On the structure of weakly acyclic games

Authors:
Alex Fabrikant;Aaron D. Jaggard;Michael Schapira
Affiliations:
Princeton University, Princeton, NJ;Colgate University, Hamilton, NY & Rutgers University, Piscataway, NJ;Yale University, New Haven, CT & UC Berkeley, Berkeley, CA
Venue:
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
Year:
2010

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Abstract

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.