Stackelberg-Pareto Synthesis with Quantitative Reachability Objectives

TL;DR

This paper investigates the Stackelberg-Pareto synthesis problem in weighted graph games with quantitative reachability objectives, establishing its NEXPTIME-completeness and extending prior work from Boolean to quantitative settings.

Contribution

It extends the analysis of Stackelberg-Pareto synthesis to weighted graphs with quantitative reachability, providing complexity results for this class of problems.

Findings

The problem is NEXPTIME-complete.

Extension from Boolean to quantitative reachability objectives.

Provides complexity classification for weighted graph games.

Abstract

In this paper, we deepen the study of two-player Stackelberg games played on graphs in which Player $0$ announces a strategy and Player $1$, having several objectives, responds rationally by following plays providing him Pareto-optimal payoffs given the strategy of Player $0$. The Stackelberg-Pareto synthesis problem, asking whether Player $0$ can announce a strategy which satisfies his objective, whatever the rational response of Player $1$, has been recently investigated for $\omega$-regular objectives. We solve this problem for weighted graph games and quantitative reachability objectives such that Player $0$ wants to reach his target set with a total cost less than some given upper bound. We show that it is NEXPTIME-complete, as for Boolean reachability objectives.