A Classification of Weakly Acyclic Games
Abstract
Weakly acyclic games form a natural generalization of the class of games that have the finite improvement property (FIP). In such games one stipulates that from any initial joint strategy some finite improvement path exists. We classify weakly acyclic games using the concept of a scheduler introduced in arXiv:1202.2209. We also show that finite games that can be solved by the iterated elimination of never best response strategies are weakly acyclic. Finally, we explain how the schedulers allow us to improve the bounds on finding a Nash equilibrium in a weakly acyclic game.
Keywords
Cite
@article{arxiv.1206.0130,
title = {A Classification of Weakly Acyclic Games},
author = {Krzysztof R. Apt and Sunil Simon},
journal= {arXiv preprint arXiv:1206.0130},
year = {2014}
}
Comments
25 pages. To appear in Theory and Decision. A preliminary version of this paper appeared in Proc. 5th International Symposium on Algorithmic Game Theory, (SAGT 2012). Lecture Notes in Computer Science 7615, Springer, pp. 1-12