On the Structure of Weakly Acyclic Games

The class of weakly acyclic games, which includes potential games and dominance-solvable games, captures many practical application domains. Informally, a weakly acyclic game is one where 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.

• Type: Journal
• Year: 2010
• Where: SAGT
• Authors: Alex Fabrikant, Aaron D. Jaggard, Michael Schapira
• Keywords: Game Theory, Pure Nash, Pure Nash Equilibria, SAGT 2010, Weakly Acyclic Game