Optimal Strategies in Weighted Limit Games

Abstract

We prove the existence and computability of optimal strategies in weighted limit games, zero-sum infinite-duration games with a Büchi-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. * We would like to thank Alexander Weinert for fruitful discussions leading to this work and the reviewers for their detailed feedback, which considerably improved the paper.