🤖 AI Summary
This paper addresses the quantitative reachability strategy synthesis problem for the leader (Player 0) in two-player Stackelberg graph games: Player 0 must commit to a strategy ensuring that, regardless of Player 1’s (the follower’s) choice of Pareto-optimal response trajectory, Player 0 reaches the target set with total cost below a given threshold. It is the first work to extend Stackelberg–Pareto synthesis to weighted graphs and quantitative reachability objectives, lifting the prior restriction to ω-regular specifications. The authors propose a decision framework based on strategy-tree encoding, Pareto-frontier enumeration, and alternating graph automata. They establish NEXPTIME-completeness of the problem—matching the complexity of its Boolean reachability counterpart. Furthermore, they provide the first exact algorithm for robust strategy synthesis under cost constraints, enabling precise quantitative guarantees in adversarial Stackelberg settings.
📝 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.
