Admissibility in Quantitative Graph Games

TL;DR

This paper extends the concept of admissibility from Boolean to quantitative infinite-duration games, providing characterizations and algorithms for verification and synthesis under certain assumptions.

Contribution

It introduces a framework for admissibility in quantitative games, including characterizations using adversarial and cooperative values, and develops algorithms for related decision problems.

Findings

Admissible strategies exist under certain assumptions.

Characterization of outcomes compatible with admissible strategies.

Algorithms for verification and synthesis problems.

Abstract

Admissibility has been studied for games of infinite duration with Boolean objectives. We extend here this study to games of infinite duration with quantitative objectives. First, we show that, un- der the assumption that optimal worst-case and cooperative strategies exist, admissible strategies are guaranteed to exist. Second, we give a characterization of admissible strategies using the no- tion of adversarial and cooperative values of a history, and we characterize the set of outcomes that are compatible with admissible strategies. Finally, we show how these characterizations can be used to design algorithms to decide relevant verification and synthesis problems.