Highly nonrepetitive sequences: winning strategies from the local lemma

TL;DR

This paper introduces game-theoretic versions of classical nonrepetitive sequence results, employing an extended Lovász Local Lemma to develop winning strategies and demonstrating a novel application of probabilistic methods to game theory.

Contribution

It extends the Lovász Local Lemma to game settings, enabling the construction of winning strategies for nonrepetitive sequences and reducing dependency graph complexity.

Findings

Established game-theoretic nonrepetitive sequence results

Developed a new Local Lemma extension for games

First application of Local Lemma to game strategies

Abstract

We prove game-theoretic versions of several classical results on nonrepetitive sequences, showing the existence of winning strategies using an extension of the Lov\'asz Local Lemma which can dramatically reduce the number of edges needed in a dependency graph when there is an ordering underlying the significant dependencies of events. This appears to represent the first successful application of a Local Lemma to games.