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.

翻译：本文深化了对图上双人Stackelberg博弈的研究，其中玩家0宣布一个策略，而玩家1具有多个目标，根据玩家0的策略理性地选择能为其提供Pareto最优收益的博弈过程。最近对于ω-正则目标，研究者探讨了Stackelberg-Pareto综合问题，即询问玩家0是否能宣布一个策略，使得无论玩家1如何理性回应，该策略都能满足其自身目标。我们针对加权图博弈和定量可达性目标（其中玩家0希望以小于给定上界的总成本到达其目标集）解决了该问题。我们证明该问题与布尔可达性目标一样，是NEXPTIME完全的。