically identify the special cases (in terms of the number of players and strategies) for which this is sufficient to guarantee weak acyclicity.
KW - Subgame stability
KW - Weak acyclicity
UR - http://www.scopus.com/inward/record.url?scp=84878505627&partnerID=8YFLogxK
U2 - https://doi.org/10.1007/s00224-013-9457-0
DO - https://doi.org/10.1007/s00224-013-9457-0
M3 - Article
SN - 1432-4350
VL - 53
SP - 107
EP - 122
JO - Theory of Computing Systems
JF - Theory of Computing Systems
IS - 1
ER -