Optimal Strategies in Weighted Limit Games

TL;DR

This paper establishes the existence and computability of optimal strategies in weighted limit games, a class of infinite-duration games with a regular winning condition, focusing on maximizing infix weights between winning prefixes.

Contribution

It introduces a framework for computing optimal strategies in weighted limit games with B"uchi-style conditions, advancing understanding of strategy synthesis in such settings.

Findings

Proves the existence of optimal strategies in weighted limit games.

Provides algorithms for computing these strategies.

Analyzes the quality measure based on maximal infix weights.

Abstract

We prove the existence and computability of optimal strategies in weighted limit games, zero-sum infinite-duration games with a B\"uchi-style winning condition requiring to produce infinitely many play prefixes that satisfy a given regular specification. Quality of plays is measured in the maximal weight of infixes between successive play prefixes that satisfy the specification.