A Classification of Weakly Acyclic Games

TL;DR

This paper classifies weakly acyclic games using schedulers, showing their relation to finite improvement paths and iterated elimination of strategies, and discusses how schedulers can optimize Nash equilibrium finding.

Contribution

It introduces a classification of weakly acyclic games via schedulers and links them to strategy elimination methods, improving equilibrium computation bounds.

Findings

Weakly acyclic games are characterized by schedulers.

Games solvable by iterated elimination are weakly acyclic.

Schedulers can improve bounds on Nash equilibrium search.

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.