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arXiv · 2308.09443

Stackelberg-Pareto Synthesis with Quantitative Reachability Objectives

Thomas Brihaye·Véronique Bruyère·Gaspard Reghem
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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.

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Thomas Brihaye, Véronique Bruyère, Gaspard Reghem. 2023-08-18. Stackelberg-Pareto Synthesis with Quantitative Reachability Objectives. https://arxiv.org/abs/2308.09443

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