On the Structure of Weakly Acyclic Games

Alex Fabrikant, Aaron D. Jaggard, Michael Schapira

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


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.

Original languageAmerican English
Pages (from-to)107-122
Number of pages16
JournalTheory of Computing Systems
Issue number1
StatePublished - Jul 2013

Bibliographical note

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.


  • Subgame stability
  • Weak acyclicity


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